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Abstract
In this work we numerically and experimentally characterize a nanorod-based metasurface, demonstrating efficient linear-to-circular polarization conversion in the technologically important mid-infrared region of the spectrum. Measurement of the Stokes parameters confirms a very high degree of circular polarization (with a value of axial ratio between 0.9 to 1) of reflected light over the wavelength range from 3.8µm to 4.8µm, with an average conversion efficiency of 80% and a maximum value of 91%. Such metasurfaces, which have subwavelength thickness, could potentially replace conventional quarter wave plates, but could also be used for circular dichroism spectroscopy in the mid-infrared region, allowing the relative easy characterization of important molecules such as proteins.
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1. Introduction
Metasurfaces are a new class of artificial structure that are engineered at the sub-wavelength scale to allow for effective-medium properties that go beyond those of their constituent elements. Metasurfaces can be exploited to enhance an anisotropic optical response to orthogonal polarizations, introducing flexibly-tailored amplitude and phase shifts to achieve light manipulation [1–3]. Due to their subwavelength thicknesses, metasurface have been investigated as a potential means of replacing bulk optic components such as quarter wave plates [4–9], polarizers [10–12] and flat lenses [13–15]. Over the last few years, much research has been focused on realizing metasurface-based quarter wave plates from the microwave to terahertz frequencies [16–20]. However, circular polarization is particularly useful for infrared circular dichroism spectroscopy. Under illumination with circularly polarized light, chiral molecules absorb different amounts dependent on their handedness, and important information about the structure of chiral biomolecules, such as proteins, can be obtained if this effect can be exploited in the infrared where many important biomolecules have strong vibrational resonances [21]. However, as most infrared light sources are linearly- or un- polarized, components that allow efficient linear-to-circular polarization are required. In addition, the strong near-fields associated with metasurfaces could also ultimately be exploited for high sensitivity measurements.
Recent results have shown that uniform metasurfaces designed with an array of identical metallic resonators, such as rods [5,7,22–24], crosses [8,9,25,26] or complementary structures [19,27], can be exploited to enable light manipulation in transmission mode. The individual resonators support an anisotropic optical response, as shown in Fig. 1(a), that originates from the dipolar resonances of the resonators under excitation of two orthogonal electric field components, decomposed from linearly polarized incident light. Through the optimization of the resonator geometries, the two components can have approximately equal amplitude and a 90 degree phase delay, therefore, linear-to-circular polarization conversion can be achieved over a relatively narrow wavelength range (marked in the grey area in Fig. 1(a)), determined by the overlapping optical response of the electric field vector components.
Fig. 1. The operation principle of three typical types of metasurfaces-based quarter wave plate. Amplitude and phase spectrum for orthogonal electric field components (${E_v}$, ${E_h}$) of (a) uniform metasurface in transmission mode (b) non-uniform metasurface in transmission mode (c) uniform metasurface in reflection mode. ${T_v}$, ${T_h}$, ${R_v}$, ${R_h}$ represent the transitivity or reflectivity of two orthogonal electric field components, $phase{\; }(v )$ and $phase{\; }(h )$ are the corresponding phase information. Grey area represents the potential wavelength range that may achieve linear-to-circular polarization conversion.
As uniform metasurfaces based on an array of identical resonators have narrow bandwidths, Yu et al. [2] investigated broadband polarization manipulation in transmission mode using a non-uniform metasurface consisting of two subunits displaced relative to each other. Eight V-shaped antennas, with varying orientation angle, in each subunit provided broadened wavelength operation due to the combined resonances. The operation principle of non-uniform metasurfaces is shown in Fig. 1(b). As the subunits are assembled from the same resonators, the amplitude of transmission stays equal over a broad wavelength range for both electric field components. The phase difference between the two polarization components of the light is induced by the offset between subunits, rather than a dipole resonance from a single element. Upon excitation of incident light, the metasurface acts like a quarter wave plate, producing two co-propagating waves with equal amplitude and 90 degree phase difference, bending the light away from the original incident direction. However, one limitation of this approach is that power can dissipate quickly in the metasurface, and the scattered circularly polarized light intensity is only 10% of the incident light in this particular case.
Recently, Chang et al. [7] proposed a novel concept (Fig. 1(c)), based on an array of micron-sized rod resonators, to enable broadband linear-to-circular polarization conversion with relatively low loss in reflection mode in the terahertz region. In this case, only one of the light components can interact with the metasurface, with an associated strong minima in reflection on resonance that introduces a nonlinear phase dispersion (the optical response is indicated with the red line in Fig. 1. (c)). The mechanism of the observed nonlinear phase modulation is due to the coupling between unit cells and between incoming and outgoing light, and can be understood by modelling the system using coupled mode theory [28] as discussed in [7]. The other component of incident light is nonresonant, with near unit reflected efficiency and linear phase dispersion. As indicated in Fig. 1(c), an approximately constant phase difference between the orthogonal components over the off-resonance wavelength range allows broadband polarization manipulation.
In this work, we investigate a metasurface consisting of an array of nanorod resonators, building on the work on metasurfaces for the terahertz region [7], for efficient linear-to-circular convertor in the mid-infrared spectrum in reflection mode. Simulations results show the metasurface provides broadband linear-to-circular polarization conversion, with near unity conversion efficiency. The polarization state of the reflected beam is obtained by measuring four Stokes parameters, which has not been done in previous work in the mid-infrared region.
2. Design and results
2.1 Simulation results
A schematic diagram, and scanning electron microscope (SEM) image, of the metasurface are shown in Figs. 2(a) and (b) respectively. Simulations were undertaken using the FDTD software Lumerical, with a single unit cell modeled with periodic boundary conditions in the x- and y-directions over a period of 2.6µm, and a light source linearly polarized in the y-direction incident along the z-direction. PML absorbing boundary conditions are set along the z direction to absorb incident light with minimal reflections.
Fig. 2. Schematic of nanorod-based metasurface. (a) The schematic of one unit cell of nanorod-based metasurface. The device is placed on the x-y plane and light travels along z direction. (b) SEM photo of fabricated sample.
The structure of a unit cell consists of a 100nm thick aluminum ground plane at the bottom, followed by a 600nm thick silicon dioxide layer, with a 3.2µm by 400nm gold rod resonator oriented at 45 degrees to the edges of the device (x axis) on the top. Values of gold and aluminum conductivity were taken as $4.5 \times {10^7}/\mathrm{\Omega}m$ and $3.75 \times {10^7}/\mathrm{\Omega}m$ respectively to be consistent with those used in previously reported mid-infrared studies [29–31], with the refractive index of silicon dioxide taken from the Lumerical database (in turn taken from Palik [[32]). The mesh size was set as 4nm in z direction, with the mesh boundary along the interface of metal and silicon dioxide to guarantee the accuracy of simulation results.
The relative orientation of the two orthogonal electric field components is indicated in Fig. 3(a), and Fig. 3(b) and (c) show the simulated amplitude and phase spectral response of the components, at normal incidence, in reflection mode. With the incident light parallel to the rod, three distinct resonances are observed in the simulated reflection spectrum (Fig. 3(b)). The resonance at 9.4µm originates from the phonon absorption of silicon dioxide, and the wavelength of this resonance does not vary with the shape of the resonators. The resonances at 3.4µm and 7.9µm, however, are based on different underlying mechanisms. The resonance at 3.4µm is consistent with the gap surface-plasmon (GSP) mode [33,34], which can be more generally understood as a magnetic resonance with the magnetic field mostly concentrated in the silicon dioxide spacer layer (as shown in inset of Fig. 3(b)), and which results from the anti-symmetric surface current distribution in the two metal layers. The GSP mode is a result of complex near-field coupling between the top and bottom metal layers as well as adjacent resonators, therefore, the resonance wavelength is controlled by spacer thickness and periodicity, as indicated in Figs. 2(e) and (f), where the resonance at lower wavelength shows significant change as the periodicity and spacer thickness increase. In comparison, the resonance at 7.9µm, doesn’t show the same magnetic enhancement and localization, and can be understood as a Fabry-Perot cavity like mode where the two layers of metal are only linked by multi-reflection in the spacer layer, with negligible near-field coupling [35]. A minima in reflection indicates that the incident light is trapped by the metasurface as a result of destructive interference between multi-reflection and direct reflection from metasurface. This is determined by the dispersive properties of dielectric spacer and shape of resonators. In Fig. 3(b) the calculated reflectivity based on simple interference theory with no near-field coupling included, is plotted as a grey line (further details of the interference calculations can be found in Section 1 of the Electronic Supplementary Material (ESM)). This calculated reflectivity has a large minima at a wavelength of 8.1µm, but not at a wavelength of 3.6µm. This is consistent with the resonance observed in the Lumerical simulations at around at 7.9µm being a Fabry-Perot cavity like mode induced by multi-reflection, whereas the resonances at 3.6µm is GSP mode excited by near-field coupling. The Fabry-Perot mode observed at 4.8µm in the interference calculations cannot be excited with normal incidence light, and as is therefore not captured in the Lumerical simulations, which for simplicity were undertaken at normal incidence.
Fig. 3. Simulation results of nanorod-based metasurface. (a) Schematic showing the polarization of the two orthogonal components in simulation. ${E_\parallel }$ (${E_ \bot }$) stands for the incident light is polarized parallel (orthogonal) to rod. (b) Amplitude and (c) phase spectrum under excitation of eignmodes by FDTD full-wave simulation. The insets in (b) is the $|H |$ near-field profile of cross section at y = 0 plane. (d) The retrieved normalized circularly polarized light reflected from metasurface. (e) and (f) are reflectivity spectrum of ${E_\parallel }$ as a function of periodicity and thickness of silicon dioxide, respectively.
As shown in Fig. 3(b), the metasurface exhibits an anisotropic optical response for the two incident orthogonal polarizations, whilst at the same time near unity reflectivity is obtained in the off-resonance between wavelengths of approximately 4µm to 7µm. When the incident electric field component is parallel to rod (marked with red curve), the two distinct resonances excited at 3.4µm and 7.9µm result in decreases in the simulated phase, as shown in Fig. 3(c). On the other hand, when the field is orthogonal to the rod (marked with blue curve), there is negligible interaction between the light and resonators and the resulting phase spectrum for ${E_ \bot }$, also shown in Fig. 3(c), is smoothly changing with relatively weak wavelength dispersion over a wide range. In the off-resonance wavelength range indicated in grey region in Fig. 3(c), from approximately 4µm to 7.5µm, the phase difference between the two light components is relatively stable with the magnitude at a value of around $\pi /2$. It is obvious that the nanorod-based metasurface functions as a quarter wave plate in this region. The calculated circular polarized state of reflected light is plotted as a function of wavelength in Fig. 3(d) and shows that the reflected light is almost pure left-handed circularly polarized light, with conversion efficiency over 90%, in the range from 4µm to 7.5µm.
2.2 Experimental results
Samples were fabricated using silicon substrates wafers with 100nm thick aluminium as the reflector, and 600nm thick silicon dioxide layer on the top. Rod shaped resonators, consisting of 5/50 nm-thick Cr/Au, were patterned on top of the silicon dioxide using electron beam lithography (the 5nm thick Cr acts as an adhesion layer). Measurements were conducted at room temperature under ambient conditions, with the reflectivity of the samples characterized using a Fourier transform infrared (FTIR) spectrometer as shown schematically in Fig. 4. The size of the optical beam emitted from the spectrometer was reduced using two off-axis parabolic mirrors, with a x15 reflecting objective lens used to focus light onto the sample. The germanium beam splitter with (ratio close to 1:1) allowed reflected light to be collected, with a third off-axis parabolic mirror used to focus the reflected light into a liquid nitrogen cooled HgCdTe detector with a 2–12 µm response, with the signal from the detector amplified by a low noise preamplifier before being passed to the FTIR spectrometer. The wire grid polarizer (L1) with its optical axis orientated along y-axis, was placed before the beam splitter to generate p-polarized incident light, in our case, the light is oriented vertically to the platform surface. The tunable quarter wave plate and linear polarizer shown in the dashed rectangular are used to measure the Stokes parameters, as discussed below. The measurement of the reflectivity of the two components was performed by rotating the sample so that the rod resonators were either parallel or orthogonal to the incident p-polarized light. The measured reflectivity was normalized to that obtained from a substrate that had no resonators.
In Fig. 5(a), the normalised measured reflectivity is plotted as a function of wavelength. Overall, there is very good agreement with the simulations, Fig. 2(b), with near unity reflectivity over the operation wavelength range for both incident polarizations. With the light parallel to the rods, minima in the measured reflectivity are observed at wavelengths of approximately 3.6µm and 7.9µm, corresponding to the gap surface plasmon (GSP) and cavity modes described earlier. In this case, there is also an additional resonance in the measured reflectivity, at 4.8µm. We believe this additional Fabry-Parot cavity like mode is observed in the experiments as light is not at perfect normal incidence to the fabricated sample.
Fig. 5. Experiment results of nanorod-based metasurface. (a) Measured reflectivity for ${E_ \bot }$ and ${E_\parallel }$. (b) Indication of ellipse parameters ${E_{ox}}$, ${E_{oy}}$ and orientation angle $\psi $. (c) Calculated ellipse parameters ${\textrm{E}_{0x}}$, ${\textrm{E}_{0y}}$ and orientation angle $\mathrm{\psi }$ based on Stokes parameters from 3.8µm to 4.8µm. (d) The schematic of polarization state of reflected beam at 4.1 µm (${\textrm{E}_{0x}} = 0.669,\; {\textrm{E}_{0y}} = 0.667,\; \psi ={-} 4.33^\circ $), 4.3 µm $({\textrm{E}_{0x}} = 0.648,\; {\textrm{E}_{0y}} = 0.685,\; \psi ={-} 3.37^\circ )$, 4.5 µm $({\textrm{E}_{0x}} = 0.654,\; {\textrm{E}_{0y}} = 0.654,\; \psi ={-} 3.35^\circ )$ and 4.7 µm $({\textrm{E}_{0x}} = 0.620,\; {\textrm{E}_{0y}} = 0.656,\; \psi ={-} 4.38^\circ )$. (e) The spectrum of polarization conversion efficiency of nanorod-based metasurface.
To further characterize the properties of the metasurface, the Stokes parameters, which give a direct physical interpretation of the state of polarization of a given electromagnetic field, were measured. To measure the Stokes parameters (see Fig.S1 in the ESM, [36]), an additional wire grid linear polarizer (L2) was placed between parabolic mirror and detector, as shown in Fig. 4 in the dashed rectangle, with its optic axis rotated at ${0^\circ }$, ${90^\circ }$, and ${45^\circ }$ to x-axis to measure the intensity of the reflected beam from the metasurface; ${P_1}({{0^\circ }} )$, ${P_2}({{{90}^\circ }} )$, ${P_3}({{{45}^\circ }} )$. To obtain the fourth Stoke’s parameter, a quarter wave plate (supplied by ALPHALAS GmbH) tunable over the spectral range 150 - 6000 nm was inserted in the beam path with its fast axis fixed at 0° to the x-axis to obtain the intensity ${P_4}({{0^\circ },{\; }{{45}^\circ }} )$. The four Stokes parameters can be expressed as:
The accurate polarization state of the reflected beam can be characterized using the value of ellipse parameters ${\textrm{E}_{0x}}$, ${\textrm{E}_{0y}}$ and orientation angle $\mathrm{\psi }$, as indicated in Fig. 5(b), with the parameters given by:
As shown in Fig. 5(c), the calculated ellipse parameters ${\textrm{E}_{0x}}$, ${\textrm{E}_{0y}}$ and orientation angle $\mathrm{\psi }$ show little wavelength dependence over the range 3.8µm to 4.8µm (the spectra from 3-10µm are shown in Fig. S2 of the ESM), so that the polarization state of the beam is stable in this range. Within the wavelength range from 3.8µm to 4.8µm where linear-to-circular polarization conversion occurs, the polarization ellipse are illustrated at 4.1µm, 4.3µm, 4.5µm and 4.7µm respectively as examples to visualize the polarization states at specific wavelength in Fig. 5(d). These clearly demonstrate that the reflected beam is circularly polarized.
In order to obtain the polarization conversion efficiency, the degree of the circular polarization (DOP) which represents the amount of circular polarization light in the detected beam is defined by:
Where ${I_c}$ stands for the amount of circular polarization light, ${I_r}$ represents the power of reflected beam. The polarization conversion efficiency will be:3. Conclusion
In conclusion, the properties of a nanorod-based metasurface has been investigated using both simulations and experiments. Experiments showed that fabricated metasurfaces exhibit excellent linear-to-circular polarization conversion, with the average conversion efficiency of 80% in the wavelength range from 3.8µm to 4.8µm, in good agreement with the simulations. Compared with conventional bulky quarter wave plates, which only provide polarization conversion at a specific wavelength, the metasurface provides a working bandwidth of ∼1µm, but with subwavelength thickness (∼λ/4). Such metasurfaces could therefore be exploited for circular dichroism spectroscopy, to characterize chiral molecules such as proteins. In addition, the combination of metasurface and active material, such as graphene, offers the potential to develop active subwavelength devices for compact and integrated photonics systems.
Funding
China Scholarship Council; Engineering and Physical Sciences Research Council (EP/R004781/1).
Acknowledgement
We gratefully acknowledge the financial support of the China Scholarship Council, the University of Exeter and the EPSRC Prosperity Partnership “The Tailored Electromagnetic and Materials Accelerator” (Grant No. EP/R004781/1), which is a collaboration with QinetiQ Ltd.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007). [CrossRef]
2. N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012). [CrossRef]
3. A. E. Minovich and A. V. Zayats, “Geometric-phase metasurfaces based on anisotropic reflection: generalized design rules,” ACS Photonics 5(5), 1755–1761 (2018). [CrossRef]
4. Y. Zhao and A. Aluì, “Tailoring the dispersion of plasmonic nanorods to realize broadband optical meta-waveplates,” Nano Lett. 13(3), 1086–1091 (2013). [CrossRef]
5. Z. Li, W. Liu, H. Cheng, S. Chen, and J. Tian, “Realizing broadband and invertible linear-to-circular polarization converter with ultrathin single-layer metasurface,” Sci. Rep. 5(1), 18106 (2016). [CrossRef]
6. D. Wang, L. Zhang, Y. Gu, M. Q. Mehmood, Y. Gong, A. Srivastava, L. Jian, T. Venkatesan, C. W. Qiu, and M. Hong, “Switchable ultrathin quarter-wave plate in terahertz using active phase-change metasurface,” Sci. Rep. 5(1), 15020 (2015). [CrossRef]
7. C. C. Chang, Z. Zhao, D. Li, A. J. Taylor, S. Fan, and H. T. Chen, “Broadband linear-to-circular polarization conversion enabled by birefringent off-resonance reflective metasurfaces,” Phys. Rev. Lett. 123(23), 237401 (2019). [CrossRef]
8. Y. Deng, C. Wu, C. Meng, S. I. Bozhevolnyi, and F. Ding, “Functional metasurface quarter-wave plates for simultaneous polarization conversion and beam steering,” ACS Nano 15(11), 18532–18540 (2021). [CrossRef]
9. M. Kobachi, F. Miyamaru, T. Nakanishi, K. Okimura, A. Sanada, and Y. Nakata, “Dynamic quarter-wave metasurface for efficient helicity inversion of polarization beyond the single-layer conversion limit,” Adv. Opt. Mater. 10(2), 2101615 (2022). [CrossRef]
10. P. C. Wu, W. Y. Tsai, W. T. Chen, Y. W. Huang, T. Y. Chen, J. W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with an aluminum plasmonic metasurface,” Nano Lett. 17(1), 445–452 (2017). [CrossRef]
11. K. Tanaka, D. Arslan, S. Fasold, M. Steinert, J. Sautter, M. Falkner, T. Pertsch, M. Decker, and I. Staude, “Chiral bilayer all-dielectric metasurfaces,” ACS Nano 14(11), 15926–15935 (2020). [CrossRef]
12. P. Yu, J. Li, and N. Liu, “Electrically tunable optical metasurfaces for dynamic polarization conversion,” Nano Lett. 21(15), 6690–6695 (2021). [CrossRef]
13. G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015). [CrossRef]
14. E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “High efficiency near diffraction-limited mid- infrared flat lenses based on metasurface reflectarrays,” Optica 3(6), 628 (2016). [CrossRef]
15. J. Burch and A. Di Falco, “Surface Topology Specific Metasurface Holograms,” ACS Photonics 5(5), 1762–1766 (2018). [CrossRef]
16. M. I. Khan and F. A. Tahir, “A compact half and quarter-wave plate based on bi-layer anisotropic metasurface,” J. Phys. D: Appl. Phys. 50(43), 43LT04 (2017). [CrossRef]
17. M. I. Khan and F. A. Tahir, “Simultaneous quarter-wave plate and half-mirror operation through a highly flexible single layer anisotropic metasurface,” Sci. Rep. 7(1), 1–9 (2017). [CrossRef]
18. M. Kiani, A. Momeni, M. Tayarani, and C. Ding, “Spatial wave control using a self-biased nonlinear metasurface at microwave frequencies,” Opt. Express 28(23), 35128 (2020). [CrossRef]
19. D. Wang, Y. Gu, Y. Gong, C.-W. Qiu, and M. Hong, “An ultrathin terahertz quarter-wave plate using planar babinet-inverted metasurface,” Opt. Express 23(9), 11114 (2015). [CrossRef]
20. M. Amin, O. Siddiqui, and M. Farhat, “Linear and circular dichroism in graphene-based reflectors for polarization control,” Phys. Rev. Appl. 13(2), 024046 (2020). [CrossRef]
21. S. M. Kelly, T. J. Jess, and N. C. Price, “How to study proteins by circular dichroism,” Biochim. Biophys. Acta, Proteins Proteomics 1751(2), 119–139 (2005). [CrossRef]
22. Z. H. Jiang, L. Lin, D. Ma, S. Yun, D. H. Werner, Z. Liu, and T. S. Mayer, “Broadband and wide field-of-view plasmonic metasurface-enabled waveplates,” Sci. Rep. 4(1), 7511 (2015). [CrossRef]
23. Z. Cai, Y. Deng, C. Wu, C. Meng, Y. Ding, S. I. Bozhevolnyi, and F. Ding, “Dual-functional optical waveplates based on gap-surface plasmon metasurfaces,” Adv. Opt. Mater. 9(11), 2002253 (2021). [CrossRef]
24. J. Bai and Y. Yao, “Highly efficient anisotropic chiral plasmonic metamaterials for polarization conversion and detection,” ACS Nano 15(9), 14263–14274 (2021). [CrossRef]
25. F. Ding, R. Deshpande, C. Meng, and S. I. Bozhevolnyi, “Metasurface-enabled broadband beam splitters integrated with quarter-wave plate functionality,” Nanoscale 12(26), 14106–14111 (2020). [CrossRef]
26. J. Bai, C. Wang, X. Chen, A. Basiri, C. Wang, and Y. Yao, “Chip-integrated plasmonic flat optics for mid-infrared polarization detection,” 2018 Conf. Lasers Electro-Optics, CLEO 2018 - Proc.7(9), (2018).
27. Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011). [CrossRef]
28. S. Fan and W. Suh, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. 20(3), 569–572 (2003). [CrossRef]
29. H. R. Barnard and G. R. Nash, “Tailoring the spectral properties of layered chiral mid-infrared metamaterials,” Appl. Phys. Lett. 119(24), 241102 (2021). [CrossRef]
30. C. Shi, I. J. Luxmoore, and G. R. Nash, “Gate tunable graphene-integrated metasurface modulator for mid-infrared beam steering,” Opt. Express 27(10), 14577 (2019). [CrossRef]
31. “Periodic Table of Elements,” https://environmentalchemistry.com/yogi/periodic/.
32. E. D. Palik, Handbook of Optical Constants of Solids, Five-Volume Set (Academic Press, 1997), p. 3224.
33. A. Pors and S. I. Bozhevolnyi, “Efficient and broadband quarter-wave plates by gap-plasmon resonators,” Opt. Express 21(3), 2942 (2013). [CrossRef]
34. A. Pors and S. I. Bozhevolnyi, “Plasmonic metasurfaces for efficient phase control in reflection,” Opt. Express 21(22), 27438 (2013). [CrossRef]
35. H.-T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20(7), 7165 (2012). [CrossRef]
36. B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75(2), 163–168 (2007). [CrossRef]
