^{1}and S. Foteinopoulou

^{1,a)}

### Abstract

We present a route to near-perfect absorption in compact photonic-crystal (PC) structures constructed from strongly absorbing media that are typically highly reflective in bulk form. Our analysis suggests that the key underlying mechanism in such PC superabsorbers is the existence of a PC-band-edge reflectionless condition. Although the latter is by default uncharacteristic in photonic crystals, we propose here a clear recipe on how such condition can be met by tuning the structural characteristics of one-dimensional lossy PC structures. Based on this recipe, we constructed a realizable three-layer SiC- -SiC PC operating within the Reststrahlen band of SiC. We demonstrate near-perfect absorption in this prototype of total thickness smaller than , where more than 90% of the impinging light is absorbed by the top deep-subwavelength layer of thickness . We believe our study will inspire new photonic-crystal-based designs for extreme absorption harnessing across the electromagnetic spectrum.

Financial support for the Ph.D. studentship of G. C. R. Devarapu by the College of Engineering, Mathematics and Physical Sciences (CEMPS) University of Exeter is acknowledged.

I. INTRODUCTION

II. PHOTONIC BAND-EDGE AND REFLECTIVITY

III. NEAR-BAND EDGE NEAR-ZERO REFLECTION AND ABSORPTION HARNESSING

IV. COMPACT SUB-λ PC-BASED ABSORBER

V. PRACTICALLY REALIZABLE SUPERABSORBER DESIGNS

VI. CONCLUSION

### Key Topics

- Photonic crystals
- 36.0
- Lattice constants
- 23.0
- Interface structure
- 10.0
- Absorption spectra
- 8.0
- Electric fields
- 8.0

## Figures

(a) Schematics of the SiC-air 1D-PC with the geometric parameters indicated. (b) Spectral response of the real (solid) and imaginary (dashed) parts of the SiC permittivity model of Eq. (3) . (c) Absorption (dashed line) and reflection (solid line) for a thick bulk SiC block.

(a) Schematics of the SiC-air 1D-PC with the geometric parameters indicated. (b) Spectral response of the real (solid) and imaginary (dashed) parts of the SiC permittivity model of Eq. (3) . (c) Absorption (dashed line) and reflection (solid line) for a thick bulk SiC block.

Spectral response of the energy velocity at the interface of a semi-infinite SiC-air PCs structure is shown as solid lines. The dashed lines depict the corresponding values for the same PCs but with 50% of their entry face being cut-off. The results in (a), (b), and (c) represent the PC cases with a lattice constant of a equal to 5 , 8 , and 10 , respectively. In all cases, the interface-energy velocity value of the reflectionless condition, of Eq. (1) , is depicted with dotted lines. Note, all energy velocity values are expressed in terms of the speed of light c. The vertical solid lines represent the spectral position of the absorption peaks that we will observe in Fig. 5 .

Spectral response of the energy velocity at the interface of a semi-infinite SiC-air PCs structure is shown as solid lines. The dashed lines depict the corresponding values for the same PCs but with 50% of their entry face being cut-off. The results in (a), (b), and (c) represent the PC cases with a lattice constant of a equal to 5 , 8 , and 10 , respectively. In all cases, the interface-energy velocity value of the reflectionless condition, of Eq. (1) , is depicted with dotted lines. Note, all energy velocity values are expressed in terms of the speed of light c. The vertical solid lines represent the spectral position of the absorption peaks that we will observe in Fig. 5 .

The energy-velocity gradient is shown for two PC systems with a lattice constant equal to 5 and 10 in panels (a) and (b), respectively. The horizontal dashed line represents the reflectionless condition value dictated by Eq. (2) . Note the coordinate within the PC entry layer, x–, is expressed in terms of the lattice constant a, while the energy velocity gradient is expressed in terms of c/a, with c being the speed of light.

The energy-velocity gradient is shown for two PC systems with a lattice constant equal to 5 and 10 in panels (a) and (b), respectively. The horizontal dashed line represents the reflectionless condition value dictated by Eq. (2) . Note the coordinate within the PC entry layer, x–, is expressed in terms of the lattice constant a, while the energy velocity gradient is expressed in terms of c/a, with c being the speed of light.

Reflection (in color-map) versus termination ratio, and free space wavelength, calculated from TMM. Panels (a) and (b) represent the result corresponding to the semi-infinite PCs with lattice constant a, of 5 and 10 , respectively. Same is shown in (c) and (d) but for 200 μm-thick PCs.

Reflection (in color-map) versus termination ratio, and free space wavelength, calculated from TMM. Panels (a) and (b) represent the result corresponding to the semi-infinite PCs with lattice constant a, of 5 and 10 , respectively. Same is shown in (c) and (d) but for 200 μm-thick PCs.

Absorptance versus free space wavelength, , for three 200 thick SiC-air PCs of 0.05 filling ratio and 50% front layer truncation. The solid, dashed, and dotted-dashed curves correspond to PCs with a lattice constant a equal to 10 , 8 , and 5 , respectively. The front SiC layer is terminated to half its original size.

Absorptance versus free space wavelength, , for three 200 thick SiC-air PCs of 0.05 filling ratio and 50% front layer truncation. The solid, dashed, and dotted-dashed curves correspond to PCs with a lattice constant a equal to 10 , 8 , and 5 , respectively. The front SiC layer is terminated to half its original size.

Complex band structure (free space wavelength versus Bloch wavevector q) for the PC cases of lattice constant a, 5 [in (a) and (b)] and 10 [in (c) and (d)]. The respective reflectionless-condition wavelengths are indicated with horizontal dashed lines. Note, both the real and imaginary parts of the Bloch wave vector q are expressed in terms of .

Complex band structure (free space wavelength versus Bloch wavevector q) for the PC cases of lattice constant a, 5 [in (a) and (b)] and 10 [in (c) and (d)]. The respective reflectionless-condition wavelengths are indicated with horizontal dashed lines. Note, both the real and imaginary parts of the Bloch wave vector q are expressed in terms of .

Dissipated to incident power ratio versus free space wavelength, , for the 200 μm thick SiC-air PCs with 50% truncated front layer, within the first PC unit cells. The result in (a) [(b)] corresponds to the PC case with 5 [10 ] lattice constant. The respective absorptance is shown for reference with the dark solid line. Note, the total number of PC unit cells, N, is 40 for the case in (a) and 20 for the case in (b).

Dissipated to incident power ratio versus free space wavelength, , for the 200 μm thick SiC-air PCs with 50% truncated front layer, within the first PC unit cells. The result in (a) [(b)] corresponds to the PC case with 5 [10 ] lattice constant. The respective absorptance is shown for reference with the dark solid line. Note, the total number of PC unit cells, N, is 40 for the case in (a) and 20 for the case in (b).

Absorptance enhancement of the two terminated SiC-air PCs with lattice constant a, 5 (dotted-dashed line with diamonds), and 10 (solid line with filled circles) with respect to the absorption of a SiC block about a wavelength-thick is plotted against the total thickness of SiC encountered by the EM wave as it travels through the PC.

Absorptance enhancement of the two terminated SiC-air PCs with lattice constant a, 5 (dotted-dashed line with diamonds), and 10 (solid line with filled circles) with respect to the absorption of a SiC block about a wavelength-thick is plotted against the total thickness of SiC encountered by the EM wave as it travels through the PC.

(a) Schematics of the compact PC-based design with all structural information indicated. (b) Reflectance (color-map) versus free space wavelength and front-layer truncation ratio . (c) Absorptance (solid lines) and reflectance (dotted lines), for the design in (a) with (c) [(d)] showing the case of [ ]. For comparison absorptance through a single layer is also shown for bulk SiC (dotted-dashed) and an ultra-thin SiC film as thick as the front layer of the structure of Fig. 9(d) . The vertical line designates the SiC Reststrahlen band-edge.

(a) Schematics of the compact PC-based design with all structural information indicated. (b) Reflectance (color-map) versus free space wavelength and front-layer truncation ratio . (c) Absorptance (solid lines) and reflectance (dotted lines), for the design in (a) with (c) [(d)] showing the case of [ ]. For comparison absorptance through a single layer is also shown for bulk SiC (dotted-dashed) and an ultra-thin SiC film as thick as the front layer of the structure of Fig. 9(d) . The vertical line designates the SiC Reststrahlen band-edge.

Electric field amplitude, , profiles (left vertical axis) versus the coordinate x within the compact superabsorber design. The depicted profiles are normalized with the incident electric field amplitude . The dotted lines represent the -decay, from the front to the back layer, as predicted by the complex band structure of Fig. 6 . The solid circles represent the ratio of incident power that is absorbed in each layer (see right vertical axis for values). Panels (a) and (b) represent the respective cases with front-to-back-layer truncation ratio of 0.05 and 0.5.

Electric field amplitude, , profiles (left vertical axis) versus the coordinate x within the compact superabsorber design. The depicted profiles are normalized with the incident electric field amplitude . The dotted lines represent the -decay, from the front to the back layer, as predicted by the complex band structure of Fig. 6 . The solid circles represent the ratio of incident power that is absorbed in each layer (see right vertical axis for values). Panels (a) and (b) represent the respective cases with front-to-back-layer truncation ratio of 0.05 and 0.5.

(a) Schematics of the realizable compact PC with all structural information indicated. (b) Same as the design in (a) but resting on a substrate made from the spacer material.

(a) Schematics of the realizable compact PC with all structural information indicated. (b) Same as the design in (a) but resting on a substrate made from the spacer material.

Energy velocity versus free space wavelength at the interface of a semi-infinite SiC- PC of lattice constant a = 3.5 μm and SiC filling ratio equal to 0.065 (dashed lines). The required optimum of Eq. (1) is shown with a solid line. The inset highlights the wavelength region where the interface energy velocity intersects with the required optimum value.

Energy velocity versus free space wavelength at the interface of a semi-infinite SiC- PC of lattice constant a = 3.5 μm and SiC filling ratio equal to 0.065 (dashed lines). The required optimum of Eq. (1) is shown with a solid line. The inset highlights the wavelength region where the interface energy velocity intersects with the required optimum value.

Reflectance (color-map), versus free space wavelength , and front-layer truncation ratio, for the SiC- system. In (a), the result of the semi-infinite PC is shown. In (b), the corresponding compact system of Fig. 11(a) is shown.

Reflectance (color-map), versus free space wavelength , and front-layer truncation ratio, for the SiC- system. In (a), the result of the semi-infinite PC is shown. In (b), the corresponding compact system of Fig. 11(a) is shown.

Absorptance [(a)] and reflectance [(b)] versus free space wavelength for the compact SiC- -SiC system corresponding to a PC with a lattice constant a = 3.5 μm and a SiC filling ratio of f = 0.065. Two cases of front-layer truncation are shown: the case of 0.05 truncation ratio with solid lines and the case of 0.5 truncation ratio with dashed lines. The corresponding circles and diamonds represent the respective result when the compact three-layer system rests on a 40 μm thick substrate made of .

Absorptance [(a)] and reflectance [(b)] versus free space wavelength for the compact SiC- -SiC system corresponding to a PC with a lattice constant a = 3.5 μm and a SiC filling ratio of f = 0.065. Two cases of front-layer truncation are shown: the case of 0.05 truncation ratio with solid lines and the case of 0.5 truncation ratio with dashed lines. The corresponding circles and diamonds represent the respective result when the compact three-layer system rests on a 40 μm thick substrate made of .

## Tables

Outline of performance of the compact superabsorber of Fig. 11(a) for two front-layer truncation ratios [A stands for absorptance and DPR stands for dissipated power ratio].

Outline of performance of the compact superabsorber of Fig. 11(a) for two front-layer truncation ratios [A stands for absorptance and DPR stands for dissipated power ratio].

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