1. Introduction

Metamaterials refer to artificial structures, which are composed of natural materials, and they have exotic properties that natural materials do not have, such as negative refraction [1], ultra-high refractive index [2], and subwavelength imaging in the near- [3–5] and the far-field [6–8]. Ideally, a perfect lens for the subwavelength imaging is made from negative-index materials (NIMs) [9], overcoming the diffraction limit. Such NIMs have both negative dielectric permittivity and magnetic permeability, which are highly challenging yet at high frequencies. Fortunately, NIMs are not necessary for near-field subwavelength imaging thanks to the decoupling of the two types of linearly polarized light, TM (transverse magnetic) and TE (transverse electric) incident waves, in the near-field zone. Instead, regardless of magnetic permeability, the materials with negative dielectric permittivity can be used for near-field superlensing [3]. As experimentally demonstrated in the literature, a silver superlens was developed for the sub-diffraction-limited imaging with a resolution of better than λ/5 at a wavelength of 365 nm [4,5]. Besides the optical superlens, the mid-infrared (MIR) superlenses were extensively investigated, which could be made from SiC, perovskite oxides, GaAs, Si₃N₄, and graphene slabs [10–16]. At the superlensing frequencies, these negative-permittivity materials support highly confined surface plasmon polaritons (SPPs) such that the evanescent waves can be enhanced and recovered at the image plane [3,4]. It can be achieved by either resonant or non-resonant enhancement of SPPs: the former is fulfilled via $-{\epsilon }_m={\epsilon }_d$, where ${\epsilon }_m$ and ${\epsilon }_d$ are the permittivities of negative-permittivity materials and surrounding dielectric media, respectively, and the latter depends on the excitation of SPPs at ultra-small plasmon wavelengths ${\lambda }_p$, as demonstrated in graphene [15, 16].

Besides the negative permittivity, the resistive loss and retardation effects should be taken into account [17], which govern the resolution limit. Therefore, a low-loss negative-permittivity slab with small thickness is preferable to both resonant and non-resonant superlenses. Concerning the near-field superlenses working at near-infrared (NIR) frequencies, the noble metals, gold and silver, have significant imaginary permittivity, as compared with them at visible frequencies, which definitely limits the imaging resolution. Apart from the conventional noble metals, the most materials for MIR superlenses could not work at NIR frequencies due to the positive permittivity. Although the permittivity of graphene is negative at NIR, it is finite and cannot enhance the evanescent waves considerably. Thus far the development of near-field superlenses working at NIR frequencies still faces the challenges. Boltasseva et al. [18–20] pointed out that transparent conducting oxides (TCOs) have metal-like optical properties in the NIR range. Indeed, TCOs, as alternative plasmonic materials, have exhibited great potential in near-perfect absorbers [21–23], negative refraction [24], nonlinear optics [25], etc. other than subwavelength imaging. It is hopeful that the implementation of TCOs achieves a low resistive loss and negligible retardation effect as well as the excitation of SPPs.

In this work, we investigated the roles of Al:ZnO (AZO, Al-doped ZnO), one of TCOs, in NIR subwavelength imaging in the near-field. Based on the calculations of the optical transfer function (OTF), the propagation of evanescent waves was studied. It was found that AZO could effectively enhance the evanescent waves in both sandwiched ZnO-AZO-ZnO and single-layered AZO structures. The investigation on the near-field electromagnetic field distribution further confirmed that the subwavelength imaging could be achieved at the wavelengths around 2 $\mu m$. These findings exhibit the overwhelming advantages of TCOs in NIR subwavelength and subsurface imaging [26], and pave the way for engineering tunable TCOs-based superlens.

2. Structures and simulations

Two types of near-field superlens structures were studied: the stratified ZnO-AZO-ZnO and single-layered AZO. The former, as shown in Fig. 1(a), is a conventional sandwich structure, where undoped ZnO is selected as a surrounding dielectric medium considering the convenient fulfillment of $-{\epsilon }_m={\epsilon }_d$; the latter, as shown in Fig. 1(b), is an AZO single layer, surrounded by air. The permittivity of AZO is described by the Drude model [18], where the plasmon ${\omega }_p$ and the collision frequencies $\Gamma$ are determined by the carrier concentration n, the mobility $\mu$, and the effective optical mass of conduction electrons m* [27].

 

Fig. 1 Schematic illustration of two types of superlenses: (a) the ZnO-AZO-ZnO stratified superlens and (b) the single-layered AZO superlens. The gold double slits with various widths (w = 50 and 100 nm) and a fixed thickness of h = 10 nm were considered.

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OTF is the transmittance |T|² through the stratified layers as a function of frequency and transverse wave vector $k_{\text{x}}$ [15]. To evaluate the propagation of evanescent waves, the OTF was calculated using a transfer matrix method [28,29]. The characteristic matrix of the j-th homogeneous layer is written as

According to the calculations of the OTF at the possible superlensing wavelengths, the corresponding imaging performance of the two types of superlenses was simulated using commercial software COMSOL based on the finite element method. As shown in Fig. 1(a) and 1(b), the gold double slits with various widths (e.g., w = 50 and 100 nm) and a fixed thickness of h were taken as objects for the superlens imaging, where only TM-polarized incident waves were considered for the excitation of SPPs. To rule out the effects of localized SPPs at the edges of the gold slits, the edges were rounded off [31]. The image plane was located at the bottom of the superlenses, d/2 away from the AZO layer. The simulations were carried out in two dimensions. The simulation domains were surrounded by the perfectly matched layer and assigned to the scattering boundary condition for mimicking the open boundary conditions [11].

3. Results and discussion

Given a carrier mobility of $\mu =30c{m}^2{\text{V}}^{-1}{s}^{-1}$ and a free carrier concentration of n = $3.81\times {10}^{20} c{m}^{-3}$, the permittivity of AZO was plotted in Fig. 2(a), together with that of ZnO calculated through Cauchy model [32, 33], which had a finite imaginary part, as shown in Fig. 2(b). For a wavelength of 2.57 $\mu m$, the permittivity values of AZO and ZnO are ${\epsilon }_{\text{AZO}}=-3.62+1.87i$ and ${\epsilon }_{\text{AZO}}=3.61$, respectively, which have the approximate absolute values with opposite signs and allow for establishing a sandwich superlens. The single-layered AZO superlens is considered at a wavelength of 2.01 $\mu m$, since here the permittivity of AZO is ${\epsilon }_{\text{AZO}}=-1+0.92i$ and has the approximate absolute value with that of surrounding medium, air. It was noted that the imaginary permittivity of AZO around 0.92~1.87 at the NIR wavelengths was comparable with that of silver in the visible wavelength, e.g., ~0.599 at a wavelength of 365 nm [34], which could guarantee the NIR subwavelength imaging of the TCO-based near-field superlenses.

 

Fig. 2 (a) Calculated real and imaginary parts of the permittivity of AZO and (b) real part of the permittivity of ZnO. (c) OTF of AZO without surrounding media as a function of the thickness d and the transverse wave vector $k_{\text{x}}$ at a wavelength of 2.57 $\text{μm}$. (d) OTF for two types of superlens structures at the resonant wavelengths, together with that in free space.

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To investigate the enhancement effects of evanescent waves in AZO with various thicknesses, the OTF was calculated without consideration of surrounding media for simplicity. The transmission coefficient T was higher than 0.57 at the relatively large transverse wave vector$k_{\text{x}}=10k_0$ when the thickness of AZO was less than 50 nm, as shown in Fig. 2(c). Thus the thickness of AZO in both the sandwich and the single-layered superlenses was fixed to d = 50 nm in both superlenses considering the enhancement of evanescent waves and the satisfactory optoelectrical properties. Accordingly, the thickness of undoped ZnO in the stratified structure was d/2, i.e., 25 nm. The OTF of both superlenses were plotted in Fig. 2(d). The evanescent wave propagation in free space was also shown for comparison. In free space, the evanescent waves ($k_{\text{x}}> k_0$,$k_0$ is the wavenumber in free space) decay exponentially [35]. The transmission coefficient at$k_{\text{x}}> k_0=10$ is T = 0.09 in free space at $\lambda =2.57 \text{μm}$, whereas it is increased to T = 0.45 at the same wavelength through the ZnO-AZO-ZnO superlens. Similarly, the transmission coefficient is increased to T = 0.24 at $\lambda =2.01 \text{μm}$ through the single-layered AZO superlens. It was found that both superlenses revealed the prominent enhancement of evanescent waves at the different wavelengths.

To illustrate the resolution capabilities of two types of superlenses intuitively, the effects of them on the imaging of gold double-slits were investigated. The amplitude distribution of x-component of electric field from object to image planes was calculated. As shown in Fig. 3(a), the electric fields through the double slits with a width of w = 100 nm are effectively transferred by the sandwich ZnO-AZO-ZnO superlens without obvious blur. For a smaller slit width of w = 50 nm, although the electric fields through the slits do not show a prominent reduction in amplitude, they are not well separated as shown in Fig. 3(b). From the line profile of energy density at the image plane in Fig. 3(c), the image contrast was calculated through $V=(I_{max}-I_{min})/(I_{max}+I_{min})$ [4]. In the case of the double slits width w = 100 nm, the value of $V$ was unity, suggesting that two distinct peaks could be clearly resolved, whereas the image contrast $V$ was only 0.23 in the case of w = 50 nm, revealing the impossible subwavelength imaging. According to image contrast, the lens could identify objects with a size around 100 nm, but could not work if the objects were smaller than 50 nm. Similarly, the resolution of the single-layered AZO superlens was studied, as shown in Fig. 3(d)-(f), where the distance between object and image planes was the same as the case of the sandwich ZnO-AZO-ZnO superlens. Figure 3(d) suggests that a clear image can be produced on image plane in the case of w = 100 nm, which is further confirmed through the image contrast $V=1$, as shown in Fig. 3(f). In the case of w = 50 nm, the electric fields through double slits merged at the image plane, as shown in Fig. 3(e). Correspondingly, the image contrast $V$ was as low as 0.07 in Fig. 3(f). It revealed that the single-layered AZO superlens had a capability for subsurface imaging of the objects with a size around 100 nm. It was found that the proposed ZnO-AZO-ZnO superlens could achieve the subwavelength imaging with a resolution of better than $\lambda /25$at a wavelength of 2.57 $\text{μm}$, and the single-layered AZO superlens had a resolution of better than$\lambda /20$ at a wavelength of 2.01$\text{μm}$.

 

Fig. 3 Amplitude distribution of x-component of electric field of the ZnO-AZO-ZnO stratified superlens imaging for the gold double silts with a width of (a) w = 100 nm and (b) w = 50 nm, and (c) their line profiles of energy density at image planes. In the case of the single-layered AZO superlens, the electric field distribution for (d) w = 100 nm, (e) w = 50 nm, and (f) the corresponding line profiles.

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4. Summary

In summary, we described the AZO-based structures, enabling the evanescent waves to be enhanced at NIR frequencies. Since AZO could easily find the surrounding media fulfilling the resonant condition with a low loss, the superresolution and subsurface imaging can be achieved by the AZO-based structures. The sandwich ZnO-AZO-ZnO superlens had a good subwavelength resolution of better than$\lambda /25$ at a wavelength of 2.57$\text{μm}$; the single-layered AZO superlens could reach a resolution over$\lambda /20$ at a wavelength of 2.01$\text{μm}$. It was revealed that TCO materials could be good candidate for NIR subsurface and subwavelength imaging beyond noble metals. Thanks to the convenient doping of TCO materials and tailoring of the optoelectronic properties, they are promising for further development of active control of superlensing wavelength and resolution.