1. Introduction

Strong light absorption in lossy materials or artificial microstructures is a fascinating topic in optic physics and has attracted much attention in recent years. Numerous novel phenomena have been observed, e.g., tree-inspired desalination [1], localized plasmon excitations [2,3], structural coloring [4], time-reversed lasing and coherent absorption [5], photothermal energy generation [6], etc. Various optical microstructures, such as nanohole [7], nanoparticles [8], nanodisks [9], gratings [10], perforated metallic films [11] and layered structures composed of two-dimensional (2D) materials [12], were designed. These exciting researches can enhance light-matter interaction and thus promote the development of novel devices such as thermal emitters [13,14], modulators [15,16], detectors [17], concealment [18], sensor [19], etc.

In the strong light-matter coupling regime, absorption is proportional to the strength of the field in the lossy materials and can be enhanced by decreasing the mode volume. Recently, it is shown that light can be effectively absorbed by planar heterostructures by utilizing a surface wave forming at the interface between a metal and a truncated photonic crystal (PhC). This is the so-called Tamm plasmon (TP) absorber [20–22]. Compared with the traditional PhC microcavity or defect, the TP mode gives a smaller mode volume due to its surface wave essence [23,24]. In contrast to conventional plasmonic absorbers, TP absorbers can be achieved directly by normally incident propagating waves for both TE and TM polarizations. However, most of conventional TP absorbers composed of normal materials are angle-dependent. The reason is that the propagating phase within the conventional TP structure will decrease with the increase of incident angle, and then the TP mode will shift toward short wavelengths to maintain the Bragg condition [25,26]. Light matter interactions can be enhanced effectively with subwavelength artificial elements and the metamaterials-based TP mode has been reported [27]. However, this requires excitation in anisotropic configuration and the TP mode exhibits strong angle-dependent. Realizing an angle-insenstive TP absorber becomes a huge challenge.

Very recently, a new candidate for metamaterials, i.e., epsilon-near-zero (ENZ) materials, has attracted much attention due to their distinct optical properties [28–30]. They can enhance the nonlinear refractive index [31–33], squeeze the light in a subwavelength scale [34–36] and realize unconventional microcavities [37–39]. Moreover, a class of unique absorption resonances attributed to the excitation of angle-insensitive radiative modes have been observed in anisotropic ENZ materials using subwavelength metal/dielectric multilayers [40]. Similar absorption resonances can also be observed using plasmon-polaritonic or phonon-polaritonic thin-films in the frequency range where the dielectric constant approaches zero, which called the Ferrell-Berreman modes [41,42]. It is worth noting that the Ferrell-Berreman mode has the surface wave-like characteristics [43], which is beneficial to the high localized TP mode. In this paper, angle-insensitive absorption in TP absorber combined with lossy isotropic ENZ materials are investigated. Unlike those hiring anisotropic ENZ materials, we emphasize on the tuning mechanism of the anti-Snell’s law refraction in lossy isotropic ENZ materials, as well as its influence on the absorption and electromagnetic (EM) localization of TP absorber. By well adjusting the reflection phase dispersion of these two structures, ENZ layer and truncated PhC, TP absorber exhibits the abilities of strong EM localization and enhanced angle-insensitive absorption. From the absorption spectra we find that the proposed TP absorbers possesses non-reciprocal effects. Theoretical calculations based on the transfer matrix method agrees well with the experimental results.

2. Experimental evidence of angle-insensitive absorption in a heterostructure containing lossy isotropic ENZ materials

As a type of plasmonic materials, the transparent conducting oxides may be seen as substantial and homogenous ENZ materials near their plasma frequencies [44,45]. In this work the heavily doped semiconductor indium-tin-oxide (ITO) near the plasma frequency is seen as the ENZ material. Figure 1(a) shows the scheme of a heterostructure formed by a truncated all-dielectric PhC and an ITO layer. Here, the positive and negative incident angles ±θ correspond to plane waves incident from the + z direction (glass side) and -z direction (air side), respectively. In the experiment, the heterostructure sample is fabricated by ion beam sputtering on a glass substrate and its scanning electron microscopy (SEM) image is shown in Fig. 1(b). The ITO layer is 60 nm thick and the optical constants of the individual constituent layers was measured with spectroscopic ellipsometry. The resultant spectral dependence of the real ($\varepsilon {^{\prime}_{\textrm{ITO}}}$) and imaginary ($\varepsilon ^{\prime}{^{\prime}_{\textrm{ITO}}}$) parts of the ITO permittivity are shown in Fig. 1(c). According to the spectroscopic data, the real part of the permittivity of ITO is close to zero ($\varepsilon {^{\prime}_{\textrm{ITO}}}$ ≈ 0.0037) at λ ≈ 1170 nm, which corresponds to an ENZ material. And the ratio of the imaginary part to the real part of the permittivity approach to 100 ($\varepsilon ^{\prime}{^{\prime}_{\textrm{ITO}}}$ ≈ 0.3448) at this wavelength. We note that there is a counterintuitive absorptive peak in the absorption spectra of single ITO film for TM-polarized waves obliquely incident at λ ≈ 1170 nm. The optical loss of the dielectric materials (Nb₂O₅ and SiO₂) used in the experiment can be neglected in the spectral region we are concerned about. However, this abnormal absorption peak for TE polarization will not appear. The physical origin can be attributed to Ferrell-Berreman mode [46].

 

Fig. 1. (a) A plane wave impinges obliquely on a planar heterostructure formed by an all-dielectric PhC and an ITO layer along z direction. The PhC is formed by pairs of SiO₂ and Nb₂O₅ layers with the thicknesses of 215 nm and 150 nm, respectively. The thickness of ITO layer is 60 nm. The number of the pairs is represented by symbol “N” (also referred to as the period of PhC). (b) Scanning electron microscope image of a representative heterostructure used in experiments (N=7). (c) Real and imaginary parts of the dielectric permittivity are shown for an isolated ITO film.

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The absorption spectra of the ENZ-based heterostructures as a function of both the incident angle θ and polarization is shown in Fig. 2. The transmittance (T) and reflectance (R) of the structures can be obtained through experiments and numerical values, respectively. Then, the absorbance can be calculated by using the formula A=1-T-R. The upper and lower band edge position of the structure can be extracted from the reflectance dips in the measured spectra. Usually, for all-dielectric one-dimensional photonic crystals (1D PhCs), photonic gaps will shift toward short wavelengths (blueshift) as the incident angle increases for both transverse magnetic (TM) and transverse electric (TE) polarizations as shown in Figs. 2(b)–2(f). For TE-polarization, the absorption is enhanced around the band edge of the PhC and independent of incidence angle as shown in Figs. 2(a)–2(c). In part (a) we show the experimental TE-polarized absorption maps as a function of both wavelength and incident angle, and in parts (b)-(c) we show the comparison between theoretical and experimental spectra at two different incident angles, ±10° and ±40°. This behavior dramatically changes when the polarization of the incident wave was switched into TM-polarization. It is then possible to induce extreme large nonreciprocal absorption around the ENZ position as shown in Figs. 2(d)–2(f) for TM-polarization. And benefit from the ENZ effect, although the absorption intensity of different angles will be slightly different, this nonreciprocal absorption always exists. In part (f) we show experimental and theoretical lines, which illustrate particularly large nonreciprocal absorption at high incidence angle of θ = ±40°. For instance, at λ ≈ 1170 nm the absorption goes from being very small at θ = −40° to nearly perfect at θ = +40°.

 

Fig. 2. Absorption in heterostructure for different polarizations of the incident radiation with respect to the x-z surface given by (a)-(c) TE-polarization, and (d)-(f) TM-polarization. The panels to the left show experimental absorption maps as a function of both the incident angle θ and wavelength of the incident radiation. The panels to the right show a comparison between experimental (solid lines) and simulated (dashed lines) spectra for θ = ±10° and θ = ±40°, highlighting the polarization-dependent ENZ position. The positions of the upper and lower band edge of heterostructure are marked for comparison to ENZ point, respectively. For the measured spectra, since the incident radiation from the + z direction is refracted by the 0.5 mm glass substrate, the experimental lines (solid) excited have an estimated 3° error.

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The enhanced nonreciprocal absorption of TP around the ENZ position can be better understood by taking a closer look at their behavior at individual wavelengths. In Figs. 3(a) and 3(b), we show the absorption of the band edge modes and TP state as a function of the angle for TE and TM polarizations. As known, for lossy case, the Bragg scattering of the photonic crystal renders high reflection which results in the nonreciprocal absorption. Thus, we see that nonreciprocal TE-polarized absorptive peaks of the band edge modes can occur at different incident angles. But this nonreciprocal effect for TE-polarized wave is so mild that the maximum difference in absorbance between the opposite incident directions is only 20%. On the other hand, the calculated TM-polarized absorption line shows that while small absorption is observed at high negative angles, near perfect absorption is achieved by TP state at their positive counterparts. And the maximum absorption difference is about 86%. Usually, the pure Ferrell-Berreman absorption peak can be attributed to the excitation of leaky modes which lie within the light cone. For individual lossy ENZ thin film, the Ferrell-Berreman mode does not support engineering of nearly perfect absorption due to the nature of radiative mode [47]. Different from the pure Ferrell−Berreman mode, the excellent improvement of ENZ material absorption can be achieved based on TP enhanced Ferrell−Berreman mode. Because the one-dimensional photonic crystal (1D PhC) acts as Bragg reflector which further enhances the electric filed in the ENZ layer [48]. We also note that, as shown in Fig. 3(b), the TM-polarized absorptive peak of the upper band edge for the positive direction was covered by the strong absorption of the TP state nearby.

 

Fig. 3. Absorption corresponding to the TP state (dotted line), the upper (solid lines) and the lower (dashed lines) band edge of the heterostructure (N=7) versus incident angle for (a) TE- and (b) TM-polarizations.

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These ENZ-assisted TP states differ from the well-known band edge modes supported by PhC. For band edge modes, energy mainly locates in the lossless dielectric layers. Whereas for ENZ-assisted TP states, energy mainly locates in the ITO layer due to the interfacial properties of TP state. To further probe this, we now discuss the ENZ-based heterostructure with reduced period of PhC (N=2), and TP-enhanced absorption supported by this sample that show slight differences from the more layers case. The SEM image of the sample is shown in Fig. 4(a). From the Fig. 3(b), it can clearly be seen that although this sample (N=2), like the case of N=7, provides a drastic enhancement for TM-polarized light absorption near the ENZ wavelength at positive incident angle, obvious absorption peaks can still be observed for negative incident angles. In fact, for smaller number of the PhC periods, a lower absorption intensity and weaker nonreciprocity can be predicted (and experimentally observed as shown in Fig. 3), despite the ITO layer used in these heterostructure samples is the same. For θ = ±10°, the difference between the absorption of the forward and backward incidence is only 5% around the ENZ point as shown in Fig. 4(c), while for θ = ±40° the difference is increased to 40% as seen in Fig. 4(d) — both are still far from the case of N = 7 under the same conditions.

 

Fig. 4. (a) Scanning electron microscope image of the heterostructure used in experiments (N=2). (b) The experimental absorption maps for the heterostructure (N=2) as a function of both the incident angle θ and wavelength of the incident radiation. The comparison between experimental (solid lines) and theoretical (dashed lines) spectra is also given for (c) θ = ±10° and (d) θ = ±40°, highlighting the polarization-dependent ENZ position.

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3. Theoretical analysis of tunneling condition: ENZ material embedded Tamm plasmons

The phenomenon observed above can be well explained by the tunable reflection phase dispersion of the PhC that modifies further the tunneling conditions in these heterostructures. The tunneling condition in an ENZ-PhC heterostructure can be described as [27]

 

Fig. 5. Imaginary parts of the effective phase shifts (the solid line) and impedances (the segmented line) of the isolated ENZ slab and PhC given by (a) and (b) θ = +40°, and (c) and (d) θ = −40°. The matched point is around 1170 nm.

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In order to confirm our scheme, we have performed numerical simulations based on the finite difference time difference technique [53] for the wave refraction in the ENZ-PhC heterostructure with N=7. At λ=1170 nm, only forward wave is effectively absorbed by the ENZ slab as shown in Fig. 6(a). By comparison, the impedance mismatching between ENZ slab and the truncated PhC for the backward wave at λ = 1170 nm leads to strong beam reflecting [Fig. 6(b)]. More detailed information can be obtained from the z-dependent field distribution for different incident direction. In Fig. 6(c), we can see that the electric field of the tunneling mode is the strongest at the interface between the ITO layer and the PhC for θ = +40°. For the TM-polarized light, the boundary conditions require that the z component of the electric displacement field, i.e., Dz = ɛEz is continuous at the interface. In results, at the zero point of permittivity of ITO, the z component of the electric field in ITO layer is enhanced greatly. Usually, for lossless ENZ materials, the fields are homogenous and maintain a constant at any place of the ENZ layer. But for real ENZ materials such as ITO, the enhanced uniform field can boost the absorptive effect noticeably, so that the field in the ENZ layer will also be attenuated, as shown in Fig. 6(c). On the other hand, the distribution of field is now highly nonreciprocal, as strong localized field is being realized in the ITO layer at high positive incident angle (θ = +40°), but very low field in the ITO layer is seen for their negative counterparts (θ = −40°) as shown in Fig. 6(d). This is because, for the ENZ-PhC heterostructure, the normal electric field of the backward wave decay away from the incident interface due to the Bragg reflection, thereby suppressing the penetration of the light into the ENZ layer.

 

Fig. 6. Distribution of the power flow in the heterostructure (N=7) illuminated by a p-polarized Gaussian beam with the incident angle of 40° from the glass side (a) and the air side (b) at the wavelength of 1146 nm. (c) and (d) are the field distributions of tunneling mode corresponding to the θ = +40° and θ = −40°, respectively. The parameters of the structure are the same as those in Fig. 1(b).

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4. Conclusions

In summary, we have used the example of ENZ-filled systems to experimentally and theoretically demonstrate that angle-insensitive nonreciprocal absorption can be achieved in simple one-dimensional ITO-PhC heterostructure due to nonreciprocal optical Tamm state. This can be achieved by controlling the direction of the incident wave, in doing so, the absorption can reach maximal value for waves incident from the ITO layer while being minimal for waves incident in the opposite direction. Moreover, when the tunneling conditions are matched, the nearly perfect absorber can be realizing at high incident angle. The phenomenon can be understood as the combination of the confinement along the propagating direction provided by Tamm state and the localization originated from the boundary condition across the ENZ interface. In future work, it will be interesting to explore schemes for nonreciprocal nonlinear photonic devices. For example, recent work has demonstrated all-optical diode using the structures with strongly nonreciprocal electric field distributions. Moreover, the designs presented here are one-dimensional, consisting of only multilayers and free from nanopatterning, offering a practical opportunity in applications such as gas sensing, narrowband IR sources, and thermophotovoltaics.