1. Introduction

Seeking materials that are both transparent to visible light and electrically conductive implies a “contradiction.” To be conductive, a material should have both high carrier concentration and carrier mobility. Although, large values of these characteristics cause the material’s plasma frequency to occur at lower wavelengths, resulting in high losses and stifling transparency. Transparent conducting oxides (TCOs) overcome this constraint due to their wide bandgap, allowing for the transmission of visible light when formed into thin films. As a result of these somewhat rare attributes, a variety of applications have been found for TCOs. For example, they have seen extensive use as transparent heating elements, especially for heavy-duty purposes such as de-icing and de-fogging aircraft windshields [1] as well as a thermal regulation coating for windows, better known as “Low-E glass” [2]. Recent studies have also examined the possibility of a more precise temperature control with microstructured TCOs [3]. TCO-based gas sensors have been devised for a variety of chemical species including carbon monoxide [4], methanol [5], ammonia [6], and many more. Recently, TCOs have even seen use as catalysts in chemical reactions with vital industrial significance [7]. However, the most effective application for TCOs is as transparent electrodes, initially in solar cells [8], but quickly transitioning into the world of consumer electronics due to the advent of touch-screen devices.

As addressed previously, many of the initial use-cases for TCOs were explicitly chosen due to their transparent and conductive properties. However, during the last decade, this focus has begun to shift, and if we are to understand the story of TCOs, it is necessary to discuss plasmonics and its growing need for alternative materials. The field of plasmonics fundamentally deals with coupling electromagnetic radiation to the collective oscillation of the electronic cloud at a dielectric–metal interface [9]. The excited optical modes are characterized by subwavelength confinement, which brings the promise of real integrated photonics below the limit of diffraction [10–12].

To this end, plasmonics offers many promising technological proofs of concepts, but very few of these concepts have been realized outside of the labs they were conceived in. Specifically, noble metals such as gold and silver, which have been the backbone of plasmonics since its inception, are the root cause of its limitations. For example, these materials suffer from incompatibility with standard CMOS fabrication techniques, limiting the mass-scale production capability of plasmonic technologies. They also lack static tunability, which allows a material’s optical constants to be tuned by carefully controlling manufacturing parameters, thus providing flexibility when designing nanophotonic devices. Further still, noble metals do not possess relevant dynamic tunability, which grants the ability to control optical properties via electric, optical, or thermal bias. Another important consideration is the damage threshold. Metal-based nanostructures and metamaterials cannot operate under high fluences due to a relatively low melting temperature of around 1000°C [13]. This severely restricts the utility of their nonlinearities, as the efficiency of these processes will scale with the fluence used. However, the most critical failing of metals is their extreme optical losses, which stem from a high carrier relaxation rate $\gamma$ and carrier concentration $N$. Here $\gamma$ and $N$ are also inextricably linked to a material’s plasmonic properties, further complicating the task of disentangling losses from plasmonics.

Due to these obstacles, there has been a considerable amount of discussion on the future of plasmonics [14–17] and numerous efforts at moving beyond these high losses have been investigated. One such attempt considered the possibility of reducing $\gamma$ in metals, and thus losses, via cryogenic cooling [18]. Still, the reduction in losses from this method was not compelling enough to justify the inherent difficulties with cryogenic cooling, and thus no real-life applications have been demonstrated successfully. Possible avenues for mitigating losses such as integration of gain media into plasmonic devices [19,20], or seeking well-suited applications for attenuative media have also been explored [21]. One such example of the latter point is thermo-plasmonics, which aims to use metallic nanostructures to generate and control heat [22]. Applications in this field range from photothermal cancer therapy [23] to nanochemistry [24]. However, the most promising solution for handling losses in plasmonics is to confront the kernel of the problem, that is, by seeking better plasmonic materials [15].

Two distinct routes have been taken toward these low-loss plasmonic materials. First, by using so-called dilute metals, it is possible to decrease the carrier concentration of metals and, consequently, reduce optical losses. This method has found success with the group of materials known as transition metal nitrides, which achieve their plasmonic properties in the visible spectral window, and are also refractory [25–28]. Several notable examples of this can be found for one of the most favoured dilute metals, TiN, which is compared with doped semiconductors in Fig. 1 [29–35]. For example, surface plasmon field enhancement from TiN has been shown to exceed that of gold in the visible [Fig. 1(a)] [29]. TiN-based metamaterials have also been investigated in [31] where a broadband absorber was fabricated with this material to have lower losses than a gold counterpart, resulting in 95% absorptionover the visible spectral range [Fig. 1(b)], and also a much higher thermal stability than metallic counterparts. Due to this refractory nature of TiN, it has promising applications toward high-power thermophotovoltaics [26]. The extent of this thermal stability is demonstrated in [36], where a three dimensional TiN broadband absorber is shown to retain its structure after 24 hours annealing at 1238$^{\circ }$C. Attempts have been made to reduce to the ohmic losses of TiN by growing the material into nanoparticle arrays, which can support plasmonic–photonic hybrid modes [Fig. 1(c)]. Further still, the high temperature tolerance of this material allows nanoparticle arrays fabricated from TiN to be used in high-power applications such as nonlinear frequency conversion [30]. In the direction of integrated nanophotonics, TiN has also shown promise for use as low-loss plasmonic interconnects, with predicted losses in the range of 0.8 dB/mm [Fig. 1(d)] [32].

 

Figure 1. Latest plasmonic applications for TiN and TCOs. (a) Comparison of localized surface plasmon field enhancement between TiN and gold [29]. (b) Schematic of a TiN-based broadband metamaterial absorber [31]. (c) TiN nanocylinder array that is able to support hybrid plasmonic–photonic modes [30]. (d) Experimentally measured modal profile of a TiN strip waveguide [32]. (e) Contour plot showing the surface plasmon resonance of an AZO film with varying thickness [33]. (f) Plasmonic Mach–Zehnder interferometric modulator based on ITO [34]. (g) Surface plasmon resonance sensor using photonic crystal fibers with an ITO coating [35]. (a) Reprinted with permission from [29] © The Optical Society. (b) Reprinted from Li et al., Adv. Mater. 26, 7959–7965 (2014) [31]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission. (c) Reprinted with permission from Kamakura et al., ACS Photonics 4, 815–822 (2017) [30]. Copyright 2017 American Chemical Society, https://pubs.acs.org/doi/abs/10.1021/acsphotonics.6b00763. (d) Reprinted with permission from [32] © The Optical Society. (e) Reprinted by permission from Journal of Optics (Springer Nature). Rajak et al., J. Opt. 43, 231–238 (2014) [33]. Copyright 2014. (f) Reprinted from [34] under a Creative Commons license. (g) Reprinted from Opt. Commun. 464, Liu et al., “Surface plasmon resonance (SPR) infrared sensor based on D-shape photonic crystal fibers with ITO coatings,” paper 125496, copyright 2020, with permission from Elsevier.

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To date, low-temperature, CMOS compatible manufacturing of these materials is still continuing to advance [37,38]. There is, however, an alternative way of creating low-loss plasmonic materials. The carrier concentration of wide bandgap oxide semiconductors, otherwise known as TCOs, can be increased through doping, on the level of 2–10% [15], granting plasmonic properties in the near-infrared (NIR). Unlike noble metals, we can tune the wavelength at which plasmonic properties occur in these materials. Several successful demonstrations have been completed, revealing TCO’s effectiveness as a plasmonic material, such as in [33], where the plasmonic resonance of aluminum zinc oxide (AZO) is characterized for various film thicknesses [Fig. 1(e)]. Applications for TCO’s metallic properties have already been demonstrated in a few distinct areas. In this regard, an indium tin oxide (ITO)-based plasmonic Mach–Zehnder interferometric modulator was fabricated in [34] [Fig. 1(f)], which is capable of gigahertz modulation speeds and has a figure of merit as low as 95 $V\mu$m (the figure of merit is defined as $V_{\pi }L$ where $V_{\pi }$ is the necessary voltage to achieve a $\pi$ phase shift and $L$ is the modulation length (a low figure of merit is desirable). For purpose of comparison, in [39], an integrated thin-film LiNbO₃ modulator has a figure of merit of 18,000 $V\mu$m. Another application for TCOs metallic properties can be found in [35], where ITO acts as the plasmonic sensing element in a photonic-crystal fiber surface plasmon sensor [Fig. 1(g)]. This was done with the sensibility of expanding the operating wavelength into the infrared while retaining a high measurement resolution, which is shown to have a peak value of $6.67 \times 10^{-6}$ refractive index units (RIU) at 2010 nm.

There are, however, more extreme paths toward nanophotonics, which bypass plasmonics altogether. One such endeavor employs high-index-contrast all-dielectric metamaterials and is developed within the context of Mie scattering theory (a more in-depth analysis of all-dielectric nanophotonics can be found in Section 3) [40,41]. Several encouraging demonstrations have been shown thus far, such as nanoresonators [42,43] and subwavelength meta-lenses [44,45]. Even so, the elimination of metallic inclusions does not just modify the list of functional materials typically employed in nanophotonics but alters the physical mechanisms at the core of many devices making use of plasmon polaritons.

For all these reasons, many nanophotonic labs are seeking a winning strategy to keep plasmonics alive through the use of “metal-like” compounds capable of:

Thanks to all these desirable features, in recent years, TCOs have strongly influenced plasmonics and metamaterials not only by initiating the new field of all-dielectric plasmonics but also by introducing new optical features and capabilities which are out of reach outside this material platform [48]. An in-depth discussion of non-reciprocal and time-varying behaviors in TCOs can be found in Section 9.

TCO-based systems devices also bring an alternative perspective to what is today represented by all-dielectric high-index-contrast devices, which has become a very attractive alternative to solve the unbearable ohmic losses intrinsic of standard (metal-based) plasmonic components [49,50].

Although the need for low-loss plasmonics can amply justify the renewed interest toward conducting oxides, this is far from being the only reason. In fact, TCOs, with their exceptionally high carrier concentration, push the characteristic plasma frequency into the NIR region, where the material permittivity approaches zero while changing sign. This allows for access into the so-called epsilon-near-zero (ENZ) regime without the need for structured materials and at wavelengths of fundamental technological interest (over the entire telecom bandwidth).

Systems with vanishing permittivity have been theoretically and experimentally proved to trigger numerous peculiar effects. Examples such as supercoupling [51], photonic doping [52,53], resonance pinning [54], and electric levitation [55] (which has only been investigated in theory) are examined in further detail in Section 5. Some ENZ properties even have a direct influence on quantum optics. For example, an effect known as superradiance, in which quantum emitters had to be in proximity to each other to achieve enhancement of coherent emission, can be enhanced inside the ENZ regime. Specifically, emitters placed inside an ENZ channel will benefit from an enhancement to their emission intensity even when randomly distributed throughout the material [56]. The exact mechanism behind ENZ-enabled long-range superradiance and other ENZ/near-zero-index (NZI) quantum applications are treated in Section 10.

The broad range of research avenues discussed above immediately placed TCOs at the center of tremendous attention. In fact, a typical strategy to access the ENZ region is via structured materials where the combined use of metals $(\epsilon <0)$ and semiconductors $(\epsilon >0)$ is exploited to create subwavelength meta-atoms forming an effective ENZ medium at a given operational wavelength [57]. However, the use of TCOs as ENZ materials leads to a large set of practical advantages in comparison with the metamaterial approach, such as simplifying fabrication processes, broadening the operational bandwidth, making the entire structure compatible with semiconductor technology, eliminating spatial dispersion, and largely increasing damage threshold. Concerning the final point, Table 1 lists a few key measurements of the damage threshold for gold, silica, ITO, AZO, and SiN. Although some experimental parameters are not controlled for between measurements, such as pulse length or sample thickness, this comparison still provides a general overview of the damage tolerance of each class of material, ranging from metals to dielectrics and TCOs. It is important to note that the authors have extensive experience working with TCOs and can attest to the exceptional resilience of the entire class of materials from first-hand lab tests. Because of all these fundamental advantages, numerous research labs interested in ENZ physics have shifted their attention toward bulk TCOs.

Table 1. Laser-Induced Damage Threshold (LIDT) for Various Materials^a

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Based on this ample pool of fundamental material properties, TCOs have sprouted into a myriad of research endeavors pertaining to many fundamental branches of optics and photonics during the last decade. Figure 2 [63–71], for instance, shows a few remarkable TCO-based experimental attainments encompassing a variety of disciplines. The initial drive toward TCOs was driven by photovoltaics as demonstrated in Fig. 2(c). Then, toward fields such as plasmonics as seen in Fig. 2(b) (Section 2) and electro/piezo-optics which are illustrated in Figs. 2(g) and 2(d), respectively (Section 11). More recent emerging applications for TCOs are also explored in this review, such as ENZ and NZI photonics, as shown in Fig. 2(a) (Section 5) and Fig. 2(e) (Section 7), respectively. Finally, the ability for these materials to function as time varying media is demonstrated in Fig. 2(f) (Section 9). These results undoubtedly demonstrate a level of technological flexibility which is hardly found in any other class of materials.

 

Figure 2. Various applications for TCOs. (a) Dynamically controlled nanocavity utilizing TCO’s enhanced nonlinearities in the NZI regime [63]. (b) Demonstration of negative refraction with a TCO acting as the plasmonic material [64]. (c) Schematic taken from study into TCO’s applicability to photovoltaics [65]. (d) Probing of the piezo-optic properties of erbium doped ZnO [66]. (e) Enhancement of emission from an ensemble of quantum emitters as a function of wavelength. Clear peak of enhancement can be seen at ENZ wavelength [67]. (f) Spectrogram of a probe pulse at various pump delays. Adiabatic frequency shift can be seen at zero delay [68]. (g) Concept for a TCO-based electro-optic modulator [69,70]. Designs for TCO-based plasmonic modulators are still being proposed [71]. (a) Reprinted with permission from Kim et al., Nano Lett. 18, 740–746 (2018) [63]. Copyright 2018 American Chemical Society, https://doi.org/10.1021/acs.nanolett.7b03919. (c) Reprinted from J. Alloys Compd. 793, Jang et al., “Comparison study of ZNO-based quaternary TCO materials for photovoltaic application,” 499–504 (2019), with permission from Elsevier [65]. (d) Data repurposed from [66]. (e) Reprinted from So et al., Appl. Phys. Lett. 117, 181104 (2020), with the permission of AIP Publishing, LLC [67]. (f) Reprinted with permission from [68] © 2020 The Optical Society. (g) Reprinted from Lee et al., Nano Lett. 14, 6463–6468 (2014). Copyright 2014 American Chemical Society, https://doi.org/10.1021/nl502998z.

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So far, we have discussed TCOs as both an alternative plasmonic platform and an ENZ material; however, this is not the end of the story. Very recently, it has been pointed out that TCOs falls within an even narrower category, the one of NZI materials, for which a very low group velocity is key for extraordinary high nonlinearities. NZI TCOs have entered the domain of all-optical photonics, showing giant complex nonlinearities and a record high figure of merit (defined in Section 8) which is very promising also for quantum information applications [72,73]. Following the enthusiasm stemming from these exceptional results, the photonics community has been primarily focused on experimental campaigns rather than on the formal development of the required nonlinear theory in TCOs. In this context, the standard approach of describing nonlinearities starting from the polynomial expansion of the material polarization works reasonably well only in specific cases. In fact, more recently, it has been underlined that the stringent assumptions at the base of the standard perturbative approach (non-dispersive permeability, small index change compared with the linear index) are no longer satisfied as long as NZI nonlinearities are concerned. Only very recently, the NZI nature of TCOs has been put into a more specific context, and the broad extent of applicability for NZI materials is finally becoming clearer. This is broadly discussed in the following paragraphs of the present review. We aim to outline the tremendous technological and scientific advancements involving TCO-based systems during the last few years and explain why this class of materials is at the center of a multifaceted research endeavor encompassing plasmonics, nonlinear optics, metamaterials, and quantum optics.

As described so far, TCO-based systems have triggered three main technological revolutions involving photovoltaic systems first, plasmonic technologies second, and more recently, nonlinear all-optical devices. This is stressed in Fig. 3 where a periodic “popularity peak” is reported for these three research fields showing steady growth in the global research interest surrounding TCO-based devices and systems (“popularity peak” is defined by finding when maximum citations per article occur for a given research topic. Data was collected via Web of Science by Clarivatae). The first milestone was reached in 2013 when material science surrounding TCOs was gaining the most traction. The prospect of TCOs for plasmonics reinvigorated the discussion on these materials, which resulted in peak popularity in 2017. This was only further intensified with the discovery of their immense nonlinear properties, which has sparked a much more recent spike in interest. The direction in which TCO research will develop in the coming decade remains an open question. Yet, perhaps the most likely scenario for TCOs is one we have already seen for SiN, that is, a marked transition from nonlinear optics toward quantum optics (see Section 10).

 

Figure 3. Three main technological revolutions triggered by TCOs. Each bar represents the year of peak popularity for that topic (identified by finding when maximum citations per article occurred). The first research fields TCOs have been vital for was fabrication and material science toward industrial purposes. In 2017 the maximum number of citations per article was reached for TCOs as a plasmonic material, and much more recently TCOs have become popular for nonlinear optics. All data was collected via Web of Science by Clarivate.

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After this introduction, our journey will continue by elucidating the fundamental limit of all-optical nanophotonic devices and looking into the intrinsic limitations plaguing standard plasmonic components. We also discuss how these issues can be strongly mitigated by the use of TCOs while also mentioning other metal-free alternatives. The discussion then broadens by looking into the multifaceted nature of TCOs, which can be seen as epsilon and NZI materials, and also time-varying media. In this direction, we also describe the ongoing discussion about the most-effective approach to model optical nonlinearities in such complex compounds before completing our review.

Our goal is to provide the readers with a new perspective that has not been proposed so far by any of the remarkable reviews already available about TCO photonics, stimulate the dialog about future perspective, and underline what is left to do in order to grasp the overall picture of a material platform which never stops providing scientists and technologists with new playgrounds.

2. Nanophotonics: State of the Art and Problems to be Solved

For over a decade, despite tremendous technological advancements, nanophotonics has been seen as a sort of contradiction in terms. In fact, this technology, which brings the promise to overcome the stringent bandwidth limitations of electronic devices, is fundamentally limited with regards to the minimum achievable size for a given operational wavelength. This is due to both Abbe’s diffraction limit, which sets the maximum level of miniaturization achievable, and the small nonlinearities available in dielectrics, which only become less significant as propagation distances are shortened. Clearly, this is not a secondary issue because, for several decades, miniaturization has been the workhorse of semiconductor industries to increase speed and reduce cost at the same time. The intrinsic limitations of both electronics and photonics are pictorially represented in Fig. 4, where TCOs are placed in the middle of these two major technologies. If we are to understand why TCOs sit between photonics and electronics, it is important to keep in mind one fundamental fact, while metals are the chosen materials for the design of electronic circuits (“frictionless” motion of electrons), dielectric and semiconductors are the preferential choices to design photonic networks (low optical losses). However, both these material classes provide distinct limitations. For electronics, ohmic losses hamper device speeds and size due to the power dissipation required for circuits with higher transistor density. This has the consequence of ending Moores law, which can be seen in Fig. 4(a), where the switching energy for transistors is recorded over the previous 80 years and extrapolated into the near future [74]. However, the switching energy is not the only parameter contributing to this decline, as minimum transistor size is nearing its limit. All these factors contribute to the energy density inside electronic systems reaching the frontier of current cooling technologies, which will only worsen as transistor density increases, whereas the decrease in ohmic losses (switching energy) of these components will begin to plateau. In the case of photonics, the issue lies mainly in miniaturization, which is restricted by Abbe’s diffraction limit (Fig. 4(b) shows the diffraction limit experienced by a collimated Gaussian beam focused via a lens). Further still, dielectrics suffer from relatively small nonlinearities, which are insignificant over the short propagation distances found in integrated systems. Initially, plasmonics presented a solution to the problems encountered by both sides of Fig. 4, allowing for the confinement of light below the diffraction limit while retaining the speed of photonics. This approach, however, suffers from unmanageable losses, so we turn toward TCOs. These hybrid materials may avoid the pitfalls of photonics by showing losses almost two orders of magnitude lower than metals. During the last decade, the synergistic exploitation of these two opposed worlds, metals on one side and dielectrics on the other, has been the technological strategy to develop plasmonics and structured materials (metamaterials). Thanks to the judicious combination of compounds with strikingly different optical behavior we have gained access to the full $\epsilon,\mu$ optical space and confined light on a deep subwavelength scale [75,76]. However, this strategy, whose theoretical homework is EMT, presents some drawbacks. For example, if we were to design an effective medium with real permittivity near zero, it would be necessary to use both metals ($\Re (\epsilon ) < 0$) and dielectrics ($\Re (\epsilon ) > 0$), meaning all the previously discussed concerns due to the presence of metals in plasmonics also apply to EMT metamaterials. These issues include challenging fabrication, high losses, and low damage thresholds, which are only worsened by the difference in thermal coefficients between metallic and dielectric layers [77]. Metamaterials designed using this method also have limited ENZ bandwidth (dependant on the resonance bandwidth of meta-atoms), strong spatial dispersion, and only possess ENZ properties perpendicular to the metal–dielectric stack.

 

Figure 4. Fundamental limitations in electronics and photonics. In (a), we see how the reduction on the minimal transistor switching energy has plateaued during the last two decades. This is mainly due to the fact that device miniaturization advances faster than the correspondent power dissipation per single device. This ultimately leads to an unaffordable power density above the damage threshold of devices. The bottom part of (a) © 2017 IEEE. Reprinted, with permission, from Theis and Wong, Comput. Sci. Eng., 19, 41–50 (2017) [74]. In (b), Abbe’s diffraction limit is shown for the minimal spot size of an optic lens. This set the fundamental miniaturization lower bound for classic photonic devices.

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The underlying mechanism at the core of both standard plasmonic and metamaterial-based devices is coupling the electromagnetic radiation to the oscillation of the electronic plasma at a metal–dielectric interface [78]. The so-called “plasmonic” modes originating from this process owe many of their peculiar properties to a strong $k(\omega )$ dispersion, which leads to large wave vectors at relatively short operational wavelength (visible–NIR). However, the same physical attributes are also the cause for high losses, short propagation distances, and a very limited capability of engineering a device’s optical properties, here defined as the possibility of tailoring the complex dielectric permittivity of the optical systems under investigation [14].

It is because of these very strong technological limitations that plasmon-based nanophotonic components, despite numerous remarkable and potentially disruptive proofs of concept, are still confined inside research labs rather than being key components for the consumer market (except for enhanced Raman spectroscopy and a few other applications). To underline this “paradox,” we recall key applications including negative refraction [79], superlensing [80], 2D optics [81], waveguide supercoupling [82], ultra-compact electro-optic modulation [83], and many others. Potentially, these experimental demonstrations could have led to the realization of optical microscope with a resolution of few nanometers, optical components (e.g., splitters, phase retarders, ultra-short focal lenses, and modulators) with nanometer-long optical paths, geometrically independent photonic channels, and many other game-changing applications which are currently “promising experimental demonstrations” rather than real-world components.

There are, of course, many important reasons why the epochal technological transition from optics to nanophotonics has not happened yet, and many believe that the primary issue deals with the choice and availability of suitable constituent materials. More specific to plasmonic technology, the typically required metallic inclusions impose unacceptable ohmic losses [14]. In addition to these fundamental limitations, the use of gold and silver de facto prevents plasmonic technologies from entering the standard semiconductor production chain due to the detrimental diffusion temperatures exceeding $400^{\circ }$C. This is, of course, a big problem hampering low-cost mass production of nanophotonic devices, especially for telecom and data processing applications. It is in response to these problems that very recently, the new emerging field of all-dielectric nanophotonics has been gaining momentum.

3. All-Dielectric Nanophotonics: Material Background

A new trend in engineering all-dielectric nanodevices is to make use of high-index contrast optical scatterers, instead of metallic nanoinclusions, to attain tightly confined resonant modes which arise from the displacement current due to the oscillation of bounded electrons [41,49,84,85]. This could bypass the need for plasmonic materials entirely. To understand how nanophotonic systems can operate without plasmonic materials, we examine Mie scattering theory [86]. Defining a size parameter $u = L/\lambda$, where $\lambda$ is the wavelength, and $L$ is the scattering object’s size, the domain of Mie scattering of interest to us is defined as $u \approx 1$. That is to say, Mie scattering allows us to find an analytical solution for the electromagnetic response of a spherical particle on the same scale as $\lambda$. Electric and magnetic resonances of the particle correspond to the Mie coefficients $a_n$ and $b_n$, defined as

It is important to note that while Mie theory can completely predict the behavior of nanospheres and other closely related systems, its usefulness concerning metasurfaces is limited.

Mie theory is not constrained to materials with $\Re (\epsilon ) > 0$, and will readily provide solutions for metallic nanoparticles with $\Re (\epsilon ) < 0$. This includes TCOs, for which epsilon lies in both ranges in the visible–NIR window. TCOs can be fabricated into nanoparticles and nanospheres via low-pressure spray pyrolysis [91], and hence can also be analyzed through the lens of Mie scattering theory. So far, TCO nanospheres and nanoparticles have been applied in several contexts. For example, in [92], hollow ZnO nanospheres were used to improve the absorption efficiency of solar cells through whispering gallery resonances, which can be analyzed through Mie theory. For instance, the left panel of Fig. 5(a) shows a diagram of AZO hollow nanospheres (HNSs) on thin-film solar cell structure and the right panel shows resonance spectra of single AZO nanosphere as calculated via finite difference time domain (FDTD) simulations [93]. The vast majority of efforts on TCO nanoparticles have been concentrated on improving harmonic generation. A recent approach placed TCO nanoparticles (in the range of 10 nm diameter) onto a high-$Q$ silica microsphere [94], which provided a threefold enhancement to the third-harmonic generation (THG) efficiency. In this regard, the left panel of Fig. 5(b) shows THG from pure silica microsphere as compared with ITO-coated microsphere and the right panel displays the relative third harmonic (TH) emitted by both configurations. In both [95] and [96] TCO nanoparticles were placed in the hotspot of a plasmonic gap antenna, resulting in an enhancement to the TH intensity, with the former work demonstrating a 256% gain to TH power, and the latter work demonstrating a twofold enhancement to the THG efficiency as compared with the antenna alone. Figure 5(c) shows intensity enhancement due to a gold nanoantenna structure with ITO nanoparticle embedded [95] and Fig. 5(d) shows a scanning electron microscopy (SEM) image of a gap antenna array with ITO nanoparticles incorporated [96].

 

Figure 5. (a) Left panel shows schematic of AZO HNSs assembled on a thin-film solar cell in order to improve the absorption efficiency by coupling light to whispering gallery modes, whereas the right panel shows the resonance spectra of a single AZO HNS as calculated by FDTD simulations [92]. (b) Left panel displays an image of generated TH light for a pure silica microsphere and for an ITO-nanoparticle-coated microsphere. The right panel gives exact power measurements for THs. With a pump at 1550 nm, a 256% gain in TH power is observed when ITO nanoparticles are applied [94]. (c) Intensity enhancement due to a gold nanoantenna structure with ITO nanoparticle calculated via FDTD [95]. (d) SEM image of a gap antenna array with incorporated ITO nanoparticles. Introducing ITO nanoparticles into this array doubles the emitted TH intensity [96]. (a) Reproduced from [92] with permission from the Royal Society of Chemistry. (b) Reprinted with permission from [94] © 2020 The Optical Society. (c) Reprinted by permission from Nature Nanotechnology (Springer Nature). Aouani et al., Nat. Nanotechnol. 9, 290–294 (2014). Copyright 2014 [95]. (d) Reprinted with permission from Metzger et al., Nano Lett. 14, 2867–2872 (2014). Copyright 2014 American Chemical Society, https://doi.org/10.1021/nl500913t.

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One direct advantage of employing an all-dielectric strategy for designing photonic elements is that displacement currents are not affected by ohmic losses which are instead characteristic of free electron oscillations in metals. The previously discussed failures of plasmonics, such as high losses and a lack of CMOS compatibility, do not apply here. In addition, reduced ohmic losses result in lower heat generation under optical excitation, improving damage tolerance. Moreover, high-index nanoparticles stimulated with visible light can support high-order magnetic dipole modes that occur when the nanoparticle’s diameter is equal to the wavelength of incident light. It has been shown in [90] that these optically induced magnetic dipoles can produce Fano resonances, which brings the possibility for all-dielectric subwavelength confinement. Such a resonance, as found in dielectric nanoparticles is pictorially represented in Fig. 6(b), whereas a more conventional plasmonic resonance is represented in Fig. 6(a). In this direction, few fundamental experiments have demonstrated key photonic devices such as nanoresonators [42,43], subwavelength meta-lenses [44,45], reconfigurable metamaterials [97,98], zero-index waveguides [99,100], and other nanodevices whose functionalities do not rely on the use of metallic nanoinclusions. In the direction of NZI physics, all-dielectric Dirac-cone metamaterials have also proved to be promising [101,102]. These materials are engineered to have a Dirac-cone-like dispersion profile at the center of their Brillouin zone, which results in a NZI behavior at the Dirac cone’s center frequency. This allows for a ultralow-loss NZI operation at a single frequency which can produce many interesting phenomena (see Section 12), although these metamaterials are still difficult to fabricate and suffer from strong spatial dispersion near the Dirac frequency.

 

Figure 6. (a) Light confinement via surface plasmon resonances. (b) Magnetic dipole resonance in a dielectric nanoparticle. Arrows represent flow of electric field.

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Even from this very general description, it is apparent that the elimination of metallic nanoelements from the nanophotonic world, does not just cause a reorganization in the list of constituent materials, but rather a fundamental change in the underlying physical mechanisms. In other words, if it is truth that by purging metals from all-optical technologies we eliminate a few undesired effects (loss primarily). However, from another side, we also get rid of those key characteristics which made plasmonics extremely appealing in the first place.

The authors point of view lies somewhere in the middle, supporting the ambitious goal to drive forward the emerging field of “all-dielectric plasmonics.” This new technological domain, which might sound like another contradiction in terms, has been triggered by the introduction of TCOs into photonics and takes advantage of the idea that by using a special class of highly doped semiconductors, we can drastically mitigate the drawbacks of metals while retaining their positive features. This strategy comes with the additional benefit that in most of the situations we can still refer to the basic plasmonic models developed during the last decade to engineer future technologies and we additionally are less constrained to a reduced list of high-index contrast materials.

4. TCOs: the Birth of All-Dielectric Plasmonics

TCOs are a class of wide-bandgap semiconductors capable of accepting an extremely high doping concentration without fundamental alteration of the material structure. In n-type TCOs (those at the center of the present review), extra free carriers are injected into the conduction band from localized defects such as oxygen vacancies, substitutional defects, and interstitial defects. The enhanced carrier concentration (typically of the order of 10²¹ cm${^{-3}}$) pushes the Fermi level up into the conduction band, thus effectively widening the natural energy gap of the intrinsic material via Moss–Burstein shift. In this way, both electrical conductivity and optical transparency can be promoted at the same time [103]. Another technologically relevant feature of TCOs is that their optical properties are largely tunable.

For instance, the crossover wavelength (point at which the real part of the dielectric permittivity changes its sign) of ITO can be arbitrarily set in within a broad range (e.g., ITO $\approx$ 1000 nm–1.6 $\mu$m) by changing the material stoichiometry, the fabrication procedure, and/or the deposition conditions [104]. This wavelength range is particularly interesting because the material can be used as a metal replacement for photonic elements operating in a large part of the visible window also covering part of the NIR (including the fundamental telecom window). Other positive aspects of TCOs include very mature fabrication processes and the possibility to be deposited by using various standard techniques (such as sputtering [105], laser ablation [15,106], and chemical vapor deposition [107]) which are typically available in many labs and fabrication facilities [108]. Studies are also reported about how deposition parameters are linked to the optical properties of TCOs films [105,109–112]. Table 2 (see [15,104,107,113–118]) lists the ENZ ranges that have been achieved with TCOs for various fabrication methods. This information should provide a clear picture of how flexible the optical properties of these low-loss metal-like materials are and how relatively simple it is to engineer such properties by adjusting fabrication parameters.

Table 2. Tunable ENZ Range for Various Materials and Said Materials'Fabrication Methods^a

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There are many compounds belonging to the class of TCOs, the most notable of which are ITO, indium zinc oxide (IZO), gallium zinc oxide (GZO), aluminum zinc oxide (AZO), zinc tin oxide (ZTO), cadmium oxide (CdO), indium gallium zinc oxide (IGZO), indium tin zirconium oxide (ITZO), and fluorine tin oxide (FTO). ITO is by far the most used TCO since it has been employed by industries for the fabrication of transparent electronics for over two decades due to its high transparency in the visible range [119]. However, the cost per unit mass of indium is very high due to its very low abundance in nature. In addition to this, its production, performed as by-product of other chemical synthesis, is also geographically sensitive and both the European and the North American markets are entirely dependent on external indium supplies [120]. Further still, ITO is toxic and requires deposition temperatures exceeding $400^{\circ }$C to acquire a good polycrystalline nature, preventing its applicability for producing flexible devices [121].

Thus, there is unanimous consensus that TCO-based technologies must move toward other alternative materials. During the last decade, we have assisted to a vast enlargement in the variety of available TCOs. More specifically, AZO is particularly attractive for nanophotonic applications because it possesses very high electron mobility [122], is made of abundant natural elements [123], is biocompatible, and has high transmissivity in the NIR [124]. In addition to these very desirable features, AZO (as do most of the ZnO-based TCOs) also exhibits remarkable piezoelectric, pyroelectric, and piezo-optic properties which makes it very versatile for the fabrication of different nanodevices with multiple functionalities [66,125–127]. Last but not least, AZO allows one to enter the ENZ regime at fundamental telecom wavelengths while retaining good transparency for integrated photonic applications.

Figure 7 shows (a) the ENZ wavelength range, (b) the transmission curve, and (c) the ultrafast carrier recombination dynamics (normalized transient transmissivity as a function of time delay as acquired from a pump probe setup operating in the NIR). These results were experimentally obtained from a 1-$\mu$m-thick AZO film in the photonics labs at Heriot-Watt University. The pump-probe experiment described here operates by impinging the film with a pump pulse which will incur a nonlinear refractive index change. This refractive index perturbation can then be measured via a probe pulse. By sweeping the delay of the probe across the pump, we can characterize the response time of AZO’s nonlinearity, which in our case can be considered ultrafast (e.g., in the range of 100 fs) due to the low-oxygen manufacturing process.

 

Figure 7. Fundamental optical characteristics of aluminum-doped zinc oxide thin films (experimental characterization performed on a 1-$\mu$m-thick AZO film deposited on fused silica). (a) The crossover wavelength can be set at important telecom wavelengths in the NIR whereas the ENZ region (|$\epsilon$|<1) covers a broad spectral range. (b) Within the same spectral window it shows high transparency. (c) Recombination time of photo-generated carriers can be ultrafast if specific (oxygen-deprived) deposition processes are employed.

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5. ENZ Regime: a New Paradigm in Integrated Photonics

Why is the ENZ regime so “appealing” in photonics? A system showing ENZ behavior within a specific wavelength range is linked to many special and advantageous features. Just by looking at the Maxwell curl equations in the absence of sources, we can infer that in a medium where epsilon is approaching zero the electric and magnetic field are “decoupled” as well as the spatial wavelength and the temporal frequency. These effects are accompanied by a considerable stretch of the effective wavelength and a broad variety of distinct phenomena such as supercoupling on subwavelength channels [128], photonic doping [52], superradiance [56], and electric levitation [55], which are all discussed in more detail in the following paragraphs.

One of the most intriguing peculiarities of ENZ materials is electric levitation, which can be seen in Fig. 8(a). Analogous to superconductors enabling levitation through the expulsion of magnetic fields, electric levitation could be achieved with ENZ materials via the rejection of electric fields emanating from a dipole [55]. This does, however, come with the limitation that the dipole cannot be static in time, as the ENZ condition cannot be satisfied at $\omega = 0$ (to date, no experimental proof of ENZ electric levitation has been demonstrated). A magnetic response can be elicited from ENZ media via photonic doping [see Fig. 8(b)], which is the immersion of dielectric particles in an ENZ medium to modify the effective permeability. The permittivity of the overall structure remains unaltered [52], and thus the ENZ condition is preserved. Experimental demonstrations have been performed with microwaves in a lossless 2D ENZ structure, and further still, there is also a theoretical basis for this photonic doping functioning in 3D materials, and also with losses [53]. Originally proposed in [51,82], waveguides composed of ENZ materials would allow radiation to propagate through subwavelength channels and tight bends without suffering from significant reflection losses; one such subwavelength ENZ channel is depicted in Fig. 8(c). Shortly after ENZ supercoupling was initially suggested, an experimental proof was demonstrated in the microwave spectral region [129,130], then later in the visible and NIR [57]. Supercoupling applications also include ENZ-based dielectric sensing, which utilizes the field enhancement that is present with supercoupling to detect slight permittivity variations [131]. Finally, the ENZ status relaxes the condition on superradiance, which is a quantum effect that causes the emission of quantum emitters to scale quadratically rather than linearly with the number of emitters, when said emitters are in close proximity (see Section 10. for more detail). A pictorial representation of quantum emitters embedded in an ENZ channel is shown in Fig. 8(d). Substrates made of ENZ materials also have interesting properties. In [54], gold antennas were placed onto an ENZ substrate, which has the effect of decoupling the antenna’s structural properties to its resonance frequency when operating inside the ENZ condition; this has come to be known as resonance pinning. Further still, ENZ materials can also support a form of unique mode aptly named the “ENZ mode” [132,133]. This species of confined mode could enable novel applications for ENZ materials such as thermal emission control and directional perfect absorption [134].

 

Figure 8. ENZ distinctive applications. (a) Electric levitation: in much the same way that magnetic fields cannot penetrate into a superconductor, which enables magnetic levitation, an analog can be achieved with the electric field expulsion in ENZ materials [55]. (b) Photonic doping: analogously to the standard semiconductor doping, where a very small fraction of an atomic species alter the macroscopic material properties, dielectric particles immersed in an ENZ medium modify the medium’s effective permeability while keeping its effective permittivity [52]. (c) ENZ supercoupling: transmission of EM radiation through narrow irregular channels with subwavelength transverse cross section [128]. (d) Superradiance: the emission from a collection of quantum emitters scales quadratically rather than linearly when they are embedded in an ENZ environment [56]. (a) Figure 1 reprinted with permission from Rodriguez-Fortuno et al., Phys. Rev. Lett. 112, 033902 (2014) [55]. Copyright 2014 by the American Physical Society.

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Another important consequence of operating in the ENZ regime is that in certain materials the real refractive index is below unity [52,135]. This is extremely advantageous in nonlinear optics for at least two fundamental reasons: (i) the phase matching conditions are relaxed; (ii) the nonlinear Kerr coefficient $n_2$ is enhanced enormously (in very intuitive terms we could refer to the simplified relation linking nonlinear index and permittivity changes: ${\Delta }n\approx {{\Delta }\epsilon /2\sqrt {\epsilon }}$) [136].

In this regard, we underline that after some over-optimistic belief in the development of efficient nonlinear plasmonic devices, mainly due to the exceptionally tight mode confinement peculiar of plasmons, it become evident that the fundamental figure of merit $({\rm FoM})=\frac {n_2}{\alpha }$ (where $\alpha$ is the linear absorptioncoefficient) for standard metal-based plasmonics was too low due to the ohmic losses (which were also lowering the damage threshold of the devices and, consequently, the range of possible applications) [137,138]. However, TCOs (in their ENZ window) possess losses almost two orders of magnitude lower than in metals with an $n_2$ which is intrinsically comparable [61,139]. This value of $n_2$ also can be enhanced further if angular enhancement is considered [140,141].

These numbers have recently attracted great interest in the photonics community because they bring the promise to deliver tunable and non-dissipative plasmonic technologies. Notably, the same FoM is of paramount importance in integrated quantum optics for generating non-classical states of light via nonlinear processes [142]. Recently, in the direction of characterizing and engineering the nonlinear optical behavior of TCOs, few important results have been attained. First, by engineering the deposition processes, the recombination time of interband photo-generated carriers in TCOs has been shortened by almost three orders of magnitude [143,144]. Then by combining both interband and intraband nonlinearities new material functionalities in TCOs have been enabled [145]. These results were key to prepare the ground for a new class of integrated TCO-based devices.

The present review also aims at collecting our current knowledge about the unique nonlinear properties of ENZ systems in conjunction with other alternative CMOS compatible compounds for the design of systems with record high nonlinearities and damage threshold [27]. Even though we broadly refer to TCOs as a fundamental NZI material platform throughout this article, special focus is given to AZO because of its optimal linear and nonlinear properties, ease of fabrication, and exceptional versatility in being employed in many other relevant technologies [146].

6. ENZ versus NZI

The recent wave of works on nonlinearities in TCOs started from the fundamental interest in ENZ and mu-near-zero (MNZ) materials and their peculiar optical properties. As elucidated in [135], when the fundamental optical parameters $\epsilon$ and $\mu$ approach zero, from the Maxwell curl equations

This effect is accompanied by a nearly constant phase field distribution inside the material and a considerable “stretching” of the effective wavelength. The potential technological consequences of this are remarkable. Loosening the link between frequency and wavelength may ultimately result in the possibility to design a highly compact device operating at optical frequencies, allowing for super-resolution imaging, enhanced nanoemitter emission [67,147], supercoupling, superradiance [56], subwavelength, optical/electric modulation [69,116,148], enhanced plasmonic confinement [149], etc. For all these reasons, in many cases, when studying TCO-based optical systems, the focus goes on their ENZ nature, rather than on the more peculiar feature of being NZI materials. Note that with some “abuse” of language, in numerous cases ENZ and NZI are often used interchangeably. To clarify why this happens, the refractive index as a function of wavelength for various materials is plotted onto the complex plane in Fig. 9 (Each material’s index curve is parameterized by wavelength). In this figure, ENZ is defined as $|\Re (\epsilon )| < 1$, NZI defined as $\Re (n) < 1$, $\mu$ is taken to be unity, and, as one would expect, the ENZ condition splits the complex plane into two regions, $\epsilon > 0$ (dielectrics) and $\epsilon < 0$ (metals). Examining Fig. 9, it is clear that the ENZ and NZI conditions can be satisfied simultaneously only when losses are sufficiently low. For example, gold satisfies the ENZ condition for losses remaining below unity ($\Im (n) < 1$) but does not achieve NZI, whereas TCOs such as ITO, GZO, or AZO achieve a low value of both real and imaginary $n$ in the NIR, and thus strongly satisfy the NZI condition.

 

Figure 9. Map of $\Re (n)$ versus $\Im (n)$ for various materials with $\mu = 1$. A clear distinction between NZI and ENZ can be seen, as well as a splitting of the complex plane between metallic and dielectric behaviors. TiN and gold enter the ENZ region but do not classify as NZI due to their high losses. AZO, GZO, and ITO, however, do manage to reach the NZI region. AZO has much lower losses than both GZO and ITO at most wavelengths and also achieves smaller values of $\Re (n)$. Data for gold was generated via an ERM model with two critical-point oscillators, and a single Drude pole [152], whereas data for AZO, GZO, ITO, and TiN are taken from Drude–Lorentz fits on ellipsometric data in [15]. SiN was taken from [153].

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However, as far as optical nonlinearities are concerned, it is the slow-light effect, directly connected to the low-index nature of these materials, which is responsible for the nonlinear enhancement [150]. In other words, although many of the wonderful ENZ effects mentioned previously can be attained in different optical systems, same cannot be said about highly nonlinear NZI devices. For instance, the ENZ operational range can be access via structured materials, or simply by choosing to operate in the proximity of the material crossover point (after all, most of materials are ENZ at some wavelength). However, lowering the refractive index of a medium well below unity is not an easy task, since both real and imaginary permittivity are required to be small in magnitude; a condition which is, in general, impeded by Kramers–Kronig (K-K) relations. Luckily enough, the K-K relations pertain a set of two mathematical integral relationships covering the entire infinite spectrum, but locally there is no fundamental theoretical constraint preventing both $\epsilon '$ and $\epsilon ''$ to be both relatively small within a relatively large wavelength range (we should note that for Fig. 9 this condition is automatically satisfied as we are modeling permittivity with physically consistent models). It is this “magic” condition that makes TCOs very unique and allow for identifying the greatest part of NZI photonics with the study of optical propagation in TCOs.

In this regard, it is important to underline that although both the NZI and ENZ conditions can be attained via metamaterial engineering, this would come at the cost of increased fabrication complexity, incompatibility with numerous photonics systems, spatial dispersion, and fundamental loss issues. The last problem being the most relevant and difficult to solve. Another strategy, is that one mitigating losses by designing all-dielectric NZI effective media but this solution poses serious fabrication challenge, requires compound compatibility, and it comes at the additional cost of limited bandwidth and being subject to a strong angular dependence [151]. Of course, operating at longer wavelengths (terahertz, microwaves) is also a viable option where fabrication contains are loosened and the effective material magnetic permeability can also be tailored at will. However, the present review is mostly focused on a spectral range which partially overlap with the visible window and extends in the NIR to include fundamental telecom wavelengths.

7. Describing Optical Nonlinearities in NZI TCOs

When the operational central wavelength of an optical propagating pulse falls within the NZI spectral window, nonlinear effects are enhanced enormously [99,154–156]. To provide an important term of comparison, the optically induced nonlinear refractive index change is of the order of $10^{-3}$ for femtosecond optical excitation of silicon wafers with fluences of tens of millijoules per square centimeter [157]. Under similar conditions, AZO and ITO thin films can lead to an almost unitary change of the refractive index [61,140,158,159] which can be further enhanced by coupling the NZI layer with nanoantennas [160]. This is absolutely unprecedented and, in certain cases, it forces us to account for higher-order susceptibility terms up to the fifth order to analyze NZI nonlinearity [136].

When the nonlinear benefits of operating in the NZI region were still not fully understood, studies were focused at shorter wavelength toward the visible window where TCOs are highly transparent. For instance, in [161] the nonlinear characterization of ITO thin films deposited by magnetron sputtering was performed within the frequency window 720–780 nm where the material losses are almost negligible. The recorded nonlinear behavior ($n_2= 4.1\times 10^{-14}$ cm$^2$ W$^{-1}$) is due to the large carrier concentration ($5.8\times 10^{20}$ cm$^{-3}$) favoring interband nonlinear action. However, despite the reported nonlinearities deals with intraband excitations, the recorded relaxation time of the optical Kerr effect was very slow (1 ps). Optical excitation was induced by 200-fs pulses at a repetition rate of 1 kHz.

In more recent times, the general interest of the photonics community shifted away from the visible spectrum toward longer wavelengths. This is mainly pushed by simple technological needs linked to frequency windows which are less explored, especially with regards to the telecom band’s, which have a massive technological relevance. For the case of TCOs, moving the operational wavelength from the visible to the NIR brought to light the remarkable NZI properties of these materials which exhibit an unprecedented flexibility in their nonlinear properties. In other words, due to their hybrid nature, TCOs possess both interband and intraband nonlinearities which can be ingeniously combined for different goals such as: enlarging the intrinsic material bandwidth, enabling three-state optical logic and allowing for ultrafast all-optical routing [145]. The direct link between enhanced optical nonlinearities and the ENZ nature of TCOs become much clearer in [61,140] where the nonlinear Kerr coefficient was evaluated for AZO and ITO thin films to be of the order of 10^-13 cm$^2$ W$^{-1}$ for optical probing around 1.3 µm.

While the photonic community was mostly focused on mapping the susceptibility tensor of TCOs via a set of experimental tests, the need for a revised theoretical framework outside the perturbative regime was highlighted in [136]. Here, in order to adequately fit the experimental curve of the intensity dependent index with its predicted theoretical values, the approximated relationship:

Further studies also demonstrated that the degenerated configuration where both pump and probe are at the ENZ wavelength can boost nonlinearities even further (up to $n_2=5.17\times 10^{-12}$ cm$^2$ W$^{-1}$) due to combined effects which also take advantage of an enhanced third-order susceptibility [162]. These research papers clearly mark the transition between two different ways of looking at TCOs, from alternative plasmonic materials to a new platform for nonlinear photonic applications.

Following the initial enthusiasm triggered by a conspicuous set of remarkable results, numerous experiments have been focused on mapping the third-order susceptibility in the NIR region with specific attention to nonlinear frequency conversion processes and ultrafast refractive index change. A relevant overview of experimental attainments can be found in [163–165] where the development of key areas linked to NZI photonics is also discussed.

As stated previously, the initial impulse toward TCO-based technologies was purely driven by the unprecedented magnitude of the observable nonlinear phenomena. For instance, in [47,166] an ultra-broad frequency shift as large as 60 nm is induced over a 100-fs pulse propagating through a thin NZI AZO film with a temporal dynamics of few hundreds of femtoseconds. It is important to underline that in these works the exceptionally high-frequency detuning is not fully accounted by the use of simplified nonlinear models. A more precise theoretical approach is taken in [68,167] where the nonlinearity is derived by differentiation of the Lorentz–Drude model with respect to the plasma frequency change.

These research articles point out that operating in the ENZ spectral region does not actually give an intrinsic nonlinear advantage as long as adiabatic frequency shift is concern, but that the real benefit of operating with TCOs is the direct consequence of the very much reduced group velocity close to the ENZ point, the origins of which can be understood from

8. Nature of Optical Nonlinearities in NZI Material

Most of the recent nonlinear experiments in NZI bulk materials have underlined the need for a more robust theoretical analysis. In this regard, few articles are key to describe the ongoing discussion about which strategy is best to model optical nonlinearities in NZI TCOs. Despite the nonlinear refractive index change in NZI systems being intrinsically non-perturbative (i.e., the nonlinear refractive index change is naturally much larger than the linear one), most of the initial studies about nonlinearities in NZI TCOs were still using the standard framework of polarization related nonlinearities within the perturbative model.

A key paper that considerably expanded the discussion about the nature of NZI nonlinearities in TCOs, is [169] by Secondo and coauthors. This work investigates the quantitative numerical analysis of intraband nonlinearities and demonstrates that when TCOs operates in their NZI window the largest contribution to the third order nonlinearity comes from the optically induced change of free electron effective mass. As the free carrier distribution shifts toward higher energy states, due to the optical pumping which is schematically shown in Fig. 10(a), the average effective mass increases due to the strong non-parabolicity of the conduction band. This non-parabolicity is depicted in Fig. 10(b) via the color gradient representing electron effective mass on the left-hand side of the figure and the evolving occupation distribution due to the optical pumping on the right-hand side of the figure. The relaxation process follows from the kinetic energy transfer from the hot electrons to the lattice, which will result in a permittivity shift, shown in Fig. 10(c). Within this theoretical framework, Secondo and coauthors, starting from the induced change in the momentum of electron at the Fermi surface evaluate the new electron effective mass which is then substituted into the generalized Drude formula describing the material permittivity. The intensity-dependent index is then evaluated for NZI AZO to be $n_2=8 \times 10^{-17}$ cm$^2$ W$^{-1}$ which is very close to what was experimentally evaluated in [61].

 

Figure 10. (a) Pump-probe scheme acting on an ENZ material. (b) Absorbed pump energy ($U_{abs}$) increases electron energy and, thus, the electrons effective mass ($m^{\ast }(E)$) as the band is non-parabolic. Three lines on the right-hand side of the figure show how the occupied state distribution becomes smeared due to the pump beam. (c) Change in the electron’s effective mass redshifts the plasma frequency of the material and, thus, will result in an altered permittivity. Copyright 2020 Optical Society of America [169].

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Finally, the work also contains a comparative study amongst broadly used TCOs in terms of optical nonlinearities. The study consider how the nonlinear index change is fundamentally affected by key parameters such as optical absorbance, the band non-parabolicity, and the material dispersion. All these parameters are used to define an alternative nonlinear FoM for TCOs which ultimately sees ZnO based compounds at the top of the list.

Another work where the role of hot electron scattering in TCOs nonlinearities is considered within the framework of the optically induced effects on the non-parabolic band is [170]. Here, the scattering rate is modeled as the summation of different scattering mechanisms. By fitting pump/probe experimental spectra (both in transmission and reflection) with the developed model, the scattering with ionized impurities and acoustic phonons are identified as major contributors to the change in effective mass.

A recent work by Khurgin et al. expands and completes this analysis as reported in [150], by identifying slow and fast nonlinear processes for both interband and intraband excitations in NZI TCOs. Starting from a two-level model and taking into account the electronic cloud distribution in the conduction band, the authors analyze the efficiency of four-wave mixing (FWM) and its nature for the four different excitation processes. When looking into optical transition above band-edge the separation between fast and slow processes is the most intuitive where virtual and real transition are considered respectively. When photon excitation occurs below the band edge, the authors consider on the one hand the almost instantaneous effect pertaining the non-parabolicity of the conduction band (fast nonlinearity) and on the other hand the redistribution of hot electron cloud (slow nonlinearity).

Interestingly enough, these four processes can be associated to four characteristic time constants:

The bottom-up approach by Kurghin and coauthors to model optical nonlinearities in NZI TCOs starts from the material electronic structure to describe the physical nature of the enhanced nonlinearities in conductive oxides. However, a top-down approach, that stems from the polynomial expansion of the material polarization, can also be effectively used for the quantitative investigation of NZI nonlinearities. For instance, in [172], starting from the well-known inhomogeneous wave equation fundamental effects, such as second-harmonic generation and THG are investigated in ENZ and MNZ materials. One key assumption at the core of the employed models is that the material system under analysis is non-perturbative when considering the dependence of the intensity on the refractive index, but it is still perturbative when the dependence of the material polarization versus the electric field is concerned, an assumption which is experimentally demonstrated in [136], and that is extremely convenient for evaluating (and sometimes predicting) the nonlinear optical behavior in NZI materials. Solis and coworkers also provide numerical evidence (via a FDTD solver) that the efficiency of phase-matched nonlinear propagation increases as the dielectric permittivity decreases and/or the magnetic permeability increases. The latter being a direct consequence of the inverse proportionality between the nonlinear conversion length and the material relative impedance. Finally, by accurately modeling the nonlinear refractive index change without the usual polynomial approximation, the authors proves a monotonic and asymptotic trend of the nonlinear Kerr coefficient as epsilon tends to zero. Interestingly enough, the same conclusion are reached in [150] by evaluating the fundamental effect of material dispersion for frequency conversion purposes. In this regard, this work properly highlights how NZI TCOs provide a very unique nonlinear environment because while behaving as metals these materials still behave as dielectric for higher harmonics, thus providing a hybrid platform for efficient and ultrafast nonlinear effects.

Whenever a new material is brought into play, a natural and intuitive way to describe it is by comparison with other well-known existing compounds. Thus, one important question is: what is the right material comparison to be made when describing TCOs for application in integrated photonics? Because of their hybrid nature, it is immediately evident that one single term of comparison might not suffice for solving the problem. For instance, in terms of their conductivity, TCOs are close relatives with metals, however, a wide intrinsic bandgap keep them linked to the semiconductor world.

The original impetus toward the synthesis of TCOs was dictated by the need for a compound capable of combining a metallic behavior while reducing unaffordable losses. Now that TCOs have triggered a revolution in nonlinear optics, and they have been studied well outside the domain of plasmonics, it is time to reevaluate these materials keeping an eye on a much broader plethora of possible photonic applications. In this regard, it is of fundamental use to see how TCOs “score” with respect to the well-known nonlinear FoM defined by the ratio $n_2/\alpha$, where at the numerator we find the nonlinear Kerr index and at the denominator the linear losses. This FoM is largely used by the photonics community to benchmark nonlinear optical materials for practical applications because it takes into account the cumulative nature of nonlinearities. In other words, an extremely large nonlinearity is of no practical use if losses are so high to impede an effective buildup along the given propagation length.

Because TCOs are in between metals and semiconductors, we can think to evaluate the previously mentioned FoM for few key metallic and non-metallic materials. In Table 3, a comparison is made between Au, AZO, SiO$_2$, and SiN. The choice of these materials is justified as it follows: gold is arguably the most representative metal in plasmonic technologies; AZO, as discussed in [169], is one of the most performant and material-friendly TCOs; SiO$_2$ is the fiber core material for long distance optical communication; and SiN is one of the most promising material platform in integrated nonlinear photonics. In particular, in less than a decade, SiN-based technologies have attained tremendous progresses in improving fabrication processes, and optimize on-chip nonlinear processes (e.g. self-phase modulation, frequency conversion, and supercontinuum generation) [178].

Table 3. Comparison between Au, AZO, SiO$_2$, and SiN

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As we can see from Table 3, metallic nonlinearities (dealing with the redistribution of the free electron cloud, as for Au and AZO) are over three orders of magnitude higher that dielectric nonlinearities (dealing with anharmonic oscillation of bounded electrons, as for SiN and Si). However, in our table, losses span over 12 orders of magnitude and they ultimately determine the overall picture about the nonlinear material under consideration. This is apparent when comparing AZO with silica glass. Although AZO nonlinear index is over four orders of magnitude larger than in silica, the latter has by far the highest nonlinear FoM as reported in Table 3. In other words, losses are so low in silica fiber, that in principle we could afford kilometer-long propagation to accumulate very strong nonlinear effects (dispersion is not accounted for in this instance). As a contrast, in noble metals, such as gold, the characteristic penetration depth is only a few tens of nanometers, thus preventing any kind of cumulative effect. In addition to this, the impossibility to effectively exploit nonlinearities in metals is further aggravated by a quite low damage threshold.

Although, it is clear that losses are the most important factor as long as photonic device design is concerned, it is instructive to notice that AZO and SiN have a FoM within the same order of magnitude, and SiN is one of the leading material platforms in nonlinear integrated photonics. In other words, for many photonic applications a compromise has to be found between compactness and nonlinear efficiency. Following a similar logic, Table 3 seems to say that for those nonlinear applications where the optical path is submicrometric, TCOs should be considered as the preferred option. A good example for possible applications can be flat optics, where the beam propagates for few hundreds of nanometers and optical nonlinearities could enable efficient and ultrafast tunability. An additional benefit of replacing metallic nanoantennas with TCO-based elements would be the largely increased damage threshold.

Under the light of what has just been discussed in this paragraph, one way to look at NZI TCOs is as low-loss metals rather than as highly nonlinear semiconductors and, with this general picture in mind, try to find the best possible application for this very intriguing class of compounds. It is worth mentioning that the comparison we made between different material platforms deliberately excludes those affected by nonlinear optical absorption(e.g., silicon).

From what we have just said, it is evident that TCO-based nonlinear metasurfaces immediately emerge as a possible “killer application.” For this typology of components, a very large nonlinear optical response is required over a very short (submicrometric) optical path along which moderately low losses are affordable. For the sake of comparison, THG efficiency was measured for a 300-nm-thick AZO film in the photonics labs at Heriot-Watt University. These results are compared with similar out-of-plane THG systems in Table 4 (see also [179–182]). Representative systems including 2D materials, plasmonic and dielectric metasurfaces, perovskites, and TCOs have been considered. Although a broad range of fluences have been considered in this analysis, it is important to keep in mind that this itself is a material constraint. Each material’s damage threshold limits the maximum fluence that can be used to generate harmonics and, thus, TCOs have a huge advantage due to their exceptionally high damage threshold.

Table 4. Fundamental Parameters to Facilitate a Technological Comparison^a

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FWM is another prospective optical nonlinearity that can be enhanced via operating in the NZI regime. In [183], a degenerate pump FWM in an AZO thin film is demonstrated. This setup allowed for the generation of visible light via a NIR seed and pump. Efficiencies of up to 2% were observed with additional tuning capabilities also becoming possible due to the massive nonlinear refractive index in AZO’s NZI region (see Section 9. for more details).

It is also worth recalling that the naturally remarkable nonlinearities of TCOs can also be further enhanced via resonant coupling with nanoantennas [160,184] and that the fabrication processes to create TCO-based nanostructures are developing very rapidly from the first optical nanostructures attained by e-beam lithography and lift-off procedure [108] to those fabricated via plasma induction in [185]. The latter work underlines the exceptional flexibility of TCOs materials with respect to the carrier concentration engineering.

Further work into the coupling properties between ENZ films and plasmonic antenna arrays has been completed in [186]. The peculiar optical properties of TCOs in the NIR are largely due to their large carrier concentration in this spectral region which confers metallic properties to relative transparent materials. The intrinsic carrier concentration of TCOs can be largely tuned by operating on the film thickness, deposition temperature, post-annealing process, etc. [110]. In this paper, a novel strategy is introduced where selective exposure to O₂ plasma induces a local alteration of carrier concentration which can be exploited as alternative route for device patterning. A feasibility study is developed even further by demonstrating that etchless metasurfaces fabricated by this novel approach can retain similar functionalities and optical performance to those attained in more standard devices attained by planar technology.

Still within the realm of metasurfaces, we should underline that although experimental demonstrations have been reported where metallic nanoinclusions were replaced by TCO elements [187] for static functionalities, no exploitation of NZI nonlinearities has been implemented for enabling ultrafast tuning. Few designs have been experimentally demonstrated so far where efficient modulation of the complex refractive index and polarization properties was attained by electric bias of an embedded TCO nanolayers [188–193]. However, to the best of the authors’ knowledge, a metal-free metasurface where the local modulation of the impinging wavefront is operated by TCO-based resonant structures whose optical nonlinearities are also harvested for ultrafast tunability has yet to be proved.

9. Photon Acceleration in NZI Bulk Materials

Due to an unprecedented time gradient of the optically induced refractive index change, researchers have referred to TCOs as time-varying media in numerous studies. To understand the conceptual difference between a standard nonlinear system and a time-varying environment we can refer to two very fundamental effects, which are cross-phase modulation (XPM) and time refraction (TR). In XPM, one probe optical pulse experiences a temporal phase change induced by another copropagating intense pump signal. In this case, looking at the probe temporal profile, the head of the pulse feels a different refractive index with respect to its tail. This effect is clearly cumulative as the probe propagates inside the medium and the correspondent angular frequency shift can be written as ${\Delta }\omega =-k_0 L({\frac{{\textrm{d}n}}{{\textrm{d}t}}})$, where $k_0$ is the free space wavenumber, $L$ is the propagation length, $n$ is the refractive index, and $t$ is time.

On the other hand, TR occurs when a propagating electromagnetic wave experiences a sudden change of the global refractive index [194]. This accounts as a “temporal interface” occurring at a certain time $t'$ at which, following photon momentum conservation, two more waves, one forward propagating (refracted) and one backward propagating (reflected), are generated at a different angular frequency according to $n_1\omega _1=n_2\omega _2$, where $n_1,n_2,\omega _1,\omega _2$ are the refractive indices and angular frequencies for the incident and refracted beams, respectively [195]. This process is in time what Snell’s law is in space, as the latter links the indices of refraction in the two interfaced media to the incident and refracted angels according to $n_1 \sin \theta _1=n_2 \sin \theta _2$. From this basic comparison, a key difference between XPM and TR is immediately apparent because in TR the entire pulse profile experiences the same index change. Because of the large variety of nonlinear experiments performed using femtosecond excitation on NZI thin films, it might be instrumental to refer to the pump/probe scheme in Fig. 11.

 

Figure 11. Pump/probe scheme for the nonlinear characterization of ultra-thin NZI film. An intense pump pulse induce a nonlinear change of the material optical properties (i.e., transient change of the complex refractive index) whereas another attenuated probe pulse is used to record the triggered change.

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In a typical nonlinear pump and probe process we can identify four fundamental time parameters: $t_1$, the probe duration; $t_2$, the pump duration; $t_3$, the propagation time inside the material; and $t_4$, the material response time. Here $t_1$ and $t_2$ are typically very similar, here assumed to be about 100 fs. $t_3$ can be estimated as the product of the group velocity inside the nonlinear medium and the propagation distance (i.e., film thickness). For a 500-nm-thick AZO operating at the NZI wavelength, $t_3$ is about 10 fs. With regards to $t_4$, typically it is not identifiable by one unique value, because it refers to a set of time constants each one describing a different process (e.g., carrier generation or thermalization process). However, within the context of our discussion, $t_4$ can be identified by the temporal dynamics of the “slow” optical nonlinearities in a TCO film which, as defined in [150], is of the order of 100 fs.

When exciting NZI nonlinearities in TCO thin films, a quite typical situation is one of having a material response much slower than the interaction time. Under this condition, the spectral change induced on the probe pulse, can be mostly explained as TR rather than a more typical XPM. From what we just said, the transition between TR and XPM is mediated by the ratio between $t_3$ and $t_4$ and, thus, linked to the film thickness. The dependence on material thickness can be graphically understood by examining Fig. 12 (see also [68]). The gray bar represents a probe pulse with temporal width $\tau _{probe}$ propagating through a medium with spatially and temporally varying refractive index. Three distinct regimes are depicted: (a) a simple spatial refractive index modulation from $n_2$ to $n_1$ which alters the wave vector of the pulse, (b) a refractive index modulation propagating with finite velocity, and (c) a purely temporal refractive index modulation, which results in TR. The most physically relevant case is Fig. 12(b) as refractive index modulations induced via pump pulses will travel at a finite velocity. However, this does not rule out the TR as seen in Fig. 12(c). If the thickness of the film is much smaller than the spatial extent of the probe pulse (the film thickness $L_f$ as compared with the width of the probe pulse in the $z$ direction) the refractive index variation across the film becomes negligible leaving only the temporal refractive index gradient and subsequent TR. The link between film thickness and the transition from XPM to TR can also be appreciated in simple mathematical terms. If starting from a bulk film of thickness $L$ we consider one infinitesimally thin slice of material $({\delta }L)$ with uniform optical properties for which the spectral change induced by XPM can be written as

 

Figure 12. Representation of three different regimes of refractive index change. Spatial units have been normalized and color-map represents refractive index change. Here $\tau _{prop}$ is the time it takes for the pulse to traverse the medium, $\delta \tau _{change}$ is the duration over which the refractive index modulation takes place, and $v_{change}$ is the velocity at which the refractive index modulation propagates. The gray bar pertains to the light line of the pulse with temporal width $\tau _{probe}$ propagating in mediums (a), (b), and (c). (a) Stationary spatial interface ($v_{change} = 0$). (b) Hybrid case in which the refractive index interface moves at a finite speed. The slice with thickness indicated $L_f$ denotes a film which will emulate medium (c) as the thickness is reduced below the pulse’s spatial extent [68]. (c) Temporal interface such that the refractive index changes with time uniformly across the entire medium ($v_{change} = \infty$). Copyright 2020 Optical Society of America [68].

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Within the framework of time-varying media there are few key works that must be mentioned such as [166] where an optically induced frequency shift as large as 60 nm (larger that the bandwidth of a 105 fs centered at 1400 nm) is induced by degenerate optical pumping. As the temporal phase change in the 500-nm-thick AZO film can be considered uniform during the entire pulse duration, a perfectly rigid shift of the pulse spectral fingerprint is attained. More recently an optically induced frequency shift of 15 nm was observed with an ITO thin film in [196]. In this work, the frequency shift was characterized at various angles of incidence; an in-depth theoretical treatment of this angular dependence on frequency shift can be found in [197] and further works can be found in [198,199].

In [200], following the time-reversing medium configuration theoretically proposed in [201] simultaneous negative refraction and phase conjugation are achieved with near-unit internal efficiency via a FWM process. However, the FWM observed in this work is fundamentally different than the standard cumulative effect recorded in nonlinear propagation. In fact, the required temporal gradient of the refractive index change has to be remarkable and the film thickness much smaller than the effective radiation wavelength. Under this condition the momentum conservation is only requested for the transversal component of the propagating waves, thus generating both phase-conjugated and negative-refracted beams.

Finally, in the context of optical equivalences, the time-varying properties of NZI TCOs have also been considered for the first direct experimental demonstration of photonic time crystals which are the time equivalent to what photonic crystals are in space. A detailed analysis of this intriguing application can be found in [202,203].

10. Quantum Optics with ENZ and NZI Materials

There have been a number of works suggesting that NZI materials may have strong applications toward quantum sciences, in both an applicative sense, such as enhanced superradiance or quantum networks, or as an analogous framework for other areas of physics such as quantum field theory (QFT) and early theories of the universe. In the following section, we explore the potential of NZI materials and, more specifically, TCOs for quantum optics.

Some fields of physics prove more of a challenge to study experimentally than others and, as we might expect, black hole physics is one such field. Because of these inherent limitations, it can be beneficial to study mathematically analogous systems. Specifically, in [204], it is shown that Hawking radiation has an analog in Maxwell’s equations if a refractive index perturbation of the form $\delta {n}_{max}e^{-((x-vt)/\sigma )^m}$ is traveling with the pulse (where $m$ is an even integer, $v$ is propagation velocity, $\sigma$ is pulse width, and $\delta {n}_{max}$ is the maximum shift in refractive index). For example, Fig. 13(A) displays a study on Hawking radiation emission via a simulation of a classical pulse incident onto a traveling refractive index perturbation. Panels (a)–(d) show the evolution of the electric field centered on the refractive index perturbation, whereas panels (e)–(h) show the respective spectra for each time step. In the final panel (h) two peaks which are representative of negative and positive Hawking modes can be clearly observed. Here, we can find an application for the massive refractive index modulations available in the TCOs, which could provide an opportunity to study these analogies and further explore the physics surrounding Hawking radiation and black holes.

 

Figure 13. (A) Panels (a) and (b) depict numerically calculated evolution of the electric field for an input probe pulse (shaded area represents the refractive index perturbation defined by $\delta {n}e^{-((x-vt)/\sigma )^m}$. It is important to note that each figure is centerd on the refractive index perturbation and the values on the x axis evolve accordingly. Panels (c) and (d) show the respective spectra for each step in the evolution. The final panel (d) displays two clear peaks that are labelled P, for the positive Hawking mode, and N, for the negative Hawking mode [204]. (B) Schematic layout of experiment proposed in [205], where time-varying ENZ media is used to spontaneously produce photon pairs. Reprinted from [205] under a Creative Commons license.

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Operating in a time-varying environment also has important theoretical implications within the domain of QFT. In this regard, it is worth recalling [205] where Prain and coauthors investigated optically excited NZI thin film as the theoretical equivalent of a homogenous expanding universe. The fundamental QFT predicts that the phenomenal non-adiabatic changes in the very early universe triggered a massive production of entangled photons from vacuum fluctuations. This prediction is also strongly related to the quantum theory of TR [206]. However, an experimental demonstration of such a fundamental phenomenon has been out of reach due to the required amplitude and speed change in optical properties. A schematic of the experiment proposed in [205] is shown in Fig. 13(B) where a laser pulse illuminates a homogeneous block of ENZ media at normal incidence, producing a photon pair in the same plane as the block. Nevertheless, TCO-based time-varying systems have been proved to enhance the efficiency of entangled photon generation up to seven orders of magnitude compared with standard semiconductor Kerr materials and bring this effect within the detectable range of current single-photon detectors.

In this regard, ENZ enhancements for two-plasmon spontaneous emission were recently investigated [142] [a schematic of two-plasmon spontaneous emission is depicted in Fig. 14(a)]. This study was completed numerically with a model based on a doped semiconductor thin film with ENZ frequency at half the one-photon emission frequency. Due to the slow-light effects characteristic of ENZ materials, the two-plasmon spontaneous emission rate is shown to grow by up to six orders of magnitude and become comparable to the one-photon emission rate. In [207], ENZ cavities were investigated for their effect on quantum emitters, specifically their effect on decay dynamics. An ENZ spherical-shell cavity [as depicted in the left panel of Fig. 14(b)] was modeled numerically, and it was found that deforming the cavities external boundary has no effect on said cavity’s resonance frequency. However, the same is not true of the vacuum Rabi frequency, which could theoretically be tuned while the cavity’s resonance remains constant [see Fig. 14(b), right panel]. This behavior is unique to ENZ media and could enable several more novel quantum phenomena. In a more drastic approach, where a material’s $\epsilon$ and $\mu$ tend to zero, it has been shown that quantum vacuum fluctuations are suppressed [73].

 

Figure 14. (a) Left diagram is a one-photon emission process for a degenerately doped semiconductor, whereas the right diagram is for two-plasmon spontaneous emission [142]. (b) Right panel shows the geometry of the ENZ cavity investigated in [207]. The red line in the right panel shows cavity resonance as a function of outer shell radius, whereas the blue line shows vacuum Rabi frequency. Both are normalized to the same frequency. (c) The left panel is a rendition of an ENZ quantum network, where the electric field is depicted in red. The blue circle highlights the coherence radius for quantum information. The right panel shows a comparison of electric field intensity in an ENZ waveguide (blue) as compared with air (black) as a function of distance from a central source [72]. (a) and (b) reprinted from [142] and 72] under a Creative Commons license.

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Another related quantum effect enhanced via ENZ TCOs is superradiance. That is, if $N$ quantum emitters are in close proximity and embedded into a deeply subwavelength material, their emission intensity will scale with $N^2$ rather than the classically understood factor $N$ [208]. Since its initial discovery in 1954, several relevant applications have been demonstrated, such as molecule detection [209], low-threshold lasing [210], and as an enhancement mechanism for Raman spectroscopy [211]. However, ENZ materials can relax the conditions for superradiance, allowing the effect to boost the radiation for even randomly distributed emitters [56,212], which could have a far-reaching effect on the previously mentioned applications. Although it is possible to understand this result by considering the local density of states available in the ENZ, we can also examine this effect through the context of supercoupling as both effects benefit from the same ENZ property [128]. Specifically, wavelengths become significantly large when operating in the ENZ region, allowing radiation to propagate through subwavelength bends with trivial reflection losses. In the case of superradiance, the long-wavelength at ENZ enables quantum emitters with large separation distances to emit coherently and relaxes the conditions on achieving superradiance. Interestingly enough, this effect is actually due to power flow in ENZ media being analogous to that of an ideal fluid. Recently, the ENZ condition has also been shown to enhance and prolong long-range quantum entanglement and also massively increase the energy transfer between quantum dipole emitters [213].

From the previous few paragraphs, it is clear that ENZ materials are a promising platform for quantum science. This case is only made more apparent in [72], where ENZ materials are presented as the key material for on-chip quantum networks. A quantum network requires the capacity to (see [214] for a more comprehensive analysis):

11. TCO BasedModulators and Waveguides

One of the most fundamental strengths of TCOs versus other materials is their enormous capacity for modulation, both statically and dynamically. Unlike conventional metals and dielectrics, the optical properties of TCOs can be changed during or post-deposition in several ways. The most common form of tailoring the optical properties of TCOs is by controlling the dopant concentration [115]. By doing so, we alter the carrier density, which results in a change of the permittivity via Drude dispersion. Other methods include controlling the gas ratios and substrate temperature [216] during their formation and post-deposition annealing [113]. For example, undoped zinc oxide is dielectric in the telecommunication regime and has an ENZ point near 8.5 $\mu$m, which can be changed via doping with gallium or aluminum down to 1.3 $\mu$m [61,217]. ITO is another commonly used TCO, with its ENZ at telecom utilized in a plethora of nonlinear optical demonstrations [140,167] and switching applications [218]. Dopants generally increase the dielectric losses inside the metals due to added scattering of light by the lattice imperfections, proving to be a drawback in applications such as waveguiding or metasurfaces, where losses deter the performance. Interestingly, an emerging TCO, CdO with dopants such as yttrium [159], dysprosium [219], and indium [116], has high-mobility compared with conventional TCOs, with losses ($\epsilon ''$) close to 0.1 or lower near its ENZ regimes, and is being explored for mid-infrared absorbers, switches, and for high-harmonic generation. Its low losses in the telecommunication regime also make it a viable candidate for utilization in on-chip electroabsorption modulation [220], discussed in the next section.

The tailorability of TCOs makes them a versatile tool for optical device design, but their real utility lies in their active modulation of permittivity. The low indices of conducting oxide at the telecommunication regime greatly enhance electric fields at a semiconductor/TCO interface for incident p-polarized light, according to $\epsilon _1E_1= \epsilon _2E_2$, where $\epsilon _1$ is the permittivity of the dielectric, $E_1$ is the field inside the dielectric, $\epsilon _2$ is the permittivity of the conducting oxide, and $E_2$ is the electric field inside the conducting oxide.

11.1 Electrical Tuning of TCO Permittivity

The permittivity of conducting oxides can be further tuned by applying an electric field or an optical pump, either generating or exciting free carriers. Applying a voltage on a TCO layer across a metal–insulator–semiconductor junction can accumulate electrons at the TCO–gate oxide interface, locally creating an influx of electrons in a small region close to the interface (1–2 nm) [Fig. 15(a)] [158]. The increased local density of electrons reduces the permittivity in the accumulation region by Drude dispersion. Feigenbaum et al. showed that for moderate voltages applied at a gold–silicon dioxide–ITO interface, accumulated electrons at the ITO–oxide interface can push the ITO plasma frequency to the visible range, leading to unity order permittivity changes in the accumulation region [Fig. 15(b)]. This large change in the permittivity has been utilized to achieve active control over the phase, amplitude, and polarization of light, both in the waveguiding configuration and the metasurface configurations.

 

Figure 15. (a) Metal–insulator–semiconductor schematic commonly used for electrical modulation. An applied voltage accumulates photocarriers near the gate, which locally modulates the permittivity [158]. (b) Depending on the carrier concentration, unity order permittivity changes can be observed. [158]. (c) Metal–insulator–metal slot waveguide architecture used to demonstrate the first on-chip, tunable plasmonic modulator with conducting oxides [70]. (d) Hybrid structure employing a metal–insulator–semiconductor gated junction used in most plasmonic modulator designs [221]. (a) and (b) Reprinted from Feigenbaum et al., Nano Lett. 10, 2111–2116 (2010) [158]. Copyright 2010 American Chemical Society, https://doi.org/10.1021/nl1006307. (c) Reprinted with permission from [70] © 2014 The Optical Society. (d) Reprinted from Sorger et al. (2012), Nanophoton. 1, 17–22. © 2012 Sorger et al., published by de Gruyter.

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A decreased permittivity can increase the field in the TCO [222]. As a consequence, the increased carrier concentration leads to higher absorption, which is useful for modulation purposes. This was first demonstrated in the ITO-based plasMOStor by the Atwater group. In the plasMOStor [Fig. 15(c)] [70], a voltage applied across the silicon oxide–ITO–metal interface in a plasmonic waveguide caused free carriers to accumulate near the gate, increasing the electroabsorption losses of the mode contained within the MIM waveguide, effectively turning off the signal. Once the voltage is removed, electrons flow away from the ITO, returning it to the original state with lower losses. The first demonstrated device operated at kilohertz speeds. Employing such electrical modulation schemes in plasmonic nanostructures enable the design of nanoscale optical circuits that can have terahertz bandwidth, circumventing diffraction-limited size restrictions of optical waveguides [223]. Another common configuration utilized in this type of electroabsorption modulation scheme is the metal–insulator–conducting oxide–silicon geometry, commonly referred to as the plasmonic slot waveguide configuration. In this configuration, the electromagnetic field couples into a nanometer-thick low-index region sandwiched between a high-index semiconductor (silicon) and metal layer [Fig. 15(d)]. In addition to having lower losses than conventional metal–insulator–metal (MIM) structures, these devices can be readily incorporated into silicon-based nanophotonic circuits. As accumulated electrons lower the refractive index of the conducting oxide, more light gets pulled into it, and the higher absorptionin this region turns the signal off. Sorger et al. demonstrated that extinction ratios of 1 dB/$\mu$m with electrical tuning could be achieved in a metal–insulator–semiconductor waveguide [221]. Many other demonstrations of active waveguiding schemes were proposed and demonstrated. Better designs and a combination of low-loss, CMOS compatible materials and geometries have resulted in nanoscale circuits with very small volumes [224], low-voltage operations [225], and femtojoule/bit energy consumption, operating at gigahertz to terahertz bandwidths. The authors encourage interested readers to refer to the recent reviews and perspectives by Babicheva et al. [69] and Sorger et al. [226,227].

11.2 Electroabsorption Modulation

Other than carrier accumulation, another interesting phenomenon that may occur in a metal–insulator–conducting/oxide boundary is electromigration. Under an applied voltage, small imperfections in the TCO–metal or metal–oxide interface can have large localized fields that cause metal ions to migrate into the oxide, causing filamentation. These filaments can cause the local formation of plasmons, and increase light scattering and absorption, resulting in large modulation. Electromigration-based effects can be identified by a hysteretic behavior of their current–voltage properties. When the electric field is removed in an electromigration-based device, the signal does not return to its unbiased value and requires a voltage reversal to get back. This effect was observed in a silicon oxide–metal boundary by Emboras et al., who utilized the phenomenon for all-optical memristor applications [Fig. 16(a)] [228]. This effect of ion injection into the oxide layer has been further employed utilizing conducting oxide platforms to demonstrate and a memristive modulator [229] [Fig. 16(b)], and the first atomic-scale plasmonic switch [230] [Fig. 16(c)] employing ITO as the medium.

 

Figure 16. (a) Under an applied bias, islands of metal ions can migrate into the oxide, forming resistive bridges, increasing the waveguide losses. Electromigration effects are generally slower than plasmonic effects and are identified by a hysteretic behavior [228], seen from the current–voltage graph. (b) The phenomenon of electromigration can be readily incorporated into TCO-based platforms as well, in the same silicon plasmonic waveguide configuration. A hysteretic behavior can be observed in the transmission of light versus an applied voltage, following the formation and reabsorption of the ion-channel bridge [229]. (c) The modulation can be controlled down to an atomic scale, where the injection of a single atom into a plasmonic slot can significantly alter the transmission of plasmons through the waveguide, forming an atomic scale plasmonic switch [230]. (a) Reprinted with permission from Emboras et al., Nano Lett. 13, 6151–6155 (2013) [228]. Copyright 2013 American Chemical Society, https://doi.org/10.1021/nl403486x. (b) Reprinted with permission from [229] © 2014 The Optical Society. (c) Reprinted from Emboras et al., Nano Lett. 16, 709–714 (2016) [230]. Copyright 2016 American Chemical Society, https://doi.org/10.1021/acs.nanolett.5b04537.

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Recently, other works have been done in waveguiding platforms employing different metals, and oxides to exploit this effect in memristive switches, with potential applications such as photodetection [231] and neuromorphic computing [232].

Another avenue where tunable conducting oxides are being used is metasurfaces [233,234]. Metasurfaces are artificially structured surfaces with subwavelength, nanoscale features, that alter the phase, amplitude, and polarization of light. The advent of metasurfaces utilizing metals and dielectrics has greatly revolutionized the field of light manipulation, with applications in absorbers, cloaking, and optical isolation to mention a few. Active manipulation of the material permittivities offers an added degree of real-time control of the light wavefronts, where light can be controlled in real time [235]. TCOs, with their ability to alter their optical properties either with an applied voltage or an optical pulse, have enabled many practical devices for optical switching, phase shifting, and beam steering.

During electrical or optical modulation, the permittivity change induced by an accumulated electron layer results in a change in the property of light interacting with the layer. Even though large and unity-order refractive index modulation [158] has been demonstrated, the drawback here is that this change occurs only within a subnanometer layer, making it difficult for light to undergo large changes within a single pass.

To circumvent this problem, most conventional electrically tunable metasurfaces have a MIM architecture. The MIM structure confines light into an extremely confined gap plasmon ($\approx$10 nm) [Fig. 17(a)], with most of the light being confined in the dielectric and the TCO [190]. The extreme confinement of light in this thin modulation layer greatly enhances the light-matter interaction, resulting in a large alteration of optical properties. An applied voltage reduces the refractive index of the TCO, thereby changing the effective index of the metasurface, resulting in phase, polarization, and amplitude control. Metasurfaces with the MIM architecture have been so far demonstrated in a wide array of applications covering beam phase shifters [190], amplitude modulation, and beam steering devices [Fig. 17(b)–(d)] [189]. Careful designs of the MIM structure, including dual gated structures for independent phase and amplitude control have been demonstrated for active beam steering applications [Fig. 17(d)] [237]. Utilizing several meta components for individual control of the unit cell, multifunctional metasurfaces have been demonstrated for nanofocusing and beam steering [236]. Electromigration effects have also been observed in metasurface platforms, and are currently being studied for memristive metasurface applications [238].

 

Figure 17. (a) A MIM architecture was utilized by the Brongersma group for phase and polarization modulation [190]. (b) A similar architecture was utilized by the Atwater group, where they showed beam steering by controlling a different number of meta-elements [189]. (c) Electrical control offers the advantage of individually controlling the meta-elements, thus utilizing the same metasurface for different applications such as beam steering and nanofocusing [236]. (d) Using more complex designs such as a dual gated structure, independent control over the phase and polarization of light has been shown, with application in LIDAR [237]. (a) Reprinted with permission from Park et al., Nano Lett. 17, 407–413 (2017) [190], Copyright 2017 American Chemical Society, https://doi.org/10.1021/acs.nanolett.6b04378. (b) Reprinted with permission from Huang et al., Nano Lett. 16, 5319–5325 (2016) [189]. Copyright 2016 American Chemical Society, https://doi.org/10.1021/acs.nanolett.6b00555. (c) Reprinted with permission from Shirmanesh et al., ACS Nano 14, 6912–6920 (2020) [236]. Copyright 2020 American Chemical Society, https://doi.org/10.1021/acsnano.0c01269. (d) Reprinted by permission from Springer Nature. Nat. Nanotechnol. “All-solid-state spatial light modulator with independent phase and amplitude control for three-dimensional LIDAR applications,” Park et al. [237]. Copyright 2021.

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11.3 All-Optical Switching

Electrical modulation using the MOS architecture has the advantage of power efficiency, compactness, and favors integration with existing CMOS-based technology. However, they are limited by resistive–capacitative delays that scale with devices size and limit the operation speed to a few gigahertz. All-optical switching is a method that circumvents this slow modulation speed, and TCOs have several advantages over other materials in all-optical switching platforms. First, their switching times are of the order of hundreds of femtoseconds to a few picoseconds, this is faster than what can electronics can achieve and properly timed to strongly overlap with widely available ultrafast laser systems [239]. Added to this are the benefits of tailorable optical properties, established fabrication techniques, and their ENZ resonances at the telecommunication frequencies, that enable the observation of slow-light phenomena in planar films without the need for complicated fabrication.

Conventional all-optical schemes employing conducting oxides generally operate via two mechanisms, either via interband pumping, or through intraband pumping. In interband pumping, an optical pump in the ultraviolet region, having energy greater than the bandgap of the oxide, excites photocarriers into the conduction band. These photocarriers lower the refractive index of the material via Drude dispersion, making the oxide more metallic, reducing the transmission. Large changes in the optical property of aluminum-doped zinc oxide have been demonstrated by Kinsey et al. paving the path to all-optical switching schemes in the telecom regime, with picosecond switching speeds [143].

On the other hand, intraband pumping (with pump energy lower than the bandgap) heat the existing electrons in the conduction band toward higher energies. Due to the non-parabolic nature of the conduction bands, these high-energy electrons have a greater effective mass, decreasing the plasma frequency of the oxide, making it more transparent. The carriers can cool down in subpicosecond time scales, making them suitable for all-optical amplitude modulation. Figure 18(a) shows a schematic with the two types of modulation. Pump-probe schemes utilizing interband pumps have been utilized by Alam et al. [140] and Clerici et al. [145] to demonstrate very large optical nonlinearities near the ENZ region of conducting oxides. Clerici et al. further showed that these nonlinearities caused by interband and intraband pumping can be added in femtosecond time scale, paving the way to femtosecond, all-optical transistor applications. One crucial drawback the all-optical schemes suffer from is the large power requirements of the devices, which need around millijoules per square centimeter to operate. This problem, however, can be circumvented by low-loss, high-mobility conducting oxides such as doped CdO, which support relatively sharp resonances near the ENZ regime. For example, Berreman metasurfaces utilizing CdO have been utilized to demonstrate femtosecond speed polarization switches in the infrared regimes, consuming fluences of around 339 $\mu$J cm$^{-2}$ [116]. Relatively large modulation up to 135% has also been demonstrated by Saha et al. in the mid-infrared regime, with yttrium-doped CdO [117].

 

Figure 18. (a) Mechanism of interband and intraband pumping. An interband pump increases the free carrier density by photoexciting free carriers, decreasing the transmission. An intraband pump heats electrons in the conduction band, making the material more transparent, and increasing transmission [145]. (b) In frequency translation, an optical pump pulse excites electrons and briefly changes the material’s optical properties, creating a refractive-index boundary in time. This temporal index change changes the frequency of probe light passing through the boundary while conserving the wave vector. The frequency of the probe redshifts if the pump beam lags the probe, and blueshifts if the pump leads the probe. For example, the frequency of a 1235-nm probe beam redshifts by 9.1 THz at the delay time $t_d=-60$ fs [167]. (c) In photonic time crystals, a periodic modulation of permittivity in time (left panel) opens up bandgaps in the momentum of light passing through the crystal (right panel), allowing only certain wave vectors of light to enter [202]. (a) Reprinted with permission from [145] © The Optical Society. (b) Reprinted from [167] under a Creative Commons License.

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The fundamental advantage of all-optical modulation over electrical modulation is the very-fast (femtosecond) speed of permittivity change that enables novel optical phenomena that cannot be otherwise demonstrated with electrical or other slower methods of modulation. For example, effects such as broadband frequency translation and photon acceleration require refractive-index modulation of the order of the pump and probe pulse widths, which is in the subpicosecond time scale. Utilizing the fast nonlinearities in TCOs effects such as frequency translation become attainable at optical frequencies. In frequency translation, an optical pump pulse excites electrons and briefly changes the material’s optical properties, creating a refractive-index boundary in time. This temporal index change changes the frequency of probe light passing through the boundary while conserving the wave vector. The frequency of the probe redshifts if the pump beam lags the probe, and blueshifts if the pump leads the probe [Fig. 18(b)]. Other new optical phenomena enabled by sharp refractive index transition [240] include time reflection and photonic time crystal development [202,241], where periodic modulation of permittivity in time, within femtosecond time scales open up bandgaps in the momentum [Fig. 18(c).

To gain a detailed overview of new devices and new physics enabled by the nonlinear index change in TCOs and other media, we encourage the readers to refer to the recent review by Shaltout et al. [235].

11.4 Circumventing Dopant-Induced Losses in Conducting Oxides

One big drawback of conducting oxide-based waveguides and modulators is the losses induced by doping. Doping generates free carriers, and also disrupts the crystalline lattice of oxides, resulting in absorptive losses in devices even in their ON state, which is undesirable. Several ways of circumventing the losses are being studied by the scientific community. For structures involving lossy TCOs such as ITO, one method of circumventing the losses can be to use lightly doped, heat-treated ITO with lower losses in the waveguiding region, but heavily doped ITO for contact formation, reducing the RC delays [242]. Another way is to use undoped oxides. Oxides of indium [243] or zinc [159] are intrinsically n-type-doped because of oxygen vacancies in the lattice that act as donor sites. As a result, the oxides are quite conductive, with much lower losses in the telecom region than their doped counterparts. Wood et al. have shown that indium oxide grown under varying oxygen concentrations can have ENZ points far from the telecom wavelengths, with low losses [Fig. 19(a)] [243]. Under an applied bias, the material is brought into its ENZ region, increasing the absorptive losses, while having very low losses in the ON state. Modulators with gigahertz speed have been demonstrated employing such schemes [243]. High-mobility oxides such as CdO with various dopants are also being explored for waveguide and metasurface design. Dopants such as dysprosium [219] and yttrium [244] compete with oxygen vacancies, and can even reduce oxygen vacancies in CdO, decreasing the scattering losses, offering a viable method for fast modulator design [245].

 

Figure 19. (a) Indium oxide grown at different oxygen concentrations has different intrinsic carrier densities, resulting in different ENZ regimes and losses [243]. (b) Using an ultraviolet pump, free carriers generated in undoped zinc oxide can reversibly transition it from dielectric to metal and back within 30 ps. This implies that low-loss structures can be made from dielectric ZnO, and can be optically modulated to design phase shifters, polarization rotators, and other switches [159]. (a) Reprinted with permission from [243]. Copyright Optical Society of America. (b) Reprinted from Mater. Today 43, Saha et al., pp. 27–36. copyright 2021, with permission from Elsevier [159].

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Similarly, for metasurfaces, low-loss dielectrics such as zinc oxide can be used to make dielectric or plasmonic metasurfaces. Under optical pumping, zinc oxide can undergo very large permittivity changes occurring over hundreds of nanometers as opposed to electrical tuning, and survive very large optical fluences. Saha et al. have performed a detailed analysis of the very large permittivity change that ZnO undergoes with an interband pump up to its saturation limits [159], utilizing broadband pump-probe spectroscopy [Fig. 19(b)]. The ENZ regime is also shown to reversibly shift from 8.5 $\mu$m down to 1.6 $\mu$m. Metasurfaces thus designed with ZnO can have very low ON-state losses, with the large permittivity changes offering large shifts in amplitude, phase, and polarization of an incoming wavefront. A detailed investigation of material processes, damage thresholds, and transient dynamics is key to design novel schemes for all-optical light manipulation. All-optical modulation, despite the large power requirements, offers the added benefits of decoupling from the MIM architecture, offering greater flexibility in terms of design, decoupling the devices from the inherent resistive–capacitative delays, and allowing for ultrafast operations. Electrically controlled, all-dielectric metasurfaces have also been proposed employing doped-silicon and ITO contacts, thus circumventing large ON-state losses that occur in metal contacts [246].

The versatility of applications for actively controlled waveguiding platforms employing TCOs makes them an industrially viable prospective solution to enable ultrahigh-speed data communication and modulation, with practical applications in high-speed computing and data centers. The memristive devices can be utilized for photodetection and neuromorphic computer applications. Electrically tunable devices are currently being explored for LIDAR and car vision applications. On the other hand, optically tunable, time-varying metasurfaces are key to understanding and exploring the ever-expanding world of nonlinear optical phenomena.

12. NZI Materials: Emerging Studies and Applications

After having described TCOs as an evolving material platform from plasmonics to nonlinear optics, it might be worth stressing the multifaceted nature of this set of materials which can be transformative for a broad plethora of different applications. In this section, we wish to collect a few recent key examples which have not been highlighted by other review articles.

For instance, in [247] the fundamental radiative processes are considered and theoretically studied for materials with vanishing permittivity and/or permeability. This result is made clear in Fig. 20(a), where normalized spontaneous decay rates for ENZ, MNZ, and epsilon and mu near zero (EMNZ) are calculated against frequency for 3D, 2D, and 1D NZI media in the left, center, and right panels, respectively. When a two-level system is taken into account for an NZI system it is proved that the system dimensionality is key to trigger remarkably different emission behaviors. The common framework within which the outlined analysis is developed starts from the decay rate evaluated as the product between the number of available photonic modes and the coupling strength between the NZI system and the surrounding environment. The study points out that despite the number of available radiative modes monotonically decreases as the index approaches zero, the coupling strength drastically vary its behaviors with the system dimensionality as can be seen in Fig. 20(a). This ultimately explains why immersing an emitter in a NZI environment might not be the best solution for enhancing its emission while coupling the system with plasmonic waveguides operating near the cutoff improves the emission rate.

 

Figure 20. (a) Normalized spontaneous decay rates for ENZ, MNZ, and EMNZ are plotted against frequency for 3D, 2D, and 1D NZI media in the left, center, and right panels, respectively [247]. (b) Left panel shows a schematic of a classic light-trapping scheme consisting of an absorber layer atop a mirror, whereas the right panel add an additional NZI layer, which, theoretically, should drastically improve the light-trapping capabilities of the system [248]. (c) Left panel schematically depicts a Pt Schottky junction device with an AZO substrate as well as its band diagram. Absorbed photons excite hot electrons which are then injected into the silicon and collected through the ohmic aluminum contact. Right panel plots responsivity against wavelength for the photodiode with and without an AZO film. Responsivity is enhanced by 80% with the film [249]. (d) Schematic of the proposed CdO plasmonic all-optical switching (AOS) device. Both the pump and probe light sources couple to the device through a directional coupler to allow for wavelength multiplexing. [250]. (a) Reprinted with permission from Lobet et al., ACS Photonics 7, 1965–1970 (2020) [247]. Copyright 2020 American Chemical Society, https://doi.org/10.1021/acsphotonics.0c00782. (b) Reprinted with permision from Wang et al., Appl. Phys. Lett. 109, 051101 (2016) [248]. Copyright 2016, AIP Publishing LLC. (c) Reprinted with permission from Krayer et al., ACS Photonics 6, 2238–2244 (2019) [250]. Copyright 2019 American Chemical Society, https://doi.org/10.1021/acsphotonics.9b00449.

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Moving toward novel strategies to maximize photon absorptionfor optimizing photocurrent efficiency in photovoltaic systems, it is worth recalling [248], which pertains to photon management in NZI materials. The paper points out that the standard strategy in photon management is to choose a high-index material due to the large density of photonic states and the intrinsic reduction of the escaping light cone. Starting from the well-known analysis by Yablonovitch developed within the framework of statistical ray optics [251], the authors recall that in standard multilayer absorbers the light-trapping limit is set to be $F \leq 4n_2$, as is schematically depicted in the left panel of Fig. 20(b). However, when an upper NZI layer is added this limit is proved to become $F \leq 4n_2/n_{NZI}$ which can be up to two orders of magnitude larger than in standard high-index-contrast systems [see Fig. 20(b), right panel, for a light-trapping scheme with NZI layer added]. In [252] near-perfect absorptionat visible frequencies is theorized to be possible by placing ultrathin metal films onto a NZI substrate.

In [249], Krayer and coauthors clarified the influence of NZI substrates for photonics application when highly efficient photodetectors are employed. A comparative experimental study was performed between the absorptionproperties of thin metal films and equivalent systems coupled to low-loss NZI substrates. For the sake of completeness, the study also investigated how the coupling with NZI substrate affects the photocurrent generated at a Si/Pt Schottky junction, the schematic and band diagram of which is shown in the left panel of Fig. 20(c). The NZI coupling is proved to double the absorptionin metallic thin films while the electric response of the photodiode is increased by 80% across the entire bandwidth, this can be seen in the right panel of Fig. 20(c), which plots the responsivity against wavelength for the photodiode with and without an AZO film. Despite the reported experimental results being quite convincing, few doubts remain about the initial material characterization and the reported value for the complex index of the NZI layer ($n_{NZI}=0.01+0.01i$). In [253], a transparent, flexible, self-powered photodiode constructed from perovskite–TCO was designed and characterized.

Finally, within the fundamental domain of optical modulation we wish to recall [250] by Li and Wang. In this numerical/theoretical work, an ultra-efficient (i.e., switching energy <13.5 fJ) optical modulator was investigated. The device guiding core was made out of a Si waveguide whereas the modulation was induced by a surrounding CdO ultra-thin layer [a layout of this device is shown in Fig. 20(d)]. One fundamental characteristic of the proposed configuration is that the device “OFF” state is attained by electrically biasing the TCO layer in the ENZ regime, and the “ON” state is attained via optical pumping.

13. Conclusions

Until a few years ago, TCO-based technologies were a synonym for photovoltaic systems and touch screens, with little connection with the world of nanophotonics. However, during the last decade, plasmonics opened up new frontiers toward the full integration of photonic devices with subwavelength optical confinement. Many exceptional demonstrations utilizing plasmonics have been shown, such as negative refraction, superlensing, 2D optics, waveguide supercoupling, and ultra-compact electro-optic modulation. Revolutionary nanophotonic devices could have been developed from these demonstrations, however the transition from the lab to real-world applications has not yet occurred. This issue mainly stemmed from plasmonic technology’s reliance on metallic inclusions, which impose unacceptable ohmic losses and incompatibility with standard semiconductor processes, this last point being critical for low-cost mass production of nanophotonic devices.

Different attempts moved in the direction of solving the above-mentioned issues. One of the most promising solutions was that one of eliminating metallic inclusions and exploiting electromagnetic Mie scattering resonances in high-index contrast metamaterials, a field that has come to be known as all-dielectric nanophotonics. A few key photonic devices have been demonstrated in this field, such as nanoresonators, subwavelength meta-lenses, reconfigurable metamaterials, and zero index waveguides. However, the elimination of metals from nanophotonics would eliminate many of the fundamental attributes that made plasmonics appealing in the first place, while limiting the set of suitable functional materials.

Owing to these reasons, the emerging field of “all-dielectric plasmonics” was triggered by the introduction of TCOs as replacements for metals. When TCOs are used as an alternative plasmonic material, they yield quite few fundamental advantages when compared with metals such as reduced ohmic losses, low-temperature fabrication, high damage threshold, and CMOS compatibility.

More recently, the characteristic optical properties of TCOs when operating in their epsilon and NZI wavelength region (occurring in the NIR) have been identified as a key area for research. This is well justified by the many interesting phenomena that can occur when operating in a low-permittivity regime and/or the huge nonlinearities when the real index is close to zero. Research into the ENZ regime in TCOs has introduced several remarkable experimental demonstration such as wavefront freezing, electric levitation, photonic doping, emission “pinning,” and many more. As mentioned previously, TCOs can also satisfy the more stringent condition of having a real index approaching zero at telecom wavelengths. This NZI feature can cause a slow-light effect and, in turn, enhance nonlinearities enormously. This enhancement has been demonstrated in several contexts, including harmonic generation and near-unity optical refractive index modulation.

The versatility in TCOs’ tunability, both static and dynamic, makes them an industrially viable prospective solution to enable ultrahigh-speed data communication and modulation, with practical applications in high-speed computing and data centers. Memristive devices can be utilized for photodetection and neuromorphic computer applications, whereas electrically tunable devices are currently being explored for LIDAR and car vision applications.

Furthermore, due to an unprecedented time gradient of the optically induced refractive index change, TCO can be seen as a time-varying material and find use for a large plethora of experiments within the domain of “photon acceleration.” With this, more exciting applications might be within reach, such as photonic time crystals. NZI materials, and by extension TCOs, also have many emerging applications in the realm of quantum optics, such as two-plasmon spontaneous emission, long-range superradiance, and an unprecedented control over the decay dynamics of quantum emitters to name a few.

In order to put TCOs’ massive nonlinearities into perspective, we referred to a typical FoM for nonlinear optic applications. Along this line, it was shown that TCOs are the best nonlinear platform for flat optical devices and for any other nonlinear process where extremely short propagation distances are required. From the reported material comparison, TCOs can be to nonlinear flat devices what SiN is for nonlinear integrated photonic components with centimeter-long propagation distances. All together TCOs’ unique properties, coupled with their history of industrial use, stand to set a new paradigm in integrated photonics.

Funding

Office of Naval Research (N00014-20-1-2199); U.S. Department of Energy (DE-SC0017717); Engineering and Physical Sciences Research Council (EP/P005446/1); Carnegie Trust for the Universities of Scotland (RIG009891); Royal Society of Edinburgh.

Acknowledgment

The authors would like to thank Dr. N. Kinsey and Dr. M. Clerici for very useful discussions.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data analyzed in this paper may be obtained from the authors upon reasonable request.

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Wallace Jaffray attained his master’s degree in physics with first-class honours at Heriot-Watt University in 2020. He was the recipient of The Neil Forbes/Scottish Enterprise Prize for his work on soliton dynamics in hollow-core fibers. In 2021, he began his doctoral studies at the Institute of Photonics and Quantum Sciences of Heriot-Watt University. Here, within the context of the Advanced Structured Nanophotonics (ASN) Lab, he has been focused on novel nonlinear applications for NZI TCOs and ultrafast optics. The same year, he was awarded the AFOSR International Student Exchange grant by the U.S. Air Force Office of Scientific Research, which he used at Purdue University to develop novel material models for electromagnetic FDTD simulations with a distinct focus on zero-index nonlinearities. Despite his very young age, he has already co-authored several publications and invited contributions at international conferences and topical meetings. His recent publication pertaining to visible photon generation via FWM in NZI thin films was among the top downloaded at the end of 2021.

Soham Saha is a postdoctoral research scholar in the School of Electrical and Computer Engineering at Purdue University. His research focuses on the development of optical materials for active nanophotonics, nonlinear optics, all-optical switching, waveguides, and modulators. He is the recipient of several notable awards, including the Society of Vacuum Coaters Scholarship, the SPIE (the International Society for Optics and Photonics) Education Scholarship, and the outstanding graduate research award at Purdue University.

Vladimir M. Shalaev is Scientific Director for Nanophotonics at Birck Nanotechnology Center and Distinguished Professor of Electrical and Computer Engineering at Purdue University and specializes in nanophotonics, plasmonics, optical metamaterials, and quantum photonics. He has received several awards for his research in the field of nanophotonics and metamaterials, including the APS Frank Isakson Prize for Optical Effects in Solids, the Max Born Award of the Optical Society of America for his pioneering contributions to the field of optical metamaterials, the Willis E. Lamb Award for Laser Science and Quantum Optics, the IEEE Photonics Society William Streifer Scientific Achievement Award, the Rolf Landauer medal of the ETOPIM (Electrical, Transport and Optical Properties of Inhomogeneous Media) International Association, the UNESCO Medal for the development of nanosciences and nanotechnologies, and the OSA and SPIE Goodman Book Writing Award. He is a Fellow of the IEEE, APS, SPIE, MRS, and OSA.

Alexandra Boltasseva is a Ron and Dotty Garvin Tonjes Professor of Electrical and Computer Engineering with courtesy appointment in Materials Engineering at Purdue University. She received her PhD in electrical engineering at Technical University of Denmark (DTU) in 2004. She specializes in nanophotonics, quantum photonics, nanofabrication, and optical materials. She is a 2018 Blavatnik National Award for Young Scientists Finalist and received the 2013 Institute for Electrical and Electronics Engineers (IEEE) Photonics Society Young Investigator Award, the 2013 Materials Research Society (MRS) Outstanding Young Investigator Award, the 2011 MIT Technology Review Top Young Innovator (TR35), the 2009 Young Researcher Award in Advanced Optical Technologies from the University of Erlangen-Nuremberg, Germany, and the Young Elite-Researcher Award from the Danish Council for Independent Research (2008). She is a Fellow of the National Academy of Inventors (NAI) (2020), MRS (2021), IEEE (2020), Optica [formerly the Optical Society of America (OSA)] (2017), and International Society for Optical Engineers (SPIE) (2015). She served on the MRS Board of Directors (2014–2016) and is past Editor-in-Chief for Optical Materials Express, Optica Publishing Group (2016–2021).

Marcello Ferrera attained his master’s degree in micro-electronic engineering in 2005 from the University of Palermo (Italy). This followed a one-year internship at the Microfabrication Laboratory (LMF) of the École Polytechnique in Montreal (Quebec) working on the growth and characterization of electro-/magneto-optic thin films for applications in integrated photonics. In 2007, he won the international doctoral fellowship offered by Le Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT) that sponsored his doctoral research focused on low-power nonlinear processes in doped silica glass resonators. In this direction, he obtained remarkable results dealing with on-chip broadband light generation, ultrafast data processing, and quantum optics. In 2010, he won three Canadian post-doctoral research fellowships (NSERC, FQRNT, MITACT) and accepted the economic support from the Natural Sciences and Engineering Research Council of Canada to developed silicon-nitride-based high-$Q$ photonic devices at the University of St Andrews (UK). The same year he received the Canada/UK Millennium Research Awards for his contribution in promoting joint research efforts between Canada and UK. In 2011, he was awarded the Director’s Medal by the National Institute of Scientific Research in Quebec, Canada, for his works on ultra-low-power frequency conversion in Hydex micro-cavities. In 2012, he won the Marie-Curie IOF fellowship with the project “ATOMIC” (score 96.6) which was developed at Purdue University (USA). In 2014, he was appointed Assistant Professor at the School of Engineering and Physical Sciences at Heriot-Watt University in the UK, where currently leads the Advanced Structured Nanophotonics Lab. His research efforts are focused on alternative materials for developing novel nanophotonic systems for nonlinear and quantum applications. He is also an Editorial Board Member of Scientific Reports and Member of The Order of Engineers of Palermo, Italy.