Open Access
Add to BibSonomy
Abstract
We numerically study polarisation conversion by anisotropic metasurfaces made of electro-optic material on a silica substrate and show that we can control the polarisation of transmitted waves dynamically. We predict that such metasurfaces can exhibit tunability of the cross-polarisation conversion of linear incident polarisation as well as tunable circular dichroism. We compare the metasurface performance for direct and inverse structures and find that the cross-polarisation transmission coefficient can be tuned by approximately 0.5, while the predicted tunability of circular dichroism is close to 0.8.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Ultra-fast modulation of light by free-space optics has long been a sought-after capability for various potential applications both in optics and microwave photonics [1–3]. The concept of metasurfaces was proposed to tackle the problem of light controlling both in space and frequency domains. Formed by sub-wavelength resonators [4], metasurfaces are a promising platform for ultra-small integrated optics components [5–9]. In addition, various metasurfaces are designed only for a single functionality and have fixed optical response after fabrication, hindering the practical application. To improve the range of potential applications, a number of dynamic tuning methods have been proposed and obtained exciting progress during the past decade metasurfaces [10–13]. Depending on what stimuli are used, the tunability approaches can be classified as thermal, optical, magnetic, mechanical force, and electro-optical [14,15]. Among various modulation mechanisms, electro-optical tuning is of particular interest due to the unique combination of high modulation speed, stability, and low power dissipation [16]. By applying varying external voltages via electrodes, continuous tunability can be achieved [17], providing new possibilities in applications such as holographic displays and Lidars [1].
Numerous materials with electro-optic properties such as organic nonlinear materials [18,19], Barium Titanate [20], and indium-tin-oxide [21] have been suggested for use in tunable metasurfaces for modulating their optical properties. Notably, lithium niobate (LN) historically is one of the most studied materials due to its strong linear electro-optic properties (Pockels effect) and gigahertz (GHz) tuning speed and it is, therefore, an outstanding candidate for realising ultra-fast modulation [22]. A number of studies have proposed to use LN metasurfaces for modulating the amplitude and the phase of light [23–27]. Here, we propose to go one step further and study the possibility of dynamic control of wave polarisation with metasurfaces made of lithium niobate.
The ability to control and measure the polarisation state of light is widely used in various applications, e.g. in liquid crystal displays, for material characterization, as well as for improving the capacity of the optical communication networks [28]. In addition, starting from the first works on engineering spatial phase distribution using metasurfaces [29], further studies have proven the ability of metasurfaces to control polarisation at the nanoscale. By adjusting the shape, symmetry, size, and arrangement of meta-atoms, the phase and polarisation state at the interface can be manipulated in an almost arbitrary fashion and can improve the compactness of devices that use polarisation to open up additional possibilities [30]. By breaking the mirror symmetry of meta-atoms, we can control, in general, the anisotropy and chirality of the materials [31], which can produce a variety of optical effects and offer additional freedom of polarisation manipulation. Specifically, artificial chiral structures can be designed if meta-atoms cannot be superimposed with their mirror image through translation and rotation operations, resulting in different optical responses for different circular polarisations. To date, a large number of chiral and anisotropic structures [32–36] have been proposed and demonstrated for manipulating linear polarisation or enhancing circular dichroism (CD), which manifests itself in different transmission properties for left circular polarisation (LCP) and right circular polarisation (RCP) of light.
The ability to have tunable polarisation control by anisotropic or chiral structures can be beneficial for various applications, and there are several previous works that achieved such tunability [37–42]. These earlier tunability mechanisms have typically used strong tunability methods that are usually very slow. Similar to conventional tunable metasurfaces that manipulate amplitude, the speed of polarisation modulation is an important parameter for polarisation manipulation [43]. Until now, there is still a lack of ultra-fast polarisation modulation approaches with ultra-thin metasurfaces.
In this work, we designed a direct and inverse chiral structure made of LN and evaluated its performance in modulating the polarisation of transmitted light dynamically. As one of the electro-optic materials, LN eclipses other materials in terms of modulation speed and broad transmission spectrum [44], becoming an ideal candidate to achieve ultra-fast polarisation modulation. Our main aim is to explore the possibility of controlling polarisation with ferroelectric materials with a view of making fast polarisation modulation. Modulated by external electric fields, the designed LN anisotropic structures are able to rotate the polarisation plane and then convert vertical (Y) into horizontal (X) polarisation and vice versa. The transmission difference of linear polarisation induced by negative (-E) and positive (+E) control electric fields is around 0.5. The predicted efficiency in CD tuning is close to 0.8. Such structures are excellent candidates for creating tunable filters and multiplexing metasurfaces that control the polarisation of light.
2. Results and discussion
We begin by investigating planar S-shaped meta-atoms, as they previously have shown strong static polarisation control [31]. Now we assume that the meta-atoms are made of lithium niobate (LN) and placed on a silicon dioxide substrate. At the frequencies close to resonance electromagnetic field is strongly concentrated within LN’s meta-atoms, and we expect the properties of resonance to strongly change as we tune the LN by applying the static electric field. To explore this phenomenon, we have designed a direct chiral metasurface in which Z-cut lithium niobate meta-atoms take on an S-like shape, as illustrated in Fig. 1(a). We assume that via the electro-optic effect in LN, the refractive index of the material can be changed when an external electric field is applied. We are looking at how this can be used for modulating the polarisation of transmitted light dynamically. If we apply the electric field along the z-axis, $E_z$, then the change in the refractive index in LN can be described by the following equation [44]:
where $r_{ij}$ are the linear electro-optic coefficients of LN, and the largest coefficient for LN is $r_{33} = 28.8\times 10^{-12} m/V$. The largest electric field we can apply to LN before the breakdown is $E=65 kV/mm$ [44,45], the required voltage can be calculated by multiplying this value and the specific distance between the two electrodes, which can provide the maximum change in the index of refraction of $\Delta n = 9.3\times 10^{-3}$.
Fig. 1. (a) Schematics of the unit cell of the direct LN metasurfaces. (b,c) The top view of the unit cell. The substrate is made of silicon dioxide (green solid), and the top chiral structure is made of lithium niobate (orange solid) with parameters H = 350 nm, P = 700 nm, L1 = 340 nm, L2 = 150 nm, W1 = 120 nm, and W2 = 340 nm. (d) Schematics of the unit cell of the inverse LN metasurfaces. The top chiral structure is made of lithium niobate (orange solid), and the cut-out shape with parameters H = 225 nm, P = 670 nm, L1 = 340 nm, L2 = 150 nm, W1 = 60 nm, and W2 = 340 nm.
To look for structures with larger tunability, we use commercial software CST Microwave Studio Suite based on the Finite Element Method, providing a universal spatial discretization scheme in the frequency domain. We set unit cell boundary conditions, employed a tetrahedral mesh, and conducted a parameter sweep encompassing meta-atoms height and other dimensions, as illustrated in Fig. 1(b). We realise that in such a structure the tunability by the electric field is hard to achieve, due to the difficulties of applying an electric field to individual resonators. That is why we are also considering an inverse metasurface that we call membrane metasurface. By cutting out shaped holes in the LN film to keep anisotropic performance, as shown in Fig. 1(d). This structure potentially resolves the problem of connecting electrodes, we suppose that thin layers of transparent conductive oxides can be placed on LN to form electrodes. In this work, we do not take into account these electrodes as we are looking for the fundamental properties of the structures. We study the properties of these structures in response to linear and circularly polarised waves in order to find the strongest polarisation conversion regimes as well as large circular dichroism.
2.1 Tunable linear polarisation conversion
To evaluate the performance of the LN metasurfaces for linear polarisation conversion, waves with two orthogonal linear polarisations are launched along the z-axis, as shown in Fig. 2(a). When vertical (Y) linear polarised light transmits through the direct metasurface, it is partially converted into horizontal (X) linear polarisation, and vice versa. Due to the anisotropy of the lithium niobate, the cross-polarisation transmissions are, in general, different: $T_{XY} \ne T_{YX}$. As shown in Fig. 3(a), the blue and red curves show the cross-polarisation transmission through the direct LN metasurfaces. The maximum cross-polarisation transmission is for incident y-polarisation converted to transmitted x-polarisation, which is close to 0.55. To reach this optimal performance, we performed a parameter sweep, varying the arm’s length, width, and height with the step of 5 nm. This scan identified regimes of the largest difference between $T_{XY}$ and $T_{YY}$ Then, we calculated the tunability of the properties of this structure as we emulated the application of an external electric field. When varying the external electric field, the refractive index tensor of LN changes, resulting in the dynamic manipulation of metasurfaces’ response. Figure 3(b) shows the change in the cross-polarisation transmission coefficient when we change the electric field from negative to positive values. We see that the direct LN metasurfaces show the strongest cross-polarisation transmission change from 0.45 to −0.25.
Fig. 2. (a) Schematics of the polarisation transformation of the direct LN metasurfaces. The vertical polarisation is converted to horizontally polarised light. (b) Schematics of the RCP propagation of the direct LN metasurfaces. The RCP can transmit through these metasurfaces, while the LCP is reflected.
Fig. 3. Cross-transmission tuning of the direct and inverse chiral LN metasurfaces for linear polarisation conversion. (a) The cross-transmission amplitude conversing from vertical linear polarisation into horizontal ($T_{XY}$: blue solid) and from horizontal into vertical linear polarisation ($T_{XY}$: red solid). (b) Simulated tunability of the cross-transmission amplitude ($\Delta {T}$) of the direct LN metasurface caused by the negative and positive maximum external electric field. The induced difference in the cross-transmission from vertical input to horizontal output is shown by yellow solid lines ($\Delta {T_{XY}}$); the difference of the cross-transmission from horizontal input to vertical output is shown by green solid lines ($\Delta {T_{YX}}$). (c,d) Same as (a,b) but for the inverse chiral LN metasurfaces (dash line).
We then repeat the evaluation and optimisation of linear polarisation conversion to the inverse LN metasurfaces, as shown in Fig. 3(c). It also shows the functionalities of transferring vertical linear polarisation into the horizontal state and vice versa. When adjusting the electric field from a negative to a positive maximum, the tunability of cross-transmission is from 0.17 to −0.24. It is worth noting that the amount of cross-transmission and the tunable linear conversion of the inverse chiral LN metasurfaces are the same in X to Y and in Y to X.
As can be seen, achieving the same functionalities at the same working frequency, the LN in the direct metasurfaces (H = 350 nm) is thicker than that of inverse metasurfaces (H = 225 nm). This can be explained by the calculation of the effective index of materials [46,47], where the effective index is proportional to the volume of functional materials. Similarly, to maintain the same working wavelength at 1055 nm of both structures, the lattice constant of the direct metasurfaces is 700 nm, which is larger than 670 nm in the inverse chiral LN.
2.2 Tunable circular dichroism
After achieving tunable linear polarisation conversion, we then demonstrate the possibility to modulate circular dichroism (CD) dynamically using both considered designs. As seen in Fig. 2(b), the structures can show a strong circular dichroism, when the transmission coefficients for RCP and LCP waves are strongly different. In the case shown in the figure, the LCP is almost completely reflected, while RCP is transmitted. In order to keep the consistency with the previous linear case so that the operation wavelength range is similar and to obtain the largest CD, we performed a parameter scan. The freestanding LN chiral structures were optimised with parameters P = 800 nm, H = 420 nm, L1 = 340 nm, L2 = 130 nm, W1 = 60 nm, and W2 = 330 nm. In addition, the central rotation angle $\theta$ was induced in this step to increase mirror asymmetry which allowed us to further enlarge the CD. After changing the $\theta$, it has been identified that for $\theta = 22^{\circ }$ with respect to the vertical direction we can obtain the largest circular dichroism. Figure 4(a) shows the transmission amplitudes for LCP and RCP waves. Around $90{\% }$ RCP transmit through the direct chiral metasurface, while $90{\% }$ of LCP is reflected, resulting in the CD close to 0.8.
Fig. 4. Circular dichroism tuning for the direct and inverse chiral LN metasurfaces. (a) The difference in transmission amplitude of RCP and LCP of the direct LN metasurfaces. The transmission amplitude from LCP to LCP is shown in orange; the transmission amplitude from RCP to RCP is shown in brown lines. (b) The induced circular dichroism at negative (indigo) and positive (ruby) applied an electric field for the direct LN metasurfaces. (c,d) Same as (a,b) but for inverse chiral LN metasurfaces (dash line).
In a similar way, targeting the same operation wavelength, we optimised the parameters of inverse chiral metasurfaces and found the best performance at P = 720 nm, H = 210 nm, L1 = 290 nm, L2 = 130 nm, W1 = 60 nm, W2 = 330 nm, and $\theta = -11^{\circ }$. We also note that the lattice constant and LN height of inverse chiral metasurfaces are both smaller than that of direct metasurfaces. As shown in Fig. 4(c), $90{\% }$ RCP transmits through the inverse metasurfaces, and the reflectance of LCP is close to $100{\% }$ at $\lambda$ = 1055 nm, providing a CD of $0.9$ for this metasurface.
Figures 4(b,d) show the CD of the metasurfaces for different applied bias voltages by placing the electrodes on the top and bottom sides of the LN meta-atoms. As seen in Fig. 4(b), when the external bias is changed from the negative (-E) to the positive (+E) voltage, the CD peak shifts from 1053 nm to 1056 nm. This demonstrates that the amount of LCP transmission can be modulated by the voltage from 0.1 to 0.9, and this will manipulate the CD dynamically. The same functionality in tunable CD can be achieved in the inverse metasurfaces, as shown in Fig. 4(d). Changing the bias from -E to +E, the CD resonance shifts. However, compared to the performance of the direct structure, the shifting range is reduced while the CD peak is increased by $10{\% }$. Therefore, there is a trade-off between transmission amplitude contrast and tunability that can be achieved in these structures.
3. Conclusion
In conclusion, we studied two designs of polarisation modulators based on structures made of Z-cut LN on a silica substrate. By applying an external electric field to the designed anisotropic structures, the refractive index of LN can be changed, modifying the optical response of the structure and thus controlling the polarisation of transmitted and reflected waves. We evaluated the performance of two types of metasurfaces for the cross-polarisation conversion of linear incident polarisation as well as for the tunable circular dichroism and characterised their performance. Since the response of the lithium niobate to external voltage is fast, our structures provide a platform for polarisation modulation in the GHz range.
Funding
Australian Research Council through the Centres of Excellence scheme (CE200100010).
Acknowledgments
The authors thank Q. Yang for the fruitful discussions.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
The data supporting this study’s findings are available from the corresponding author upon reasonable request.
References
1. T. Cui, B. Bai, and H.-B. Sun, “Tunable metasurfaces based on active materials,” Adv. Funct. Mater. 29(10), 1806692 (2019). [CrossRef]
2. M. Lee, H. Katz, C. Erben, D. Gill, P. Gopalan, J. Heber, and D. McGee, “Ultra-fast modulation of light using an electro-optic polymer,” Science 289, 1404–1407 (2002).
3. M. Jafari, L. J. Guo, and M. Rais-Zadeh, “An ultra-fast optical shutter exploiting total light absorption in a phase change material,” in Optical components and materials XIV, vol. 10100 (SPIE, 2017), pp. 89–95.
4. A. Fedotova, L. Carletti, A. Zilli, et al., “Lithium niobate meta-optics,” ACS Photonics 9(12), 3745–3763 (2022).
5. G. Della Valle, B. Hopkins, L. Ganzer, T. Stoll, M. Rahmani, S. Longhi, Y. S. Kivshar, C. De Angelis, D. N. Neshev, and G. Cerullo, “Nonlinear anisotropic dielectric metasurfaces for ultrafast nanophotonics,” ACS Photonics 4(9), 2129–2136 (2017). [CrossRef]
6. P. Genevet and F. Capasso, “Holographic optical metasurfaces: a review of current progress,” Rep. Prog. Phys. 78(2), 024401 (2015). [CrossRef]
7. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013). [CrossRef]
8. D. Benedikovic, P. Cheben, J. H. Schmid, et al., “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015). [CrossRef]
9. A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), aag2472 (2016). [CrossRef]
10. I. V. Shadrivov and D. N. Neshev, “Tunable metamaterials,” Singapore: World Scientific 9, 387–418 (2017).
11. Z. Li, M.-H. Kim, C. Wang, et al., “Controlling propagation and coupling of waveguide modes using phase-gradient metasurfaces,” Nat. Nanotechnol. 12(7), 675–683 (2017). [CrossRef]
12. Y. Hu, X. Luo, Y. Chen, Q. Liu, X. Li, Y. Wang, N. Liu, and H. Duan, “3d-integrated metasurfaces for full-colour holography,” Light: Sci. Appl. 8(1), 86 (2019). [CrossRef]
13. Z. Yang, M. Liu, A. Komar, L. Xu, and D. N. Neshev, “Phase-only tuning of extreme huygens metasurfaces enabled by optical anisotropy,” Adv. Opt. Mater. 10(2), 2101893 (2022). [CrossRef]
14. O. Tsilipakos, A. C. Tasolamprou, A. Pitilakis, et al., “Toward intelligent metasurfaces: the progress from globally tunable metasurfaces to software-defined metasurfaces with an embedded network of controllers,” Adv. Opt. Mater. 8(17), 2000783 (2020). [CrossRef]
15. Y.-W. Huang, H. W. H. Lee, R. Sokhoyan, R. A. Pala, K. Thyagarajan, S. Han, D. P. Tsai, and H. A. Atwater, “Gate-tunable conducting oxide metasurfaces,” Nano Lett. 16(9), 5319–5325 (2016). [CrossRef]
16. T. Badloe, J. Lee, J. Seong, and J. Rho, “Tunable metasurfaces: the path to fully active nanophotonics,” Adv. Photonics Res. 2(9), 2000205 (2021). [CrossRef]
17. A. Forouzmand, M. M. Salary, G. K. Shirmanesh, R. Sokhoyan, H. A. Atwater, and H. Mosallaei, “Tunable all-dielectric metasurface for phase modulation of the reflected and transmitted light via permittivity tuning of indium tin oxide,” Nanophotonics 8(3), 415–427 (2019). [CrossRef]
18. H. Xu, F. Liu, D. L. Elder, L. E. Johnson, Y. de Coene, K. Clays, B. H. Robinson, and L. R. Dalton, “Ultrahigh electro-optic coefficients, high index of refraction, and long-term stability from diels–alder cross-linkable binary molecular glasses,” Chem. Mater. 32(4), 1408–1421 (2020). [CrossRef]
19. I.-C. Benea-Chelmus, S. Mason, M. L. Meretska, D. L. Elder, D. Kazakov, A. Shams-Ansari, L. R. Dalton, and F. Capasso, “Gigahertz free-space electro-optic modulators based on mie resonances,” Nat. Commun. 13(1), 3170 (2022). [CrossRef]
20. A. Karvounis, V. V. Vogler-Neuling, F. U. Richter, E. Dénervaud, M. Timofeeva, and R. Grange, “Electro-optic metasurfaces based on barium titanate nanoparticle films,” Adv. Opt. Mater. 8(17), 2000623 (2020). [CrossRef]
21. G. K. Shirmanesh, R. Sokhoyan, P. C. Wu, and H. A. Atwater, “Electro-optically tunable multifunctional metasurfaces,” ACS Nano 14(6), 6912–6920 (2020). [CrossRef]
22. E. L. Wooten, K. M. Kissa, A. Yi-Yan, et al., “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000). [CrossRef]
23. A. Weiss, C. Frydendahl, J. Bar-David, R. Zektzer, E. Edrei, J. Engelberg, N. Mazurski, B. Desiatov, and U. Levy, “Tunable metasurface using thin-film lithium niobate in the telecom regime,” ACS Photonics 9(2), 605–612 (2022). [CrossRef]
24. H. Weigand, V. V. Vogler-Neuling, M. R. Escalé, D. Pohl, F. U. Richter, A. Karvounis, F. Timpu, and R. Grange, “Enhanced electro-optic modulation in resonant metasurfaces of lithium niobate,” ACS Photonics 8(10), 3004–3009 (2021). [CrossRef]
25. D. Barton III, M. Lawrence, and J. Dionne, “Wavefront shaping and modulation with resonant electro-optic phase gradient metasurfaces,” Appl. Phys. Lett. 118(7), 071104 (2021). [CrossRef]
26. E. Klopfer, S. Dagli, D. Barton III, M. Lawrence, and J. A. Dionne, “High-quality-factor silicon-on-lithium niobate metasurfaces for electro-optically reconfigurable wavefront shaping,” Nano Lett. 22(4), 1703–1709 (2022). [CrossRef]
27. L. Wang and I. Shadrivov, “Electro-optic metasurfaces,” Opt. Express 30(20), 35361–35368 (2022). [CrossRef]
28. J. Dong and H. Zhou, “Polarimeters from bulky optics to integrated optics: A review,” Opt. Commun. 465, 125598 (2020). [CrossRef]
29. 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(6054), 333–337 (2011). [CrossRef]
30. Y. Hu, X. Wang, X. Luo, X. Ou, L. Li, Y. Chen, P. Yang, S. Wang, and H. Duan, “All-dielectric metasurfaces for polarization manipulation: principles and emerging applications,” Nanophotonics 9(12), 3755–3780 (2020). [CrossRef]
31. C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced jones calculus for the classification of periodic metamaterials,” Phys. Rev. A 82(5), 053811 (2010). [CrossRef]
32. S. Yang, Z. Liu, H. Yang, A. Jin, S. Zhang, J. Li, and C. Gu, “Intrinsic chirality and multispectral spin-selective transmission in folded eta-shaped metamaterials,” Adv. Opt. Mater. 8(4), 1901448 (2020). [CrossRef]
33. A. Y. Zhu, W. T. Chen, A. Zaidi, Y.-W. Huang, M. Khorasaninejad, V. Sanjeev, C.-W. Qiu, and F. Capasso, “Giant intrinsic chiro-optical activity in planar dielectric nanostructures,” Light: Sci. Appl. 7(2), 17158 (2017). [CrossRef]
34. B. M. Maoz, R. van der Weegen, Z. Fan, A. O. Govorov, G. Ellestad, N. Berova, E. Meijer, and G. Markovich, “Plasmonic chiroptical response of silver nanoparticles interacting with chiral supramolecular assemblies,” J. Am. Chem. Soc. 134(42), 17807–17813 (2012). [CrossRef]
35. S. Yin, W. Ji, D. Xiao, Y. Li, K. Li, Z. Yin, S. Jiang, L. Shao, D. Luo, and Y. J. Liu, “Intrinsically or extrinsically reconfigurable chirality in plasmonic chiral metasurfaces,” Opt. Commun. 448, 10–14 (2019). [CrossRef]
36. C. Wang, Z. Li, R. Pan, W. Liu, H. Cheng, J. Li, W. Zhou, J. Tian, and S. Chen, “Giant intrinsic chirality in curled metasurfaces,” ACS Photonics 7(12), 3415–3422 (2020). [CrossRef]
37. T. Cao, L. Zhang, R. E. Simpson, C. Wei, and M. J. Cryan, “Strongly tunable circular dichroism in gammadion chiral phase-change metamaterials,” Opt. Express 21(23), 27841–27851 (2013). [CrossRef]
38. H. Liu, Z. Shang, X. Wu, C. Dou, and J. Zhang, “Tunable circular dichroism of bilayer b-type chiral nanostructures,” Opt. Commun. 448, 76–81 (2019). [CrossRef]
39. Y. Zárate, S. Babaee, S. H. Kang, D. N. Neshev, I. V. Shadrivov, K. Bertoldi, and D. A. Powell, “Elastic metamaterials for tuning circular polarization of electromagnetic waves,” Sci. Rep. 6(1), 28273 (2016). [CrossRef]
40. Q. Yang, M. Liu, S. Kruk, Y. Xu, Y. K. Srivastava, R. Singh, J. Han, Y. Kivshar, and I. V. Shadrivov, “Polarization-sensitive dielectric membrane metasurfaces,” Adv. Opt. Mater. 8(20), 2000555 (2020). [CrossRef]
41. M. Liu, D. A. Powell, R. Guo, I. V. Shadrivov, and Y. S. Kivshar, “Polarization-induced chirality in metamaterials via optomechanical interaction,” Adv. Opt. Mater. 5(16), 1600760 (2017). [CrossRef]
42. W. Zhu, A. Liu, T. Bourouina, D. P. Tsai, J. Teng, X. Zhang, G. Lo, D. Kwong, and N. Zheludev, “Microelectromechanical maltese-cross metamaterial with tunable terahertz anisotropy,” Nat. Commun. 3(1), 1274 (2012). [CrossRef]
43. J. Kim, A. S. Rana, Y. Kim, I. Kim, T. Badloe, M. Zubair, M. Q. Mehmood, and J. Rho, “Chiroptical metasurfaces: Principles, classification, and applications,” Sensors 21(13), 4381 (2021). [CrossRef]
44. R. Weis and T. Gaylord, “Lithium niobate: Summary of physical properties and crystal structure,” Appl. Phys. A 37(4), 191–203 (1985). [CrossRef]
45. M. Luennemann, U. Hartwig, G. Panotopoulos, and K. Buse, “Electrooptic properties of lithium niobate crystals for extremely high external electric fields,” Appl. Phys. B 76(4), 403–406 (2003). [CrossRef]
46. W. Theiß, “The use of effective medium theories in optical spectroscopy,” Adv. Solid State Phys. 33, 149–176 (1993). [CrossRef]
47. L. Genzel and T. Martin, “Infrared absorption by surface phonons and surface plasmons in small crystals,” Surf. Sci. 34(1), 33–49 (1973). [CrossRef]
