1. Introduction

The study of light manipulation has a long history and is of great importance in numerous electromagnetic and photonic applications. Recently, with the rise of metamaterials and metasurfaces that go beyond natural materials in many aspects, dynamic control of light becomes feasible by incorporating tunable materials [1–7], including liquid crystals [8–10], phase-change materials (PCMs) [11–17], etc. Up to now, various multifunctional meta-devices that can control light transmission, reflection, absorption and diffraction have been proposed [18–22]. The control of light transmission/absorption is shown in two extreme anomalies: perfect transmission or transparency [23,24] and perfect absorption [25–28]. Realizing dynamic switch between the two opposite anomalies is of particular interest. Very recently, the idea of the perfect transmission-to-absorption switching has been demonstrated in microwaves using metasurfaces incorporating PIN diodes [29–32]. In the infrared region, PCM-assisted metamaterials were proposed for polarization-insensitive functionality [33] and circular polarization [34]. However, due to the resonant nature of meta-structures, the operating bandwidth in these previous works is inherently limited. This would lead to restrictions on practical applications that require broad working bandwidth, such as broadband optical modulator [35] and thermal emission control [36,37].

In this work, we propose a non-resonant tilted anisotropic metamaterial (TAM) exhibiting broadband perfect transmission-to-absorption switching functionality in the infrared region. The dynamically switchable functionality is bestowed by its PCM component, which can switch between different phase states as a function of an external bias like heat [38,39], photon [40,41], or electric energy [42], offering a pronounced change of its dielectric function. We find that when the phase transition of PCM germanium telluride (GeTe) from amorphous phase to crystalline phase occurs, the functionality of the TAM can be switched from perfect transparency to perfect absorption over a broad spectrum. This rare effect is bestowed by the occurrence of anomalous Brewster effect, which establishes ultrabroadband impedance matching between free space and anisotropic absorptive materials, thus enabling reflectionless manipulation of light in an unprecedented wide spectrum [43,44]. Based on this principle, gradient TAMs exhibiting broadband perfect transmission-to-absorption switching functionality for incident light with almost arbitrary wavefront are further demonstrated. Compared with the previously reported schemes on transparency-to-absorption switching [29–34], our proposed TAMs are simple but of a clear advantage of broad operating bandwidth. Compared with the seminal works on anomalous Brewster effect [43,44], this work demonstrates a highly efficient approach to realize dynamic switching between two opposite anomalies, i.e. perfect transparency and perfect absorption, based on the anomalous Brewster effect, which may find applications in sensing, advanced and intelligent optical devices.

2. Dynamically controllable TAM and anomalous Brewster effect for reflectionless manipulation of light

The schematic graph of the proposed dynamically controllable TAM is shown in Fig. 1(a). It is composed of a periodic array of tilted ultrathin PCM GeTe films (relative permittivity ${\varepsilon _{\textrm{GeTe}}}$, tilt angle $\alpha $, thickness t along the normal direction of GeTe films) aligned along the y direction embedded in a dielectric host (relative permittivity ${\varepsilon _\textrm{d}}$, thickness $d$). The separation distance between two adjacent GeTe films is a along the y direction, which is much larger than t (i.e. $a \gg t$), but much smaller than free-space wavelength ${\lambda _0}$ (i.e. $a \ll {\lambda _0}$).

 

Fig. 1. (a) Schematic drawing of a dynamically controllable TAM consisting of a subwavelength tilted PCM film array embedded in a dielectric host, whose functionality can be switched from perfect transparency (upper) to perfect absorption (lower) under external bias. (b) Left panel: perfect transparency due to the traditional Brewster effect under ${\theta _i} = {\theta _\textrm{B}}$. Right panel: perfect transparency in amorphous phase (upper) and perfect absorption in crystalline phase (lower) due to the anomalous Brewster effect under ${\theta _i} = {\theta _{\textrm{AB}}} ={-} {\theta _\textrm{B}}$. (c) Real and (d) imaginary parts of the relative permittivity ${\varepsilon _{\textrm{GeTe}}}$ of PCM GeTe in amorphous (blue lines) and crystalline (red lines) phases.

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The GeTe is an especially promising PCM as it possesses the ability of rapidly switching between different phases in a reversible way. The phase transition can be achieved optically or through Joule heating and is proven to be reliable, fast, and repeatable. For instance, by using laser irradiation, the change in optical properties on the phase transition can be realized on the nanosecond timescale (<100 ns) [45]. We note that both crystalline and amorphous phases of GeTe are stable at room temperature, resulting in zero static power consumption [4,46]. Figures 1(c) and 1(d) show, respectively, the real and imaginary parts of its relative permittivity ${\varepsilon _{\textrm{GeTe}}}$ in amorphous (blue lines) and crystalline (red lines) phases, which are taken from [4]. We see that the loss coefficient of GeTe is negligibly small in amorphous phase over the spectrum of 3-11$\mathrm{\mu }\textrm{m}$, as the amorphous GeTe possesses a “window of low losses” in the mid-infrared frequency range [4,47]. While the loss coefficient is quite large in crystalline state. This unique property provides us a route to dynamically switch the functionality of the TAM from perfect transparency (upper panel) to perfect absorption (lower panel) over a broad spectrum, as illustrated in Fig. 1(a).

Here, we study the TAM from the perspective of effective medium model. Since the TAM satisfies $a \ll {\lambda _0}$, it can be approximately homogenized as an effective anisotropic medium with ${\varepsilon _ \bot } = \frac{{a{\varepsilon _{\textrm{GeTe}}}{\varepsilon _\textrm{d}}\textrm{cos}\alpha }}{{({a\; \textrm{cos}\alpha - t} ){\varepsilon _{\textrm{GeTe}}} + t{\varepsilon _\textrm{d}}}}$ and ${\varepsilon _\parallel } = {\varepsilon _\textrm{d}} + \frac{{{\varepsilon _{\textrm{GeTe}}} - {\varepsilon _\textrm{d}}}}{{a\; \textrm{cos}\alpha }}t$ [48,49], which are, respectively, the effective permittivities normal and parallel to the GeTe films, as illustrated in Fig. 1(b). Considering the limit of $a \gg t$, the ${\varepsilon _ \bot }$ can be simplified to ${\varepsilon _ \bot } \approx {\varepsilon _\textrm{d}}$.

Now, we assume a transverse-magnetic (TM, magnetic field along the x direction) polarized wave incident from dielectric background (relative permittivity ${\varepsilon _\textrm{b}}$) onto the TAM. The magnetic fields of the incident and reflected waves can be expressed as

The magnetic field of transmitted wave in the TAM can be expressed as

Considering the continuity boundary conditions of tangential electric and magnetic fields at the air-TAM interface, the reflection coefficient r can be derived as,

By substituting the permittivity tensor (Eq. (6)) and dispersion relations (Eqs. (3) and (5)) into Eq. (7), the zero-reflection condition (i.e., $r = 0$) can be derived as,

Here, we are more interested in a unique solution of Eq. (8) that is ${\varepsilon _\parallel }$-independent. This requires that the first derivative of the left term in Eq. (8) versus ${\varepsilon _\parallel }$ is zero, thus we have ${\varepsilon _\textrm{d}}{\cos ^2}{\theta _i} = {\varepsilon _\textrm{b}}{\cos ^2}\alpha $. Substituting this condition into Eq. (8) yields,

Equation (9) is the condition of ${\varepsilon _\parallel }$-independent zero reflection. We note that the ${\varepsilon _\parallel }$-independence is equivalent to the ${\varepsilon _{\textrm{GeTe}}}$-independence as ${\varepsilon _ \bot }$ is irrespective of ${\varepsilon _{\textrm{GeTe}}}$. Therefore, when the condition of Eq. (9) is fulfilled, we will always have zero reflection, irrespective of the phase states of GeTe. This endows the TAM with a remarkable ability of reflectionless manipulation of light through switching the phase states of GeTe.

When ${\varepsilon _\textrm{b}} \ne {\varepsilon _\textrm{d}}$, the solution of Eq. (9) is

One may notice that the required incident angle by Eq. (10) is the Brewster’s angle ${\theta _\textrm{B}}$ [50] at the interface of background dielectric and TAM in the absence of GeTe films. Figure 1(b) presents a geometrical interpretation of this result. First, we assume a TAM without GeTe films. Reflection disappears under the Brewster’s angle ${\theta _\textrm{B}} = \arctan \sqrt {{\varepsilon _\textrm{d}}/{\varepsilon _\textrm{b}}} $, and the refracted light is normal to the direction of specular reflection [50]. Thus, the angle of refraction is found to be $\pi /2 - {\theta _\textrm{B}}$. Then, we insert ultrathin GeTe films parallel to the direction of refracted light (i.e. $\alpha = \pi /2 - {\theta _\textrm{B}}$) in the dielectric host, such that the electric field $\textbf{E}$ of refracted light is perpendicular to the GeTe films. Interestingly, in this case, the Brewster effect won’t be destroyed as the refracted light cannot “see” such ultrathin GeTe films [51], and therefore the zero reflection preserves irrespective of the presence of GeTe films, as illustrated in the left panel of Fig. 1(b).

It becomes interesting when the reciprocity principle [52] is applied when flipping the incident angle from ${\theta _\textrm{B}}$ to $- {\theta _\textrm{B}}$ (right panel of Fig. 1(b)). According to the reciprocity principle, the reflection coefficients are exactly the same under incident angles of ${\pm} {\theta _i}$ for reciprocal media, i.e., $r({{\theta_i}} )= r({ - {\theta_i}} )$ [52]. Therefore, the zero reflection remains unchanged irrespective of the existence of GeTe films. However, different from the situation under the incident angle of ${\theta _\textrm{B}}$, the refracted light under $- {\theta _\textrm{B}}$ is no longer normal to the direction of specular reflection, and would be affected by the GeTe films as its electric field is no longer perpendicular to the GeTe films. In this sense, we denote the angle $- {\theta _\textrm{B}}$ as anomalous Brewster’s angle ${\theta _{\textrm{AB}}} \equiv{-} {\theta _\textrm{B}}$, and the reflectionless phenomenon as anomalous Brewster effect [43,44], which endows the TAM with an extraordinary ability of reflectionless manipulation of light, including tunable refraction and absorption. Through switching the GeTe from amorphous phase to crystalline phase, the functionality of the TAM can be switched from perfect transparency to perfect absorption for TM-polarized light under ${\theta _i} = {\theta _{\textrm{AB}}}$.

It is noteworthy that the operating bandwidth in principle can cover an ultra-broad spectrum, far beyond those techniques based on resonant meta-structures [29–34]. From Eq. (10), we see that the anomalous Brewster’s angle and the zero-reflection behavior are solely determined by the permittivities ${\varepsilon _\textrm{b}}$ and ${\varepsilon _\textrm{d}}$. When utilizing dielectric materials possessing low dissipation loss and low chromatic dispersion, such as silica (SiO₂) and silicon (Si) in the infrared region, perfect transmission-to-absorption switching can be realized over a broad spectrum.

3. Numerical proof of broadband perfect transmission-to-absorption switching

Figure 2 shows direct numerical proof of the above theory. Here we choose air as the background (${\varepsilon _\textrm{b}} = 1$), and SiO₂ as the host of TAM. The geometrical parameters of the TAM are set as $d = 5\mathrm{\mu }\textrm{m}$, $a = 500\textrm{nm}$ and $t = 50\textrm{nm}$. Dispersive permittivity of SiO₂ is considered in the calculation of reflection, transmission and absorption in the following, which is taken from [53]. We shall note that the tilt angle of GeTe films would vary with working wavelength according to Eq. (10). However, we notice that the chromatic dispersion of SiO₂ is relatively low in the wavelength range of 3-7$\mathrm{\mu }\textrm{m}$. Therefore, we approximately choose the averaged relative permittivity (∼1.796) in this wavelength range to obtain a fixed tilt angle, i.e. $\alpha = 36.73^\circ $. Then, the traditional (or anomalous) Brewster’s angle is ${\theta _\textrm{B}} = 53.27^\circ $ (or ${\theta _{\textrm{AB}}} ={-} 53.27^\circ $).

 

Fig. 2. (a) Simulated ${H_x}/{H_0}$-distributions in the TAM with GeTe in amorphous phase when TM-polarized light of ${\lambda _0} = 7\mathrm{\mu }\textrm{m}$ is incident from air under ${\theta _i} = {\theta _\textrm{B}} = 53.27^\circ $ (left) and ${\theta _i} = {\theta _{\textrm{AB}}} ={-} 53.27^\circ $ (right). The TAM consists of tilted GeTe films ($a = 500\textrm{nm}$, $t = 50\textrm{nm}$, $\alpha = 36.73^\circ $) in a SiO₂ host with a thickness of $d = 5\mathrm{\mu }\textrm{m}$. (b) Reflectance R, transmittance T and absorptance A as the function of incident angle at ${\lambda _0} = 7\mathrm{\mu }\textrm{m}$. The solid lines and dots denote, respectively, the theoretical results of the effective medium model and numerical results of the actual TAM. (c) Reflectance R and (d) transmittance T of the actual TAM as functions of the incident angle and working wavelength. The areas bounded by the black dashed lines denote the regions with $R \le 0.1$ in (c) and $T \ge 0.9$ in (d). The white dashed lines denote the Brewster’s angle ${\theta _\textrm{B}} = 53.27^\circ $ and anomalous Brewster’s angle ${\theta _{\textrm{AB}}} ={-} 53.27^\circ $.

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We first consider the TAM with GeTe in amorphous phase. Figure 2(a) shows simulated normalized magnetic-field ${H_x}/{H_0}$ distributions under the illumination of TM-polarized light of ${\lambda _0} = 7\mathrm{\mu }\textrm{m}$ with ${\theta _i} = {\theta _\textrm{B}}$ (left) and ${\theta _i} = {\theta _{\textrm{AB}}}$ (right). ${H_x}$ is the $x$-component of magnetic field. The simulation is performed using the software COMSOL Multiphysics. Periodic boundary conditions are set on the left and right boundaries. A port is set on the upper boundary to generate TM-polarized plane waves under oblique incidence of ${\theta _i}$, and another port is set on the lower boundary to evaluate and absorb the transmitted waves. In Fig. 2(a), perfectly reflectionless transmission is observed. We note that when considering an imaginary part of ${\varepsilon _{\textrm{GeTe}}}$ of 0.05, the transmittance is still as high as 0.99. For further verification, the reflectance R, transmittance T and absorptance A as the function of the incident angle ${\theta _i}$ are plotted in Fig. 2(b). The solid lines and dots denote, respectively, the theoretical results of the effective medium model using transfer matrix method [54] and numerical results of the actual TAM using the software COMSOL Multiphysics, showing very good coincidence. From Fig. 2(b), we clearly see total transmission under ${\theta _i} = {\theta _\textrm{B}}$ and ${\theta _i} = {\theta _{\textrm{AB}}}$. Moreover, we calculate the R and T of the actual TAM with respect to the working wavelength ${\lambda _0}$, as plotted in Figs. 2(b) and 2(c), respectively. Zero reflection and complete transmission under ${\theta _\textrm{B}}$ and ${\theta _{\textrm{AB}}}$ are observed over the spectrum of 3-7$\mathrm{\mu }\textrm{m}$, demonstrating the broadband perfect transparency of the TAM with GeTe in amorphous phase for incident light under ${\theta _\textrm{B}}$ and ${\theta _{\textrm{AB}}}$.

Then, we consider the crystalline phase of GeTe, in which case the GeTe is a lossy material. The simulated ${H_x}/{H_0}$-distribution in Fig. 3(a) shows an extreme angular asymmetric behavior, that is, perfect transmission under ${\theta _i} = {\theta _\textrm{B}}$ (left), while perfect absorption under ${\theta _i} = {\theta _{\textrm{AB}}}$ due to the anomalous Brewster effect (right) [44]. We note that in the case of ${\theta _i} = {\theta _\textrm{B}}$, the refracted light in the TAM cannot “see” the GeTe films, thus maintaining the perfect transmission. Intriguingly, in the case of ${\theta _i} = {\theta _{\textrm{AB}}}$, the electric field of the refracted light is no long perpendicular to the GeTe films. In this case, the incident energy would be dissipated on lossy GeTe films. Meanwhile, zero reflection remains as strictly protected by the reciprocity principle. This is because the reflection coefficients are exactly the same under incident angles of ${\pm} {\theta _i}$ for reciprocal media, i.e., $r({{\theta_i}} )= r({ - {\theta_i}} )$ [52]. Such an extreme angular asymmetric behavior is further demonstrated by both theoretical results of the effective medium model (solid lines) and numerical results of the actual TAM (dots), as presented in in Fig. 3(b). Moreover, we find that the reflectionless high absorption under ${\theta _i} = {\theta _{\textrm{AB}}}$ can be obtained over a broad spectrum, as shown by the reflectance R and absorptance A in Figs. 3(c) and 3(d), respectively. Notably, the absorptance under ${\theta _i} = {\theta _{\textrm{AB}}}$ can be further increased to be unity for all wavelengths through simply increasing the thickness d of the TAM, thus realizing broadband perfect absorption in crystalline state.

 

Fig. 3. (a) Simulated ${H_x}/{H_0}$-distributions in the TAM with GeTe in crystalline phase when TM-polarized light of ${\lambda _0} = 7\mathrm{\mu }\textrm{m}$ is incident from air under ${\theta _i} = {\theta _\textrm{B}} = 53.27^\circ $ (left) and ${\theta _i} = {\theta _{\textrm{AB}}} ={-} 53.27^\circ $ (right). The TAM consists of tilted GeTe films ($a = 500\textrm{nm}$, $t = 50\textrm{nm}$, $\alpha = 36.73^\circ $) in a SiO₂ host with a thickness of $d = 5\mathrm{\mu }\textrm{m}$. (b) Reflectance R, transmittance T and absorptance A as the function of incident angle at ${\lambda _0} = 7\mathrm{\mu }\textrm{m}$. The solid lines and dots denote, respectively, the theoretical results of the effective medium model and numerical results of the actual TAM. (c) Reflectance R and (d) absorptance A of the actual TAM as functions of the incident angle and working wavelength. The areas bounded by the black dashed lines denote the regions with $R \le 0.1$ in (c) and $A \ge 0.9$ in (d). The white dashed lines denote the Brewster’s angle ${\theta _\textrm{B}} = 53.27^\circ $ and anomalous Brewster’s angle ${\theta _{\textrm{AB}}} ={-} 53.27^\circ $.

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The above results manifest that the functionality of the TAM can be tuned from perfect transparency to perfect absorption over a broad spectrum through changing the phase states under the anomalous Brewster’s angle ${\theta _{\textrm{AB}}}$. Although the spectrum of 3-7$\mathrm{\mu }\textrm{m}$ is considered here, the operating bandwidth actually can be further broadened as long as the dissipation loss and chromatic dispersion of the dielectric host are small and the effective medium approximation of the TAM is valid.

We note that the TAM is quite flexible in the material selection of the dielectric host. For demonstration, we compare the performance of TAMs with dielectric hosts made of SiO₂ and Si, whose relative permittivities are marked by vertical dashed lines in Fig. 4(a). Based on Eq. (10), the required tilt angle $\alpha $ and the corresponding ${\theta _{\textrm{AB}}}$ are plotted in Fig. 4(a). Figures 4(b) and 4(c) show, respectively, transmission spectrum in amorphous phase and absorption spectrum in crystalline phase when ${\theta _i} = {\theta _{\textrm{AB}}}$. The TAM is the same as that in Figs. 2 and 3 except that different kinds of dielectric hosts are utilized here. Since the ${\theta _{\textrm{AB}}}$ relies on ${\varepsilon _\textrm{d}}$, the incident angle ${\theta _i}$ is changed accordingly for different dielectric hosts. It is seen that near-perfect transmission in amorphous phase and high absorption in crystalline phase are obtained over the spectrum of 3-7$\mathrm{\mu }\textrm{m}$.

 

Fig. 4. (a) The anomalous Brewster’s angle ${\theta _{\textrm{AB}}}$ and tilt angle $\alpha $ as a function of the relative permittivity ${\varepsilon _\textrm{d}}$ of dielectric host based on Eq. (10). The vertical dashed lines denote the values of ${\varepsilon _\textrm{d}}$ of SiO₂ and Si. (b) Transmission spectrum in amorphous phase and (c) absorption spectrum in crystalline phase. The TAM is the same as that in Figs. 2 and 3 except for the material of dielectric host. (d) Normalized decay rate of waves in TAM with GeTe in crystalline phase as the function of ${\varepsilon _\textrm{d}}$ (black solid lines). The vertical dashed lines denote the values of ${\varepsilon _\textrm{d}}$ of SiO₂ and Si. (e) Simulated ${H_x}/{H_0}$-distributions when the host dielectric material is SiO₂ (left) or Si (right). (f) Absorptance by the TAM with GeTe in crystalline phase with increasing the thickness d. In (b)-(f), the wavelength of incidence is $7\mathrm{\mu }\textrm{m}$, and the incident angle is the anomalous Brewster’s angle.

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It is noteworthy that the imperfection of absorption in Fig. 4(c) attributes to finite decay rate and limited thickness d of the TAM. To quantitively evaluate the decay rate of the wave in the TAM, we rewrite the magnetic field in TAM (i.e. Equation (4)) as

Base on the dispersion relation of Eq. (5), we plot the normalized decay rate $|\kappa |/{k_0}$ with respect to ${\varepsilon _\textrm{d}}$ (black solid lines in Fig. 4(d)). The vertical dashed lines denote the values of ${\varepsilon _\textrm{d}}$ of SiO₂ and Si. We find that the decay rate decreases when the dielectric host is changed from SiO₂ to Si, thus leading to relatively low absorption in the TAM with a Si host, as observed in Fig. 4(c). For visualization, we simulate the ${H_x}/{H_0}$-distributions in the TAM with a SiO₂ (left) or Si (right) host under the anomalous Brewster angle ${\theta _{\textrm{AB}}}$, as shown in Fig. 4(e). We see that the wave in the TAM with a SiO₂ host decays more quickly than that in the TAM with a Si host. We note that the reflection is absent under the anomalous Brewster angle, therefore we can easily increase the light absorption to near-100% through simply increasing the thickness d of the TAM, as verified in Fig. 4(f). These results demonstrate the flexibility in the material selection of the dielectric host. As long as the TAM is thick enough, the broadband perfect transmission-to-absorption switching is realizable.

It is noteworthy that the broadband switching functionality is robust against the variations of geometrical parameters. In Fig. 5(a), the separation distance a between two adjacent GeTe films is changed from 500 nm to 1000 nm when the thickness of GeTe films is fixed at $t = 50$nm and $\alpha = 36.73^\circ $. The blue and red lines denote, respectively, transmittance through the TAM with GeTe in amorphous phase and absorptance by the TAM with GeTe in crystalline phase under the anomalous Brewster’s angle ${\theta _{\textrm{AB}}} ={-} 53.27^\circ $ at ${\lambda _0} = 7\mathrm{\mu }\textrm{m}$. The TAM is the same as that in Figs. 2 and 3 except that the a is changed. We see that the near-perfect transmission in amorphous phase is almost unchanged, and the absorption in crystalline phase is still very high (>0.98), showing a robust near-perfect switching behavior. Moreover, in Fig. 5(b), the thickness t of GeTe films is changed from 40 nm to 100 nm with fixed $a = 500$nm and $\alpha = 36.73^\circ $. In Fig. 5(c), the tilt angle $\alpha $ is changed from $33.06^\circ $ to $40.40^\circ $ with fixed $a = 500$nm and $t = 50$nm. Still, the switching between near-perfect transmission in amorphous phase (blue lines) and high absorption in crystalline phase (red lines) is observed.

 

Fig. 5. [(a)-(c)] Transmittance through the TAM with GeTe in amorphous phase (blue lines) and absorptance by the TAM with GeTe in crystalline phase (red lines) when (a) the separation distance a is changed with fixed $t = 50\textrm{nm}$ and $\alpha = 36.73^\circ $, (b) the thickness of GeTe films t is changed with fixed $a = 500\textrm{nm}$ and $\alpha = 36.73^\circ $, (c) the tilt angle $\alpha $ is changed with fixed $a = 500\textrm{nm}$ and $t = 50\textrm{nm}$. The TAM is the same as that in Figs. 2 and 3 except that the a, t or $\alpha $ is changed. The wavelength is $7\mathrm{\mu }\textrm{m}$, and the incident angle is ${\theta _{\textrm{AB}}} ={-} 53.27^\circ $, i.e. the anomalous Brewster’s angle. (d) Schematic graph of a TAM with random a, t and $\alpha $ in different transversal positions. The a varies randomly in the range from $0.9{a_0}$ to $1.1{a_0}$ with ${a_0} = 500\textrm{nm}$, the t varies randomly in the range from $0.9{t_0}$ to $1.1{t_0}$ with ${t_0} = 50\textrm{nm}$, and the $\alpha $ varies randomly in the range from $0.9{\alpha _0}$ to $1.1{\alpha _0}$ with ${\alpha _0} = 36.73^\circ $. (e) Illustration of the random TAM slab in the air background. (f) Simulated ${H_x}/{H_0}$-distributions under the illumination of a TM-polarized Gaussian beam under ${\theta _{\textrm{AB}}} ={-} 53.27^\circ $ at ${\lambda _0} = 7\mathrm{\mu }\textrm{m}$ when the GeTe is in amorphous (upper) or crystalline (lower) phase.

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For further verification of the robustness against the variations of geometrical parameters. We consider a TAM with random a, t and $\alpha $ in different transversal positions, as shown schematically in Fig. 5(d). The a varies randomly in the range from $0.9{a_0}$ to $1.1{a_0}$ with ${a_0} = 500\textrm{nm}$, the t varies randomly in the range from $0.9{t_0}$ to $1.1{t_0}$ with ${t_0} = 50\textrm{nm}$, and the $\alpha $ varies randomly in the range from $0.9{\alpha _0}$ to $1.1{\alpha _0}$ with ${\alpha _0} = 36.73^\circ $. Figure 5(e) illustrates the random TAM slab in the air background. Figure 5(f) presents the ${H_x}/{H_0}$-distribution under the illumination of a TM-polarized Gaussian beam under the anomalous Brewster’s angle ${\theta _{\textrm{AB}}} ={-} 53.27^\circ $ at ${\lambda _0} = 7\mathrm{\mu }\textrm{m}$. In the simulation, transition boundary condition is applied to the GeTe films for simplicity. The upper (or lower) panel denotes the TAM with GeTe in amorphous (or crystalline) phase. The simulation results clearly show the occurrence of near-perfect transmission in amorphous phase and near-perfect absorption in crystalline phase. These results demonstrate the robustness of near-perfect transmission-to-absorption switching functionality in the presence of imperfections, which cloud facilitate practical fabrication in experiments.

4. Gradient TAMs exhibiting broadband perfect transmission-to-absorption switching for light with an almost arbitrary wavefront

In the above, we have demonstrated the broadband perfect transmission-to-absorption switching in the case of ${\varepsilon _\textrm{b}} \ne {\varepsilon _\textrm{d}}$ (i.e., the host dielectric material of TAM is different from the background dielectric material), which requires a particular tilt angle $\alpha $ (Eq. (10)) when the host of TAM is fixed. In the following, we’d like to show the solution of Eq. (10) in the case of ${\varepsilon _\textrm{b}} = {\varepsilon _\textrm{d}}$, that is, the host dielectric material of TAM is the same as the background dielectric material. In this case, the value of $\alpha $ can be arbitrarily chosen irrespective of the material selection of the dielectric host of TAM, that is,

As an example, we assume that both the background and host dielectric materials are SiO₂, as illustrated in Fig. 6(a). Based on effective medium model and Eq. (7), the reflectance at SiO₂-TAM interface with respect to $\alpha $ and ${\theta _i}$ for TM-polarized light of ${\lambda _0} = 7\mathrm{\mu }\textrm{m}$ is calculated, as presented in Fig. 6(b). The geometrical parameters of the TAM are $a = 500\textrm{nm}$ and $t = 50\textrm{nm}$. As expected, zero reflection can be obtained for any value of $\alpha $ as long as the condition ${\theta _i} ={\pm} \alpha $ is satisfied. For further verification, in Fig. 6(c) we simulate the ${H_x}/{H_0}$-distributions when TM-polarized light is incident from SiO₂ onto the TAM ($\alpha = 45^\circ $, $d = 5\mathrm{\mu }\textrm{m}$) with GeTe in amorphous (left) or crystalline (right) phase under the incident angle of ${\theta _i} ={-} 45^\circ $. Clearly, the switching between perfect transmission and perfect absorption is observed when the phase transition of GeTe occurs. Moreover, in Fig. 6(d) we change the rotation angle $\alpha $ to $60^\circ $ and re-simulate the ${H_x}/{H_0}$-distributions under ${\theta _i} ={-} 60^\circ $, also showing the perfect switching functionality. These results demonstrate that the perfect transmission-to-absorption switching behavior can be obtained for any value of $\alpha $ as long as the condition ${\theta _i} ={\pm} \alpha $ is satisfied. We shall note that the operating bandwidth can also cover a broad regime due to the non-resonant nature of the proposed TAM.

 

Fig. 6. (a) Illustration of a TAM in a dielectric background. The host dielectric material of the TAM is the same as the background dielectric material. (b) Reflectance at the SiO₂-TAM interface as functions of the incident angle ${\theta _i}$ and tilt angle $\alpha $ for TM-polarized light of ${\lambda _0} = 7\mathrm{\mu }\textrm{m}$. The TAM consists of periodic tilted GeTe films with $a = 500\textrm{nm}$ and $t = 50\textrm{nm}$ in a SiO₂ host. The calculation is based on the effective medium model and Eq. (7). [(c) and (d)] Simulated ${H_x}/{H_0}$-distributions for TM-polarized light of ${\lambda _0} = 7\mathrm{\mu }\textrm{m}$ incident from SiO₂ under (c) ${\theta _i} ={-} 45^\circ $ and (d) ${\theta _i} ={-} 60^\circ $ when the GeTe in TAM is in amorphous (left) or crystalline (right) phase. The thickness of the TAM is $d = 5\mathrm{\mu }\textrm{m}$.

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This interesting result can also be understood geometrically. We first assume that light impinges onto the TAM in the absence of GeTe films, in which case, there is no reflection for all wavelengths and the propagation direction of light won’t change due to ${\varepsilon _\textrm{b}} = {\varepsilon _\textrm{d}}$. Then inserting ultrathin GeTe films into the TAM along the propagation direction of light (i.e. $\alpha = {\theta _i}$), the broadband zero-reflection property won’t be destroyed. Next, considering the principle of reciprocity by flipping the incident angle from ${\theta _i}$ to $- {\theta _i}$, the reflection remains as zero when ${\theta _i} ={-} \alpha $. Nevertheless, the light entering the TAM will “see” the GeTe films and be affected by them, but with no reflection. In this way, we can tune the light transmission/absorption through changing the phase states of GeTe without any reflection, thus realizing the broadband perfect transmission-to-absorption switching.

Superior to the configuration of ${\varepsilon _\textrm{b}} \ne {\varepsilon _\textrm{d}}$, the value of tilt angle $\alpha $ can be arbitrarily chosen in the configuration of ${\varepsilon _\textrm{b}} = {\varepsilon _\textrm{d}}$. This unique feature suggests that through harnessing the local tilt angle of each GeTe film, it is possible to obtain dynamically switchable functionality in gradient TAMs for light with almost arbitrary wavefront.

As an example, we propose a gradient TAM that can realize the perfect switching behavior for light with a cylindrical wavefront. The TAM consists of ultrathin GeTe films in a SiO₂ host, as shown schematically in the upper panel in Fig. 7(a). The tilt angle of GeTe films at different transversal positions is engineered, so that the condition ${\theta _i} ={-} \alpha $ is satisfied locally for emitted light from a point source (lower panel). Based on the above analysis, we know that the emitted light from the point source in the lower plane can penetrate into the TAM with no reflection and then be controlled by the embedded GeTe films. The numerical verification is performed through examining the radiation of a vertical electric dipole source (dipole moment 1A·m) above the TAM. Figure 7(b) displays simulated ${H_x}$-distributions for ${\lambda _0} = 4\mathrm{\mu }\textrm{m}$ (left) and ${\lambda _0} = 7\mathrm{\mu }\textrm{m}$ (right) when GeTe is in amorphous (upper) or crystalline (lower) phase. Here, transition boundary condition is applied to the GeTe films for simplicity. The well-defined dipole radiation patterns without clear interference patterns induced by reflection indicate the near-omnidirectional zero reflection on the TAM. As expected, the emitted light in the lower plane can totally transmit through the TAM with GeTe in amorphous phase, while is almost perfectly absorbed by the TAM with GeTe in crystalline phase, irrespective of the working wavelength.

 

Fig. 7. (a) Upper panel: schematic graph of a gradient TAM consisting of GeTe films with varied tilt angle $\alpha $. Lower panel: the tilt angle of GeTe films varies with the transversal position, and satisfies the condition ${\theta _i} ={-} \alpha $ everywhere for emitted light from a point source. (b) Simulated ${H_x}$-distributions when an electric dipole source of ${\lambda _0} = 4\mathrm{\mu }\textrm{m}$ (left) and ${\lambda _0} = 7\mathrm{\mu }\textrm{m}$ (right) is placed above the gradient TAM in the SiO₂ background. The upper and lower panels correspond to the TAMs with GeTe in amorphous and crystalline phases, respectively.

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5. Conclusion

In summary, we have demonstrated a simple but highly efficient approach to realize broadband perfect transmission-to-absorption switching using TAMs consisting of ultrathin PCM films. Through changing the phase states of the PCM, the functionality of the TAM can be dynamically switched from perfect transparency to perfect absorption. Compared with the newly emerging schemes based on resonant meta-structures [29–34], our proposed TAM is non-resonant, and therefore the operating bandwidth can cover a broad spectrum. The underlying physics of the reflectionless transmission/absorption manipulation lies in the anomalous Brewster effect. In addition, we have demonstrated gradient TAMs exhibiting dynamically switchable functionality for incident light with almost arbitrary wavefront. Our proposed TAMs are quite flexible in the material selection of both dielectric hosts and PCMs. Any dielectric material possessing low dissipation loss and low chromatic dispersion can be utilized. Besides the studied GeTe, other PCMs that possess a reversible phase transition under external bias can also be exploited, such as vanadium dioxide (VO₂) [11–13] and germanium antimony telluride (Ge₂Sb₂Te₅) [14–17]. Moreover, we find that the switching functionality is quite robust against the variations of geometrical parameters of the TAMs. Our findings offer a simple path towards high-efficiency dynamically controllable functionality with a broad bandwidth.