Abstract

Optical metamaterials are building blocks for the control of light behaviors and designs of photonic devices, where the inner interfaces in deep-subwavelength features are expected to have little impact on light transport, based on the concept of homogenization. Here we theoretically and experimentally study a new type of photonic interface (namely a hyperinterface) inside an optical metamaterial made of a zigzag alternating multilayer structure [namely structured metamaterials (SMMs)] in the deep-subwavelength regime. It is found that the subwavelength hyperinterfaces play a great role in the optical properties of such SMMs, and the electromagnetic properties of the hyperinterfaces can be effectively manipulated in a feasible way. In particular, the absorption of the SMMs strongly depends not only on the intrinsic absorption of the SMMs’ unit cells, but also on the structural absorption that is induced by the hyperinterfaces inside the SMMs and their period $p$, even for the long wavelength limitation. These outcomes are attributed to the dispersion relations of the hyperinterfaces, that is, the interplay of the angle formed by the asymptotes of the iso-frequency contour (hyperbola) of the SMMs’ unit cells and the geometric rotating angle of zigzag structures. Such interplay leads to an effect of clipping and the recombination of energy flow distributions at the hyperinterfaces. Our findings may pave the way to the manipulation of a light field to enhance the conversion efficiency of optoelectronic devices, e.g., solar cells and photodetectors.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Over the past few decades, artificial optical materials [1] have attracted extensive attention from the community, because they provide new building blocks for arbitrary control of light behaviors and designs of novel photonic devices [212]. Currently these include metamaterials and photonic crystals, distinguished by inherent geometric scale. For metamaterials, the characteristic sizes of unit elements are much smaller than the operating wavelength. Based on the homogenization concept that the change of the light field on this scale can be approximately uniform, these structured materials can be regarded as a uniform medium. As a result, their optical properties can be described by effective permittivity and permeability tensors based on effective medium theory (EMT). For photonic crystals, their characteristic sizes are comparable to the wavelength, and the photonic band diagram needs to be calculated and analyzed to uncover their optical properties. For instance, the simplest case of metamaterials is a flat structure of alternating multilayers of deep-subwavelength thickness. In particular, for opposite signs of the dielectric permittivity components in two orthogonal directions, such metamaterials are referred to as hyperbolic metamaterials (HMMs) [13], which provide a new route for light–matter interactions [1418].

Today, one of the challenges in metamaterials is experimental realizations. Due to their complex structures, most optical metamaterials cannot be implemented. In particular, as the research goes on, metamaterials have exhibited significant application prospects, such as advanced imaging, solar cells, and photoelectric detection. However, they pose challenges for large-scale preparation and/or low cost in the future. This implies that relatively simple and easily realized structures are desirable in designing metamaterials. Certainly, you cannot have your cake and eat it too; simple structures may lead to trivial optical properties. This requires explorations of new manners of light control beyond traditional methods.

In this work, we design and study a new type of photonic interface inside a simple optical metamaterial. The metamaterial is made of a zigzag multilayer structure, which is obtained by rotating the multilayer HMM [Fig. 1(a)] clockwise and counterclockwise, respectively, and constructing them together [Fig. 1(b)]. For convenience, we call it structured metamaterial (SMM). This seemingly simple SMM is actually highly nontrivial because its period-dependent optical properties can be neither predicted from uniform field-based EMT nor analyzed clearly by a band structure diagram, although its period is in the deep-subwavelength regime ($p \ll \lambda$). The proposed SMM also differs from the photonic hypercrystals [19,20] whose optical properties can still be well explained using the photonic band diagram. Instead, it is found that the photonic band structure of HMM/HMM interfaces (namely hyperinterfaces) inside SMMs plays a significant role in the optical properties of the SMMs. Besides, the photonic band structure at the hyperinterfaces can be arbitrarily tuned by adjusting their geometry and the associated HMM’s features. This is analogous to the interface physics in condensed matter where electron transportation at the interface is determined by the tailored band structure of electrons at the interface. We also show that these simple rotations lead to a new effect of clipping and the recombination of energy flow distributions at the hyperinterfaces. With the experimental technology we developed, the proposed hyperinterfaces can be experimentally prepared in large areas, reaching wafer scale, and the measured results confirm our findings.

 

Fig. 1. Concepts of the SMMs and the photonic hyperinterfaces. (a) Deep-subwavelength silver/silicon multilayer structure of HMMs. (b) Left, structure of the designed SMMs by rotating the initial HMMs; right, the rotated HMMs are equivalent to two homogeneous media, MA and MB, based on EMT. In SMMs, there are two different hyperinterfaces, ${{\rm{IF}}_{\rm AB}}$ (red dashed arrow) and ${{\rm{IF}}_{\rm BA}}$ (white dashed arrow). (c) Real parts of the effective permittivity of initial HMMs. Two different types of HMMs are seen over the whole wavelength range, with the critical wavelength $\lambda = 623$ nm. (d) Image of a 2-inch wafer-scale zigzag substrate. (e) Cross-sectional TEM images (marked by blue dashed lines) of the zigzag patterns. (f) Top-down SEM images at different locations (marked by green dashed lines). (g) Cross-sectional TEM image of the fabricated SMM (hyperinterfaces).

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2. MODELING AND PREPARATION

Let us begin with the modeling of the hyperinterfaces. Figure 1(a) shows a multilayer structure, where the blue and gray layers correspond to silicon and silver, respectively, with their permittivities provided in Section I of Supplement 1. The thickness of each layer is set to be 5 nm, so the thickness of an alternating cycle $t$ is 10 nm, being deep-subwavelength compared with the working wavelengths of interest, ranging from 400 nm to 800 nm. Based on EMT [1], Fig. 1(c) shows the real parts of the effective permittivity components of the multilayer structure over the whole spectra. It is seen that the corresponding permittivity components have opposite signs in two orthogonal directions. In this case, the multilayer structure can be referred to as HMMs at different wavelengths, and a critical wavelength $\lambda = 623\,\,{\rm nm}$, where ${\mathop{\rm Re}\nolimits} [{\varepsilon _u}] = {\mathop{\rm Re}\nolimits} [{\varepsilon _v}] = 0$, divides all these HMMs into two types, type I and type II [13]. The left panel in Fig. 1(b) shows the considered SMM made of a zigzag multilayer structure, where two rotated HMM cells with two rotating angles $\alpha$ and ${-}\alpha$, respectively, are periodically arranged along the $y$ axis, with a period $p = 50\,\,{\rm nm}$ and $\alpha = {18^ \circ}$. Note that the two rotated HMM cells in Fig. 1(b) are obtained by rotating the HMM in Fig. 1(a) clockwise and counterclockwise, respectively. Due to $p \ll \lambda$, two such rotated HMMs can be treated as two homogeneous media: medium A (MA) and medium ${{B}}$ (MB), as shown in the right panel of Fig. 1(b) (the yellow and green regions). Then the hyperinterfaces are the interfaces between the rotated HMMs MA and MB, which are marked as ${\rm IF_{\rm AB}}$ and ${\rm IF_{\rm BA}}$ in Fig. 1(b).

A two-step method including the nanopattening by “reverse epitaxy” [21,22] and multilayer deposition [23,24] was developed to fabricate the wafer-scale hyperinterfaces. First, the nanogroove patterns were formed on an epi-ready GaAs (001) substrate, which serves as a zigzag substrate [21]. Then, the alternating silver and silicon layers was deposited on the zigzag substrate. More specifically, the wafer-scale GaAs substrate with ordered nanogroove patterns on it is formed by the normal incidence of ${\rm{A}}{{\rm{r}}^ +}$ irradiation at the elevated temperature (e.g.,  410°C). The irradiation ion fluence is $1 \times {10^{19}}{\rm cm^{- 2}}$. Silver and silicon layers were alternately deposited on the zigzag substrate by reactive magnetic sputtering to form the periodic HMM cells—the MA and MB structures. Since the tilt angle and the period of MA and MB are controlled by the zigzag substrate, changing the nanogroove patterns on the zigzag substrate [23] will modify the structural parameters and the optical properties of the hyperinterfaces and the SMMs. Note that the symmetry of the patterns reflects the crystal symmetry of the substrate surface, and different patterns can be obtained with different substrates [21]; thus diverse large-scale nanostructures can be prepared using this “reverse epitaxy” technology.

Figures 1(d)1(f) show the image of a 2-inch wafer-scale zigzag substrate, the cross-sectional TEM images of the zigzag nanopatterns, and the high-resolution scanning electron microscope (SEM) images of the zigzag nanopatterns at four different locations in a large-scale range, respectively. Figure 1(g) shows the cross-sectional view of the fabricated SMM sample with 17 periods of alternated silicon and silver layers, which means $h = 170\,\,{\rm nm}$. The measured period $p$ is about 43 nm. As each layer of material is deposited during preparation, the orientation modulation of the zigzag substrate will get slowly washed out because of surface oxidation or sputtering and mass redistribution together with surface relaxation mechanisms. Given these, the zigzag multilayers become more and more flat from the substrate to the surface.

3. RESULTS AND DISCUSSION

Based on EMT [1], the permittivity tensors of MA and MB are given by (more analysis in Section II of Supplement 1)

$$\overleftrightarrow{\varepsilon }\!(\alpha )=\left[ \begin{array}{*{20}{c}} {{\varepsilon }_{xx}} & {{\varepsilon }_{xy}} \\ {{\varepsilon }_{yx}} & {{\varepsilon }_{yy}} \\ \end{array} \right],$$
where ${\varepsilon _\textit{xx}}(\alpha) = {\varepsilon _u}{\cos ^2}\alpha + {\varepsilon _v}{\sin ^2}\alpha$, ${\varepsilon _\textit{yy}}(\alpha) = {\varepsilon _v}{\cos ^2}\alpha + {\varepsilon _u}{\sin ^2}\alpha$, ${\varepsilon _\textit{xy}}(- \alpha) = - {\varepsilon _\textit{xy}}(\alpha) = ({\varepsilon _u} - {\varepsilon _v})\sin (2\alpha)/2$, $1/{\varepsilon _u} = f/{\varepsilon _1} + (1 - f)/{\varepsilon _2}$, ${\varepsilon _v} = f{\varepsilon _1} + (1 - f){\varepsilon _2}$, and $f$ is the filling ratio of silver. Here ${\varepsilon _u}$ and ${\varepsilon _v}$ are the effective permittivity components of the initial HMM [Fig. 1(c)]. Note that for an individual MA (MB) of infinite size, the MA (MB) with a flat surface has almost identical absorption to that of the MA (MB) with a zigzag surface with $p = 50\,\,{\rm nm}$. The reason lies in the tiny surface undulation compared to the working wavelength of interest, leading to neglected influence on their optical properties (more analysis in Section III of Supplement 1). Given this, the flat cases will be used instead for concrete analysis. The absorption is given analytically by (more analysis in Section IV of Supplement 1)
$${A_{\rm MA}}(\omega) = {A_{\rm MB}}(\omega) = 1 - {\left| {2/\left({1 + \sqrt {\frac{{{\varepsilon _\textit{xx}}(\omega) - {{\sin}^2}\theta}}{{{\varepsilon _u}(\omega){\varepsilon _v}(\omega){{\cos}^2}\theta}}}} \right) - 1} \right|^2},$$
where $\theta$ is the angle of incidence (AOI). Note that as the substrate (GaAs of 500 µm) is too thick, the transmissivity is zero for the whole spectrum and all incidences. Therefore, the absorption is simply given by $A = 1 - R$, where $R$ is the reflectivity.

Based on Eqs. (1) and (2), one can clearly see that MA and MB have identical absorption spectra. Figure 2(a) shows the corresponding absorption of MA (MB) versus the wavelength and the AOI, which is also almost the same as that of the initial HMM shown in Fig. 1(a) (more analysis in Section IV of Supplement 1). For $\lambda \gt 623\,\,{\rm nm}$, ${\mathop{\rm Re}\nolimits} [{\varepsilon _u}] \gt 0$, and ${\mathop{\rm Re}\nolimits} [{\varepsilon _v}] \lt 0$ [Fig. 1(c)], the initial HMM is referred to as type-II HMM, as well as MA (MB). In this case, the corresponding iso-frequency contour (IFC) of MA (MB) will have a momentum gap of ${k_y}$ [for instance, at $\lambda = 765\,\,{\rm nm}$; see Fig. 3(d)], which will lead to reflection for some incidences, resulting in relatively weak absorption. Meanwhile, for $\lambda \lt 623\,\,{\rm nm}$, the corresponding IFC of MA (MB) will have a continuous ${k_y}$ from minus infinity to infinity [for instance, at $\lambda = 612\,\,{\rm nm}$; see Fig. 3(c)], which indicates that arbitrary incidences of light from air can be coupled into MA (MB), resulting in relatively strong absorption. Intuitively, the absorption of the SMM should coincide to that of MA or MB because the SMM is just constructed by putting MA and MB together. However, this is not true here. Figure 2(b) plots the optical absorption map of the SMM based on numerical calculations, where the absorption spectra of the SMM and MA (MB) are very similar in region I, but widely different in region II. Figure 2(c) shows the details of the corresponding results of MA (MB) and SMMs for $\theta = {0^ \circ}$. In region II, the SMM achieves its minimum absorption at $\lambda \approx 612\,\,{\rm nm}$ (the point A), while the absorption of MA is large there; the absorption of SMM reaches the maximum at $\lambda \approx\,\,{765\,\,\rm nm}$ (the point B), while the absorption of MA is relatively weak.

 

Fig. 2. (a) Absorption spectra of MA (MB) and (b) absorption spectra of the SMM. In (b), the purple and white dashed lines indicate the positions of the critical point and the minimum absorption point at different incident angles, respectively. (c) Absorption curves of MA and the SMM when $\theta = {0^ \circ}$. (d) Intersection angle $\beta$ of HMMs over the wavelength range from 400 to 800 nm. (e) Measured absorption spectra of the fabricated SMM and the initial HMM at an incident angle $\theta = {30^ \circ}$. The blue curve is for the initial HMM, and the red is for the SMM.

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Fig. 3. Physics behind this extraordinary optical absorption. (a) and (b) show the IFCs (blue curves) of the initial HMMs at $\lambda =612$ and 765 nm, respectively. The orange circles denote the IFCs of the air, the green dashed lines denote the symmetry axes of the IFCs (hyperbolas), and the black dashed lines denote the asymptotes of the IFCs. (c) and (d) show the rotated IFCs of the initial HMMs by the geometric angle $\alpha$ (purple curves) and ${-}\alpha$ (blue curves), at $\lambda =612$ and 765 nm, respectively. The red/black dashed arrow denotes the direction of energy flow of the incident/refraction light, occurring at the hyperinterface ${{\rm{IF}}_{\rm AB}}$ or ${{\rm{IF}}_{\rm BA}}$. (e) and (f) show the simulated time-averaged energy flow patterns in the SMM for a normally incident TM wave when $\lambda =765$ and 612 nm, respectively. In (e) and (f), (E1)–(E5) and (F1)–(F5) show the physical process of the clipping and recombination of energy flow inside the SMM, resulting from the tailored dispersion relations of the initial HMMs by rotating angle $\alpha$.

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The physics behind this extraordinary optical absorption in the SMM stems from the rotated dispersion relations of MA and MB and the tailored dispersion relations of the hyperinterfaces IF$_{\rm AB}$ and IF$_{\rm BA}$. For illustration, we first take two cases of $\lambda =765$ and 612 nm for discussion. Figures 3(e) and 3(f) show the simulated time-averaged energy flow inside the SMM for a normal incidence from the air with wavelength of 765 nm and 612 nm, respectively. It can be seen clearly that most of energy of light is inside the black dashed triangles and is converged to the hyperinterfaces ${{\rm{IF}}_{\rm AB}}$ and ${{\rm{IF}}_{\rm BA}}$ ($\lambda =765\,\,{\rm nm}$), leading to high intensity and strong localizations. Meanwhile, for $\lambda =612\,\,{\rm nm}$, light departs from the interfaces. These seemingly confused energy patterns are actually clear and comprehensible from the following process. First, let us consider a point source mimicked by a tiny circle with a current of 1 A in simulations, embedded in an initial HMM. For the $\lambda =765\,\,{\rm nm}$ case, Fig. 3(E1) shows the corresponding energy flow pattern with only the right diagram, owing to a fact that the light in Fig. 3(e) is incident from the left. It is featured with two flow branches, and the intersection angle of each branch and the $x$ axis is about 17º. These outcomes can actually be predicted from the corresponding IFC in Fig. 3(b), where the angle between the ${k_y}$ axis and the asymptotes of the hyperbola of IFC, noted as $\beta$, is 17º, which dominates the energy flow direction of light inside the HMMs. As for MA and MB, the corresponding IFCs as well as the energy flow directions will be rotated accordingly to the geometric rotating angles $\alpha$ and ${-}\alpha$, as shown in Figs. 3(b) and 3(d) (more analysis in Section V of Supplement 1). In simulations, Figs. 3(E2) and 3(E3) show the rightward energy flow patterns of light inside MA and MB, respectively, which fully coincides with that achieved through rotating the energy flow inside the HMMs by $-18$º and 18º, respectively.

To our knowledge, it has never been found before that simply assembling MA and MB together will lead to the clipping and recombination of energy flow distributions, which contributes to the rightward energy flow distributions at hyperinterfaces ${{\rm{IF}}_{\rm AB}}$ and ${{\rm{IF}}_{\rm BA}}$. Specifically, by cutting the flow patterns in Figs. 3(E2) and 3(E3) into upper and lower parts along the direction of the $x$ axis, respectively, and putting the upper part pattern of MA (marked as 3@) and the lower part pattern of MB (marked as 2@) together, we can construct the rightward energy flow pattern at hyperinterface ${{\rm{IF}}_{\rm BA}}$ [see Fig. 3(E4)]. Note that if we put the point source directly at the hyperinterface ${{\rm{IF}}_{\rm BA}}$, it will induce the same energy flow patterns shown in Figs. 3(E4) and 3(E5) (more analysis in Section VI of Supplement 1). One can see that the energy flow at ${{\rm{IF}}_{\rm BA}}$ [Fig. 3(E4)] agrees well with the rightward energy flow pattern at ${{\rm{IF}}_{\rm BA}}$ in Fig. 3(e). Due to tailored hyperbolic dispersion, there exists an intersection angle 34º [Fig. 3(e)], which exactly equals to $2\beta$, defining a limited region as shown by the blue arrows for EM wave propagations. All energy from two opposite directions flows to hyperinterface ${{\rm{IF}}_{\rm BA}}$, leading to a very large energy density therein. Likewise, by putting the lower part pattern of MA (marked as 4@) and upper part pattern of MB (marked as 1@) together, we can construct the rightward energy flow pattern of hyperinterface ${{\rm{IF}}_{\rm AB}}$, as shown in Fig. 3(E5). The energy flow around ${{\rm{IF}}_{\rm AB}}$ [Fig. 3(E5)] matches the rightward energy flow pattern around ${{\rm{IF}}_{\rm AB}}$ in Fig. 3(e), and is mostly confined to the interfaces and propagates along it. It should be noted that in both cases, due to the confined energy and the rightward energy flows, the tailored dispersions of MA (MB) and the formed hyperinterfaces will lead to more dissipated energy as the EM wave propagates inward, compared to that of the corresponding flat case where high reflection occurs.

 

Fig. 4. Simulated absorption curves of the SMM as a function of (a) tailored angle $\alpha$ and (b) period $p$ of the HMM cells.

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For $\lambda = 612\,\,{\rm nm}$, the energy flow patterns of a point source inside an initial HMM and the tailored one in MB and MA are shown in Figs. 3(F1)3(F3), respectively; the spliced and recombined rightward energy flow patterns at hyperinterfaces ${{\rm{IF}}_{\rm BA}}$ and ${{\rm{IF}}_{\rm AB}}$ are shown in Figs. 3(F4) and 3(F5), respectively. In contrast to the case of $\lambda = 765\,\,{\rm nm}$, the tailored hyperbolic dispersion leads to no energy converged at hyperinterface ${{\rm{IF}}_{\rm BA}}$ [Fig. 3(F4)] and hyperinterface ${{\rm{IF}}_{\rm AB}}$ [Fig. 3(F5)]. Instead, only two beam-like energies flow away from ${{\rm{IF}}_{\rm AB}}$, which agrees well with the rightward energy flow patterns at ${{\rm{IF}}_{\rm AB}}$ in Fig. 3(f). More interestingly, because of the IFCs of MA and MB [Fig. 3(c)], where the red dashed arrow (labeled as ${S_i}$) denotes the corresponding Poynting vector of the incident wave while the black dashed arrow (labeled as ${S_r}$) denotes that of the refraction wave, the incident energy flow in MB will be negatively refracted in MA and vice versa. Therefore, as shown in Fig. 3(f), when the beam-like energy from the ${{\rm{IF}}_{\rm AB}}$ reaches the ${{\rm{IF}}_{\rm BA}}$, as indicated by the purple and deep blue arrows, negative refraction occurs, which results in most of the refracted energy flowing back or propagating outward. Therefore, although MA and MB themselves have very strong optical absorption, the effect of no energy flow converged at the interfaces and negative refraction of the energy flow results in declined absorption of the SMM.

For other wavelengths, similar analysis can be applied (more analysis in Section VII of Supplement 1). One can see that due to different topological features of the IFCs of MA (MB), two distinct outcomes are known cursorily: for $\lambda \gt 623\,\,{\rm nm}$ (type-II HMMs), the hyperinterfaces ${{\rm{IF}}_{\rm AB}}$ and ${{\rm{IF}}_{\rm BA}}$ (formed by periodically arranged HMM cells MA and MB) will lead to enhanced absorption of MA (MB), while for $\lambda \lt 623\,\,{\rm nm}$ (type-I HMMs), decreased absorption will occur. It is true, and reinforced by the results in Fig. 2(c), where the enhanced absorption is seen when $\lambda \gt 640\,\,{\rm nm}$, while the decreased absorption occurs when $540 \le \lambda \le 640\,\,{\rm nm}$. Note that due to the interplay between the intrinsic absorption of the rotated HMM cells (MA and MB) and the structural absorption induced by the hyperinterfaces [see Figs. 3(E1)3(E5) and 3(F1)3(F5)], the actual critical point for the same absorption of MA(MB) and the SMM is not exactly at $\lambda = 623\,\,{\rm nm}$, but deviates from it a little bit. In addition, due to such interplay, the minimum absorption of the SMM occurs not exactly at $\lambda = 612\,\,{\rm nm}$ but at a wavelength around it. This insight is confirmed by the results in Fig. 2(b), where the purple and white dashed lines indicate the wavelengths (positions) of the actual critical point and the minimum absorption point for different incidences, respectively. Note that the increasing incident angle will lead to a small change of the intrinsic absorption of MA (MB) [see Fig. 2(a)]. Both the critical point and the minimum absorption point are slightly offset accordingly, but in a small range (${\lt}20\,\,{\rm nm}$).

The degree of enhancement or decrease of absorption strongly depends on the relationship between two angles: the tailored angle $\alpha$ and the intersection angle $\beta$. Figure 2(d) shows the calculated $\beta$ of the initial HMMs in the considered spectrum ranging from 400 nm to 800 nm. It is found that for $\lambda \gt 623\,\,{\rm nm}$, $\beta$ increases with the wavelength, and the degree of enhancement is positively related to it. In particular, when $\lambda = 765\,\,\rm nm$, $\beta \approx \alpha$, where the maximum absorption occurs. For $\lambda \lt 623\,\,{\rm nm}$, $\beta$ deceases with the wavelength. Interestingly, when $\lambda = 524\,\,{\rm nm}$, $\beta \approx \alpha$, where the absorption is also maximum [see Fig. 2(c)]. Due to the tailored dispersion relations, such a special wavelength is actually a transition point where the refraction phenomenon of the light energy at hyperinterface ${{\rm{IF}}_{\rm AB}}$ (${{\rm{IF}}_{\rm BA}}$) changes from positive (propagates inward the SMM) to negative (outward). Details are provided in Section VII of Supplement 1. Furthermore, the special wavelength ($\lambda = 524\,\,{\rm nm}$) divides the wavelength range of 400 nm to 623 nm (type-I HMMs) into two segments. For $524 \lt \lambda \lt 623\,\,{\rm nm}$, the negative refraction occurs and the degree of decrease is also positively related to $\beta$. Meanwhile, for $\lambda \lt 524\,\,{\rm nm}$, the positive refraction occurs, and all energy will propagate inward. In this case, the intrinsic absorption of the rotated HMMs themselves is already high [see Fig. 2(a)], so that most energy will be dissipated in the individual MA or MB before arriving at the hyperinterfaces ${{\rm{IF}}_{\rm AB}}$ and ${{\rm{IF}}_{\rm BA}}$, resulting in similar absorption spectra in both the SMM and the MA (MB). Similarly, due to the aforementioned interplay between two kinds of absorption, the actual critical point of balanced absorption (where the SMM and MA or MB have the same absorption) is shifted from 524 nm to 540 nm [see Fig. 2(c)].

This uncovered transition is solidly confirmed by the measured absorption spectra as shown by Fig. 2(e), although the sample quality in Fig. 1(g) is not good enough. Therein the blue curve is for MA (MB) (i.e., HMM) and the red is for the SMM. It is shown that compared with MA (MB), the absorption of the SMM is enhanced when $\lambda \gt \approx 620\,\,{\rm nm}$, while it is significantly suppressed when $524 \le \lambda \lt 620\,\,{\rm nm}$. The transition is at about $\lambda = 620\,\,{\rm nm}$. Obviously, the enhanced absorption stems from the hyperinterfaces of the tailored HMMs, as revealed above. These results agree well with our findings in theory, although the measured absorption spectra of the SMMs have a slight variation from the simulations especially for wavelengths below 600 nm. It stems from two aspects: one is that the structure used in simulations and that in experimental measurements are not exactly the same, because the fabricated zigzag multilayers become more and more flat from the substrate to the surface; the other is that the optical properties of the deposited Ag and Si layers may be slightly different from those used in simulations. When the incident angle changes from 15º to 60º, the corresponding measured absorption spectra in Section VIII of Supplement 1 reveal similar conclusions, which greatly proves our findings.

Furthermore, such revealed physics indicates that the absorption spectrum of the SMM can be further manipulated by adjusting the properties of the hyperinterfaces, that is, the tailored angle $\alpha$ or the period $p$. As shown in Fig. 4(a), when $\alpha$ changes from 12° to 21°, the maximum absorption points (appearing at the positions where $\beta \approx \alpha$) in the region of $\lambda \gt 623\;{\rm nm}$ are gradually red shifted from 706 nm to 779 nm, and those in the range of $\lambda \lt 623\;{\rm nm}$ are gradually blue shifted from 543 nm to 510 nm. For the minimum absorption points, they remain almost the same, appearing at a small spectrum range (599–609 nm) around $\beta \approx 0^{\circ}$. In addition, for a fixed $\alpha$, Fig. 4(b) shows the influence of the period $p$ of the HMMs on the absorption spectrum. It is found that although the period $p$ is deep-subwavelength, decreasing $p$ makes the abovementioned finding more pronounced: a smaller $p$ leads to a further enhanced optical absorption of the SMM for $\lambda \gt 623\;{\rm nm}$, and further decreased optical absorption of the SMM for $524 \lt \lambda \lt 623\,\,{\rm nm}$. This is due to a fact that a smaller $p$ leads to a higher spatial density of hyperinterfaces $\rm IF_{\rm BA}$ and $\rm IF_{\rm AB}$. As a result, for $\lambda \gt 623\;{\rm nm}$, more $\rm IF_{\rm BA}$ and $\rm IF_{\rm AB}$ means more converged energy at the hyperinterfaces, while for $524 \lt \lambda \lt 623\,\,{\rm nm}$, more $\rm IF_{\rm BA}$ and $\rm IF_{\rm AB}$ implies that more incident energy will return back, due to the negative refractions at the inner interfaces. As mentioned above, the tailored angle and the period of SMMs in experiments are strongly dependent on the geometry of the zigzag substrate, which can actually be controlled by adjusting the incident irradiation temperature [23]. Thus the fabrications of the discussed SMMs in Fig. 4 are expected and feasible based on the developed experiment technique of reverse epitaxy.

4. CONCLUSIONS

We have designed and studied a new type of photonic interface (hyperinterface) inside a simple optical metamaterial (SMM) made of rotated HMM cells. It is found that the absorption of the SMM is determined not only by the intrinsic absorption of each HMM cell, but also by the hyperinterfaces and their periods. Different from most of the metamaterials demonstrated so far, the hyperinterfaces inside the SMM play a great role in determining the optical properties of the designed metamaterials, beyond the scope of EMT and the photonic band diagram, thereby expanding the capacity of controlling the light behaviors. The experimental results partially confirm our findings in theory, though showing slight variation from the simulation results (due to the gradually smoothed profile of the zigzag layers). Because of the wide-angle enhanced absorption, the proposed hyperinterfaces may provide a new approach for designing high-efficiency solar cells and photodetectors, finding their values in fundamental explorations of solar energy conversion [24] and photoelectric detection based on hot electrons [25,26]. Considering the progress of the Purcell effect in HMMs [27], our proposed hyperinterfaces provide a new platform for the study of Purcell effect enhancement by controlling the rotation angles. In addition, the 2-inch wafer-scale zigzag substrate fabricated by the “reverse epitaxy” method has an extremely high line density (above ${{20000}}\;{\rm{lines}}\;{\rm{m}}{{\rm{m}}^{- 1}}$) of the nanograting, which shows great potential in the application of an x-ray spectrometer with coated multilayer structures. Conventionally, it is still challenging to obtain high line density with current nano-fabrication technology [28], such as e-beam lithography.

Funding

National Key Research and Development Program of China (2017YFE0131300); National Natural Science Foundation of China (11774252, 11874311, 11974010, 61851406, 61874128, U1732268); Frontier Science Key Program of CAS (QYZDY-SSW-JSC032); K. C. Wong Education Foundation (GJTD-2019-11); Program of Shanghai Academic Research Leader (19XD1404600); Chinese-Austrian Cooperative RD Project (GJHZ201950); Natural Science Foundation of Jiangsu Province (BK20171206); China Postdoctoral Science Foundation (2018T110540); Qing Lan project; “333” project (BRA2015353); Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions; Shanghai Science and Technology Innovation Action Plan Program (19511107200).

Acknowledgment

We thank Prof. Zhaowei Liu from UCSD for numerous helpful discussions and Prof. Sannian Song from SIMIT for assisting in the thin film deposition. S. Zhang, Y. Xu, and H. Chen equally contributed to this work.

Disclosures

The authors declare no conflicts of interest.

 

See Supplement 1 for supporting content.

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8. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011). [CrossRef]  

9. Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013). [CrossRef]  

10. S.-C. Jiang, X. Xiong, Y.-S. Hu, Y.-H. Hu, G.-B. Ma, R.-W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).

11. Y. Xu, Y. Fu, and H. Chen, “Planar gradient metamaterials,” Nat. Rev. Mater. 1, 16067 (2016). [CrossRef]  

12. Y. Fu, C. Shen, Y. Cao, L. Gao, H. Chen, C. Chan, S. A. Cummer, and Y. Xu, “Reversal of transmission and reflection based on acoustic metagratings with integer parity design,” Nat. Commun. 10, 2326 (2019). [CrossRef]  

13. D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003). [CrossRef]  

14. H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science 336, 205–209 (2012). [CrossRef]  

15. A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013). [CrossRef]  

16. M. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. Bonner, M. Mayy, Z. Jacob, and E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35, 1863–1865 (2010). [CrossRef]  

17. K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15, 621–627 (2016). [CrossRef]  

18. W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015). [CrossRef]  

19. E. E. Narimanov, “Photonic hypercrystals,” Phys. Rev. X 4, 041014 (2014). [CrossRef]  

20. C. T. Riley, J. S. Smalley, J. R. Brodie, Y. Fainman, D. J. Sirbuly, and Z. Liu, “Near-perfect broadband absorption from hyperbolic metamaterial nanoparticles,” Proc. Natl. Acad. Sci. USA 114, 1264–1268 (2017). [CrossRef]  

21. X. Ou, K.-H. Heinig, R. Hübner, J. Grenzer, X. Wang, M. Helm, J. Fassbender, and S. Facsko, “Faceted nanostructure arrays with extreme regularity by self-assembly of vacancies,” Nanoscale 7, 18928–18935 (2015). [CrossRef]  

22. D. Voronov, E. Gullikson, F. Salmassi, T. Warwick, and H. Padmore, “Enhancement of diffraction efficiency via higher-order operation of a multilayer blazed grating,” Opt. Lett. 39, 3157–3160 (2014). [CrossRef]  

23. Q. Huang, J. Feng, H. Huang, X. Yang, J. Grenzer, K. Huang, S. Zhang, J. Lin, H. Zhou, and T. You, “Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy,” Nat. Commun. 10, 2437 (2019). [CrossRef]  

24. C. Clavero, “Plasmon-induced hot-electron generation at nanoparticle/metal-oxide interfaces for photovoltaic and photocatalytic devices,” Nat. Photonics 8, 95–103 (2014). [CrossRef]  

25. M. L. Brongersma, N. J. Halas, and P. Nordlander, “Plasmon-induced hot carrier science and technology,” Nat. Nanotechnol. 10, 25–34 (2015). [CrossRef]  

26. A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Unrelenting plasmons,” Nat. Photonics 11, 8–10 (2017). [CrossRef]  

27. D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9, 48–53 (2014). [CrossRef]  

28. L. J. P. Ament, M. Van Veenendaal, T. P. Devereaux, J. P. Hill, and J. V. Den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011). [CrossRef]  

References

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  1. W. Cai and V. M. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010), Vol. 10.
  2. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [Crossref]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
    [Crossref]
  4. Y. Xu and H. Chen, “Total reflection and transmission by epsilon-near-zero metamaterials with defects,” Appl. Phys. Lett. 98, 113501 (2011).
    [Crossref]
  5. I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11, 149–158 (2017).
    [Crossref]
  6. Y. Xu, S. Du, L. Gao, and H. Chen, “Overlapped illusion optics: a perfect lens brings a brighter feature,” New J. Phys. 13, 023010 (2011).
    [Crossref]
  7. H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
    [Crossref]
  8. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
    [Crossref]
  9. Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
    [Crossref]
  10. S.-C. Jiang, X. Xiong, Y.-S. Hu, Y.-H. Hu, G.-B. Ma, R.-W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).
  11. Y. Xu, Y. Fu, and H. Chen, “Planar gradient metamaterials,” Nat. Rev. Mater. 1, 16067 (2016).
    [Crossref]
  12. Y. Fu, C. Shen, Y. Cao, L. Gao, H. Chen, C. Chan, S. A. Cummer, and Y. Xu, “Reversal of transmission and reflection based on acoustic metagratings with integer parity design,” Nat. Commun. 10, 2326 (2019).
    [Crossref]
  13. D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
    [Crossref]
  14. H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science 336, 205–209 (2012).
    [Crossref]
  15. A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
    [Crossref]
  16. M. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. Bonner, M. Mayy, Z. Jacob, and E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35, 1863–1865 (2010).
    [Crossref]
  17. K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15, 621–627 (2016).
    [Crossref]
  18. W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
    [Crossref]
  19. E. E. Narimanov, “Photonic hypercrystals,” Phys. Rev. X 4, 041014 (2014).
    [Crossref]
  20. C. T. Riley, J. S. Smalley, J. R. Brodie, Y. Fainman, D. J. Sirbuly, and Z. Liu, “Near-perfect broadband absorption from hyperbolic metamaterial nanoparticles,” Proc. Natl. Acad. Sci. USA 114, 1264–1268 (2017).
    [Crossref]
  21. X. Ou, K.-H. Heinig, R. Hübner, J. Grenzer, X. Wang, M. Helm, J. Fassbender, and S. Facsko, “Faceted nanostructure arrays with extreme regularity by self-assembly of vacancies,” Nanoscale 7, 18928–18935 (2015).
    [Crossref]
  22. D. Voronov, E. Gullikson, F. Salmassi, T. Warwick, and H. Padmore, “Enhancement of diffraction efficiency via higher-order operation of a multilayer blazed grating,” Opt. Lett. 39, 3157–3160 (2014).
    [Crossref]
  23. Q. Huang, J. Feng, H. Huang, X. Yang, J. Grenzer, K. Huang, S. Zhang, J. Lin, H. Zhou, and T. You, “Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy,” Nat. Commun. 10, 2437 (2019).
    [Crossref]
  24. C. Clavero, “Plasmon-induced hot-electron generation at nanoparticle/metal-oxide interfaces for photovoltaic and photocatalytic devices,” Nat. Photonics 8, 95–103 (2014).
    [Crossref]
  25. M. L. Brongersma, N. J. Halas, and P. Nordlander, “Plasmon-induced hot carrier science and technology,” Nat. Nanotechnol. 10, 25–34 (2015).
    [Crossref]
  26. A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Unrelenting plasmons,” Nat. Photonics 11, 8–10 (2017).
    [Crossref]
  27. D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9, 48–53 (2014).
    [Crossref]
  28. L. J. P. Ament, M. Van Veenendaal, T. P. Devereaux, J. P. Hill, and J. V. Den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
    [Crossref]

2019 (2)

Q. Huang, J. Feng, H. Huang, X. Yang, J. Grenzer, K. Huang, S. Zhang, J. Lin, H. Zhou, and T. You, “Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy,” Nat. Commun. 10, 2437 (2019).
[Crossref]

Y. Fu, C. Shen, Y. Cao, L. Gao, H. Chen, C. Chan, S. A. Cummer, and Y. Xu, “Reversal of transmission and reflection based on acoustic metagratings with integer parity design,” Nat. Commun. 10, 2326 (2019).
[Crossref]

2017 (3)

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11, 149–158 (2017).
[Crossref]

A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Unrelenting plasmons,” Nat. Photonics 11, 8–10 (2017).
[Crossref]

C. T. Riley, J. S. Smalley, J. R. Brodie, Y. Fainman, D. J. Sirbuly, and Z. Liu, “Near-perfect broadband absorption from hyperbolic metamaterial nanoparticles,” Proc. Natl. Acad. Sci. USA 114, 1264–1268 (2017).
[Crossref]

2016 (2)

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15, 621–627 (2016).
[Crossref]

Y. Xu, Y. Fu, and H. Chen, “Planar gradient metamaterials,” Nat. Rev. Mater. 1, 16067 (2016).
[Crossref]

2015 (3)

X. Ou, K.-H. Heinig, R. Hübner, J. Grenzer, X. Wang, M. Helm, J. Fassbender, and S. Facsko, “Faceted nanostructure arrays with extreme regularity by self-assembly of vacancies,” Nanoscale 7, 18928–18935 (2015).
[Crossref]

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

M. L. Brongersma, N. J. Halas, and P. Nordlander, “Plasmon-induced hot carrier science and technology,” Nat. Nanotechnol. 10, 25–34 (2015).
[Crossref]

2014 (5)

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9, 48–53 (2014).
[Crossref]

E. E. Narimanov, “Photonic hypercrystals,” Phys. Rev. X 4, 041014 (2014).
[Crossref]

D. Voronov, E. Gullikson, F. Salmassi, T. Warwick, and H. Padmore, “Enhancement of diffraction efficiency via higher-order operation of a multilayer blazed grating,” Opt. Lett. 39, 3157–3160 (2014).
[Crossref]

C. Clavero, “Plasmon-induced hot-electron generation at nanoparticle/metal-oxide interfaces for photovoltaic and photocatalytic devices,” Nat. Photonics 8, 95–103 (2014).
[Crossref]

S.-C. Jiang, X. Xiong, Y.-S. Hu, Y.-H. Hu, G.-B. Ma, R.-W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).

2013 (2)

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
[Crossref]

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref]

2012 (1)

H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science 336, 205–209 (2012).
[Crossref]

2011 (4)

Y. Xu and H. Chen, “Total reflection and transmission by epsilon-near-zero metamaterials with defects,” Appl. Phys. Lett. 98, 113501 (2011).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

L. J. P. Ament, M. Van Veenendaal, T. P. Devereaux, J. P. Hill, and J. V. Den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
[Crossref]

Y. Xu, S. Du, L. Gao, and H. Chen, “Overlapped illusion optics: a perfect lens brings a brighter feature,” New J. Phys. 13, 023010 (2011).
[Crossref]

2010 (2)

2003 (1)

D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[Crossref]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref]

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Alapan, Y.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15, 621–627 (2016).
[Crossref]

Ament, L. J. P.

L. J. P. Ament, M. Van Veenendaal, T. P. Devereaux, J. P. Hill, and J. V. Den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
[Crossref]

Barnakov, Y. A.

Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
[Crossref]

Béri, B.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Bonner, C.

Brodie, J. R.

C. T. Riley, J. S. Smalley, J. R. Brodie, Y. Fainman, D. J. Sirbuly, and Z. Liu, “Near-perfect broadband absorption from hyperbolic metamaterial nanoparticles,” Proc. Natl. Acad. Sci. USA 114, 1264–1268 (2017).
[Crossref]

Brongersma, M. L.

M. L. Brongersma, N. J. Halas, and P. Nordlander, “Plasmon-induced hot carrier science and technology,” Nat. Nanotechnol. 10, 25–34 (2015).
[Crossref]

Cai, W.

W. Cai and V. M. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010), Vol. 10.

Cao, Y.

Y. Fu, C. Shen, Y. Cao, L. Gao, H. Chen, C. Chan, S. A. Cummer, and Y. Xu, “Reversal of transmission and reflection based on acoustic metagratings with integer parity design,” Nat. Commun. 10, 2326 (2019).
[Crossref]

Capasso, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Chan, C.

Y. Fu, C. Shen, Y. Cao, L. Gao, H. Chen, C. Chan, S. A. Cummer, and Y. Xu, “Reversal of transmission and reflection based on acoustic metagratings with integer parity design,” Nat. Commun. 10, 2326 (2019).
[Crossref]

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref]

Chen, H.

Y. Fu, C. Shen, Y. Cao, L. Gao, H. Chen, C. Chan, S. A. Cummer, and Y. Xu, “Reversal of transmission and reflection based on acoustic metagratings with integer parity design,” Nat. Commun. 10, 2326 (2019).
[Crossref]

Y. Xu, Y. Fu, and H. Chen, “Planar gradient metamaterials,” Nat. Rev. Mater. 1, 16067 (2016).
[Crossref]

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref]

Y. Xu, S. Du, L. Gao, and H. Chen, “Overlapped illusion optics: a perfect lens brings a brighter feature,” New J. Phys. 13, 023010 (2011).
[Crossref]

Y. Xu and H. Chen, “Total reflection and transmission by epsilon-near-zero metamaterials with defects,” Appl. Phys. Lett. 98, 113501 (2011).
[Crossref]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref]

Clavero, C.

C. Clavero, “Plasmon-induced hot-electron generation at nanoparticle/metal-oxide interfaces for photovoltaic and photocatalytic devices,” Nat. Photonics 8, 95–103 (2014).
[Crossref]

Cummer, S. A.

Y. Fu, C. Shen, Y. Cao, L. Gao, H. Chen, C. Chan, S. A. Cummer, and Y. Xu, “Reversal of transmission and reflection based on acoustic metagratings with integer parity design,” Nat. Commun. 10, 2326 (2019).
[Crossref]

De Luca, A.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15, 621–627 (2016).
[Crossref]

Den Brink, J. V.

L. J. P. Ament, M. Van Veenendaal, T. P. Devereaux, J. P. Hill, and J. V. Den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
[Crossref]

Devereaux, T. P.

L. J. P. Ament, M. Van Veenendaal, T. P. Devereaux, J. P. Hill, and J. V. Den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
[Crossref]

Dryden, D.

Du, S.

Y. Xu, S. Du, L. Gao, and H. Chen, “Overlapped illusion optics: a perfect lens brings a brighter feature,” New J. Phys. 13, 023010 (2011).
[Crossref]

ElKabbash, M.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15, 621–627 (2016).
[Crossref]

Engheta, N.

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11, 149–158 (2017).
[Crossref]

Facsko, S.

X. Ou, K.-H. Heinig, R. Hübner, J. Grenzer, X. Wang, M. Helm, J. Fassbender, and S. Facsko, “Faceted nanostructure arrays with extreme regularity by self-assembly of vacancies,” Nanoscale 7, 18928–18935 (2015).
[Crossref]

Fainman, Y.

C. T. Riley, J. S. Smalley, J. R. Brodie, Y. Fainman, D. J. Sirbuly, and Z. Liu, “Near-perfect broadband absorption from hyperbolic metamaterial nanoparticles,” Proc. Natl. Acad. Sci. USA 114, 1264–1268 (2017).
[Crossref]

Fang, F.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Fassbender, J.

X. Ou, K.-H. Heinig, R. Hübner, J. Grenzer, X. Wang, M. Helm, J. Fassbender, and S. Facsko, “Faceted nanostructure arrays with extreme regularity by self-assembly of vacancies,” Nanoscale 7, 18928–18935 (2015).
[Crossref]

Feng, J.

Q. Huang, J. Feng, H. Huang, X. Yang, J. Grenzer, K. Huang, S. Zhang, J. Lin, H. Zhou, and T. You, “Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy,” Nat. Commun. 10, 2437 (2019).
[Crossref]

Fernández-Domínguez, A. I.

A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Unrelenting plasmons,” Nat. Photonics 11, 8–10 (2017).
[Crossref]

Fu, Y.

Y. Fu, C. Shen, Y. Cao, L. Gao, H. Chen, C. Chan, S. A. Cummer, and Y. Xu, “Reversal of transmission and reflection based on acoustic metagratings with integer parity design,” Nat. Commun. 10, 2326 (2019).
[Crossref]

Y. Xu, Y. Fu, and H. Chen, “Planar gradient metamaterials,” Nat. Rev. Mater. 1, 16067 (2016).
[Crossref]

Fullerton, E. E.

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9, 48–53 (2014).
[Crossref]

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Gao, L.

Y. Fu, C. Shen, Y. Cao, L. Gao, H. Chen, C. Chan, S. A. Cummer, and Y. Xu, “Reversal of transmission and reflection based on acoustic metagratings with integer parity design,” Nat. Commun. 10, 2326 (2019).
[Crossref]

Y. Xu, S. Du, L. Gao, and H. Chen, “Overlapped illusion optics: a perfect lens brings a brighter feature,” New J. Phys. 13, 023010 (2011).
[Crossref]

Gao, W.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

García-Vidal, F. J.

A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Unrelenting plasmons,” Nat. Photonics 11, 8–10 (2017).
[Crossref]

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Grenzer, J.

Q. Huang, J. Feng, H. Huang, X. Yang, J. Grenzer, K. Huang, S. Zhang, J. Lin, H. Zhou, and T. You, “Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy,” Nat. Commun. 10, 2437 (2019).
[Crossref]

X. Ou, K.-H. Heinig, R. Hübner, J. Grenzer, X. Wang, M. Helm, J. Fassbender, and S. Facsko, “Faceted nanostructure arrays with extreme regularity by self-assembly of vacancies,” Nanoscale 7, 18928–18935 (2015).
[Crossref]

Gu, C.

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref]

Gullikson, E.

Gurkan, U. A.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15, 621–627 (2016).
[Crossref]

Halas, N. J.

M. L. Brongersma, N. J. Halas, and P. Nordlander, “Plasmon-induced hot carrier science and technology,” Nat. Nanotechnol. 10, 25–34 (2015).
[Crossref]

Heinig, K.-H.

X. Ou, K.-H. Heinig, R. Hübner, J. Grenzer, X. Wang, M. Helm, J. Fassbender, and S. Facsko, “Faceted nanostructure arrays with extreme regularity by self-assembly of vacancies,” Nanoscale 7, 18928–18935 (2015).
[Crossref]

Helm, M.

X. Ou, K.-H. Heinig, R. Hübner, J. Grenzer, X. Wang, M. Helm, J. Fassbender, and S. Facsko, “Faceted nanostructure arrays with extreme regularity by self-assembly of vacancies,” Nanoscale 7, 18928–18935 (2015).
[Crossref]

Hill, J. P.

L. J. P. Ament, M. Van Veenendaal, T. P. Devereaux, J. P. Hill, and J. V. Den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
[Crossref]

Hinczewski, M.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15, 621–627 (2016).
[Crossref]

Hou, B.

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref]

Hu, Y.-H.

S.-C. Jiang, X. Xiong, Y.-S. Hu, Y.-H. Hu, G.-B. Ma, R.-W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).

Hu, Y.-S.

S.-C. Jiang, X. Xiong, Y.-S. Hu, Y.-H. Hu, G.-B. Ma, R.-W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).

Huang, H.

Q. Huang, J. Feng, H. Huang, X. Yang, J. Grenzer, K. Huang, S. Zhang, J. Lin, H. Zhou, and T. You, “Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy,” Nat. Commun. 10, 2437 (2019).
[Crossref]

Huang, K.

Q. Huang, J. Feng, H. Huang, X. Yang, J. Grenzer, K. Huang, S. Zhang, J. Lin, H. Zhou, and T. You, “Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy,” Nat. Commun. 10, 2437 (2019).
[Crossref]

Huang, Q.

Q. Huang, J. Feng, H. Huang, X. Yang, J. Grenzer, K. Huang, S. Zhang, J. Lin, H. Zhou, and T. You, “Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy,” Nat. Commun. 10, 2437 (2019).
[Crossref]

Hübner, R.

X. Ou, K.-H. Heinig, R. Hübner, J. Grenzer, X. Wang, M. Helm, J. Fassbender, and S. Facsko, “Faceted nanostructure arrays with extreme regularity by self-assembly of vacancies,” Nanoscale 7, 18928–18935 (2015).
[Crossref]

Ilker, E.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15, 621–627 (2016).
[Crossref]

Iorsh, I.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
[Crossref]

Jacob, Z.

H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science 336, 205–209 (2012).
[Crossref]

M. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. Bonner, M. Mayy, Z. Jacob, and E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35, 1863–1865 (2010).
[Crossref]

Jiang, S.-C.

S.-C. Jiang, X. Xiong, Y.-S. Hu, Y.-H. Hu, G.-B. Ma, R.-W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).

Kan, J. J.

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9, 48–53 (2014).
[Crossref]

Kats, M. A.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Kivshar, Y.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
[Crossref]

Kretzschmar, I.

H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science 336, 205–209 (2012).
[Crossref]

Krishnamoorthy, H. N.

H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science 336, 205–209 (2012).
[Crossref]

Lai, Y.

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref]

Lawrence, M.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Li, H.

Li, J.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref]

Liberal, I.

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11, 149–158 (2017).
[Crossref]

Lin, J.

Q. Huang, J. Feng, H. Huang, X. Yang, J. Grenzer, K. Huang, S. Zhang, J. Lin, H. Zhou, and T. You, “Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy,” Nat. Commun. 10, 2437 (2019).
[Crossref]

Liu, F.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Liu, Z.

C. T. Riley, J. S. Smalley, J. R. Brodie, Y. Fainman, D. J. Sirbuly, and Z. Liu, “Near-perfect broadband absorption from hyperbolic metamaterial nanoparticles,” Proc. Natl. Acad. Sci. USA 114, 1264–1268 (2017).
[Crossref]

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9, 48–53 (2014).
[Crossref]

Lu, D.

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9, 48–53 (2014).
[Crossref]

Ma, G.-B.

S.-C. Jiang, X. Xiong, Y.-S. Hu, Y.-H. Hu, G.-B. Ma, R.-W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).

Martín-Moreno, L.

A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Unrelenting plasmons,” Nat. Photonics 11, 8–10 (2017).
[Crossref]

Mayy, M.

Menon, V. M.

H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science 336, 205–209 (2012).
[Crossref]

Narimanov, E.

H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science 336, 205–209 (2012).
[Crossref]

M. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. Bonner, M. Mayy, Z. Jacob, and E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35, 1863–1865 (2010).
[Crossref]

Narimanov, E. E.

E. E. Narimanov, “Photonic hypercrystals,” Phys. Rev. X 4, 041014 (2014).
[Crossref]

Nataraj, G.

Noginov, M.

Nordlander, P.

M. L. Brongersma, N. J. Halas, and P. Nordlander, “Plasmon-induced hot carrier science and technology,” Nat. Nanotechnol. 10, 25–34 (2015).
[Crossref]

Ou, X.

X. Ou, K.-H. Heinig, R. Hübner, J. Grenzer, X. Wang, M. Helm, J. Fassbender, and S. Facsko, “Faceted nanostructure arrays with extreme regularity by self-assembly of vacancies,” Nanoscale 7, 18928–18935 (2015).
[Crossref]

Padmore, H.

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref]

Peng, R.-W.

S.-C. Jiang, X. Xiong, Y.-S. Hu, Y.-H. Hu, G.-B. Ma, R.-W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).

Poddubny, A.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
[Crossref]

Riley, C. T.

C. T. Riley, J. S. Smalley, J. R. Brodie, Y. Fainman, D. J. Sirbuly, and Z. Liu, “Near-perfect broadband absorption from hyperbolic metamaterial nanoparticles,” Proc. Natl. Acad. Sci. USA 114, 1264–1268 (2017).
[Crossref]

Salmassi, F.

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref]

Schurig, D.

D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[Crossref]

Shalaev, V. M.

W. Cai and V. M. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010), Vol. 10.

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref]

Shen, C.

Y. Fu, C. Shen, Y. Cao, L. Gao, H. Chen, C. Chan, S. A. Cummer, and Y. Xu, “Reversal of transmission and reflection based on acoustic metagratings with integer parity design,” Nat. Commun. 10, 2326 (2019).
[Crossref]

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref]

Sirbuly, D. J.

C. T. Riley, J. S. Smalley, J. R. Brodie, Y. Fainman, D. J. Sirbuly, and Z. Liu, “Near-perfect broadband absorption from hyperbolic metamaterial nanoparticles,” Proc. Natl. Acad. Sci. USA 114, 1264–1268 (2017).
[Crossref]

Smalley, J. S.

C. T. Riley, J. S. Smalley, J. R. Brodie, Y. Fainman, D. J. Sirbuly, and Z. Liu, “Near-perfect broadband absorption from hyperbolic metamaterial nanoparticles,” Proc. Natl. Acad. Sci. USA 114, 1264–1268 (2017).
[Crossref]

Smith, D.

D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[Crossref]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref]

Sreekanth, K. V.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15, 621–627 (2016).
[Crossref]

Strangi, G.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15, 621–627 (2016).
[Crossref]

Sun, C.

S.-C. Jiang, X. Xiong, Y.-S. Hu, Y.-H. Hu, G.-B. Ma, R.-W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).

Tetienne, J. P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Van Veenendaal, M.

L. J. P. Ament, M. Van Veenendaal, T. P. Devereaux, J. P. Hill, and J. V. Den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
[Crossref]

Voronov, D.

Wang, M.

S.-C. Jiang, X. Xiong, Y.-S. Hu, Y.-H. Hu, G.-B. Ma, R.-W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).

Wang, X.

X. Ou, K.-H. Heinig, R. Hübner, J. Grenzer, X. Wang, M. Helm, J. Fassbender, and S. Facsko, “Faceted nanostructure arrays with extreme regularity by self-assembly of vacancies,” Nanoscale 7, 18928–18935 (2015).
[Crossref]

Warwick, T.

Xiong, X.

S.-C. Jiang, X. Xiong, Y.-S. Hu, Y.-H. Hu, G.-B. Ma, R.-W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).

Xu, Y.

Y. Fu, C. Shen, Y. Cao, L. Gao, H. Chen, C. Chan, S. A. Cummer, and Y. Xu, “Reversal of transmission and reflection based on acoustic metagratings with integer parity design,” Nat. Commun. 10, 2326 (2019).
[Crossref]

Y. Xu, Y. Fu, and H. Chen, “Planar gradient metamaterials,” Nat. Rev. Mater. 1, 16067 (2016).
[Crossref]

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref]

Y. Xu and H. Chen, “Total reflection and transmission by epsilon-near-zero metamaterials with defects,” Appl. Phys. Lett. 98, 113501 (2011).
[Crossref]

Y. Xu, S. Du, L. Gao, and H. Chen, “Overlapped illusion optics: a perfect lens brings a brighter feature,” New J. Phys. 13, 023010 (2011).
[Crossref]

Yang, B.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Yang, X.

Q. Huang, J. Feng, H. Huang, X. Yang, J. Grenzer, K. Huang, S. Zhang, J. Lin, H. Zhou, and T. You, “Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy,” Nat. Commun. 10, 2437 (2019).
[Crossref]

You, T.

Q. Huang, J. Feng, H. Huang, X. Yang, J. Grenzer, K. Huang, S. Zhang, J. Lin, H. Zhou, and T. You, “Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy,” Nat. Commun. 10, 2437 (2019).
[Crossref]

Yu, N.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Zhang, S.

Q. Huang, J. Feng, H. Huang, X. Yang, J. Grenzer, K. Huang, S. Zhang, J. Lin, H. Zhou, and T. You, “Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy,” Nat. Commun. 10, 2437 (2019).
[Crossref]

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Zhou, H.

Q. Huang, J. Feng, H. Huang, X. Yang, J. Grenzer, K. Huang, S. Zhang, J. Lin, H. Zhou, and T. You, “Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy,” Nat. Commun. 10, 2437 (2019).
[Crossref]

Zhu, G.

Appl. Phys. Lett. (1)

Y. Xu and H. Chen, “Total reflection and transmission by epsilon-near-zero metamaterials with defects,” Appl. Phys. Lett. 98, 113501 (2011).
[Crossref]

Nanoscale (1)

X. Ou, K.-H. Heinig, R. Hübner, J. Grenzer, X. Wang, M. Helm, J. Fassbender, and S. Facsko, “Faceted nanostructure arrays with extreme regularity by self-assembly of vacancies,” Nanoscale 7, 18928–18935 (2015).
[Crossref]

Nat. Commun. (3)

Q. Huang, J. Feng, H. Huang, X. Yang, J. Grenzer, K. Huang, S. Zhang, J. Lin, H. Zhou, and T. You, “Realization of wafer-scale nanogratings with sub-50 nm period through vacancy epitaxy,” Nat. Commun. 10, 2437 (2019).
[Crossref]

Y. Xu, C. Gu, B. Hou, Y. Lai, J. Li, and H. Chen, “Broadband asymmetric waveguiding of light without polarization limitations,” Nat. Commun. 4, 2561 (2013).
[Crossref]

Y. Fu, C. Shen, Y. Cao, L. Gao, H. Chen, C. Chan, S. A. Cummer, and Y. Xu, “Reversal of transmission and reflection based on acoustic metagratings with integer parity design,” Nat. Commun. 10, 2326 (2019).
[Crossref]

Nat. Mater. (2)

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15, 621–627 (2016).
[Crossref]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref]

Nat. Nanotechnol. (2)

M. L. Brongersma, N. J. Halas, and P. Nordlander, “Plasmon-induced hot carrier science and technology,” Nat. Nanotechnol. 10, 25–34 (2015).
[Crossref]

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9, 48–53 (2014).
[Crossref]

Nat. Photonics (4)

A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Unrelenting plasmons,” Nat. Photonics 11, 8–10 (2017).
[Crossref]

C. Clavero, “Plasmon-induced hot-electron generation at nanoparticle/metal-oxide interfaces for photovoltaic and photocatalytic devices,” Nat. Photonics 8, 95–103 (2014).
[Crossref]

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7, 948–957 (2013).
[Crossref]

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11, 149–158 (2017).
[Crossref]

Nat. Rev. Mater. (1)

Y. Xu, Y. Fu, and H. Chen, “Planar gradient metamaterials,” Nat. Rev. Mater. 1, 16067 (2016).
[Crossref]

New J. Phys. (1)

Y. Xu, S. Du, L. Gao, and H. Chen, “Overlapped illusion optics: a perfect lens brings a brighter feature,” New J. Phys. 13, 023010 (2011).
[Crossref]

Opt. Lett. (2)

Phys. Rev. Lett. (3)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref]

D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[Crossref]

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Phys. Rev. X (2)

E. E. Narimanov, “Photonic hypercrystals,” Phys. Rev. X 4, 041014 (2014).
[Crossref]

S.-C. Jiang, X. Xiong, Y.-S. Hu, Y.-H. Hu, G.-B. Ma, R.-W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4, 021026 (2014).

Proc. Natl. Acad. Sci. USA (1)

C. T. Riley, J. S. Smalley, J. R. Brodie, Y. Fainman, D. J. Sirbuly, and Z. Liu, “Near-perfect broadband absorption from hyperbolic metamaterial nanoparticles,” Proc. Natl. Acad. Sci. USA 114, 1264–1268 (2017).
[Crossref]

Rev. Mod. Phys. (1)

L. J. P. Ament, M. Van Veenendaal, T. P. Devereaux, J. P. Hill, and J. V. Den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
[Crossref]

Science (3)

H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science 336, 205–209 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref]

Other (1)

W. Cai and V. M. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010), Vol. 10.

Supplementary Material (1)

NameDescription
» Supplement 1       Supplement 1: the document provides supplementary information to Photonic hyperinterfaces for light manipulations.

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Figures (4)

Fig. 1.
Fig. 1. Concepts of the SMMs and the photonic hyperinterfaces. (a) Deep-subwavelength silver/silicon multilayer structure of HMMs. (b) Left, structure of the designed SMMs by rotating the initial HMMs; right, the rotated HMMs are equivalent to two homogeneous media, MA and MB, based on EMT. In SMMs, there are two different hyperinterfaces, ${{\rm{IF}}_{\rm AB}}$ (red dashed arrow) and ${{\rm{IF}}_{\rm BA}}$ (white dashed arrow). (c) Real parts of the effective permittivity of initial HMMs. Two different types of HMMs are seen over the whole wavelength range, with the critical wavelength $\lambda = 623$ nm. (d) Image of a 2-inch wafer-scale zigzag substrate. (e) Cross-sectional TEM images (marked by blue dashed lines) of the zigzag patterns. (f) Top-down SEM images at different locations (marked by green dashed lines). (g) Cross-sectional TEM image of the fabricated SMM (hyperinterfaces).
Fig. 2.
Fig. 2. (a) Absorption spectra of MA (MB) and (b) absorption spectra of the SMM. In (b), the purple and white dashed lines indicate the positions of the critical point and the minimum absorption point at different incident angles, respectively. (c) Absorption curves of MA and the SMM when $\theta = {0^ \circ}$. (d) Intersection angle $\beta$ of HMMs over the wavelength range from 400 to 800 nm. (e) Measured absorption spectra of the fabricated SMM and the initial HMM at an incident angle $\theta = {30^ \circ}$. The blue curve is for the initial HMM, and the red is for the SMM.
Fig. 3.
Fig. 3. Physics behind this extraordinary optical absorption. (a) and (b) show the IFCs (blue curves) of the initial HMMs at $\lambda =612$ and 765 nm, respectively. The orange circles denote the IFCs of the air, the green dashed lines denote the symmetry axes of the IFCs (hyperbolas), and the black dashed lines denote the asymptotes of the IFCs. (c) and (d) show the rotated IFCs of the initial HMMs by the geometric angle $\alpha$ (purple curves) and ${-}\alpha$ (blue curves), at $\lambda =612$ and 765 nm, respectively. The red/black dashed arrow denotes the direction of energy flow of the incident/refraction light, occurring at the hyperinterface ${{\rm{IF}}_{\rm AB}}$ or ${{\rm{IF}}_{\rm BA}}$. (e) and (f) show the simulated time-averaged energy flow patterns in the SMM for a normally incident TM wave when $\lambda =765$ and 612 nm, respectively. In (e) and (f), (E1)–(E5) and (F1)–(F5) show the physical process of the clipping and recombination of energy flow inside the SMM, resulting from the tailored dispersion relations of the initial HMMs by rotating angle $\alpha$.
Fig. 4.
Fig. 4. Simulated absorption curves of the SMM as a function of (a) tailored angle $\alpha$ and (b) period $p$ of the HMM cells.

Equations (2)

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ε ( α ) = [ ε x x ε x y ε y x ε y y ] ,
A M A ( ω ) = A M B ( ω ) = 1 | 2 / ( 1 + ε xx ( ω ) sin 2 θ ε u ( ω ) ε v ( ω ) cos 2 θ ) 1 | 2 ,

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