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Abstract
We propose and experimentally demonstrate that giant asymmetric reflection of circularly polarized light based on asymmetric coupling can be achieved in single-layer extrinsic chiral metasurfaces at oblique incidence. The asymmetric coupling and asymmetric reflection in the extrinsic chiral metasurfaces are caused by extrinsic chirality, allowing them to have extremely high values. An asymmetric reflection of approximately 40% is measured. Furthermore, the asymmetric reflection of extrinsic chiral metasurfaces is demonstrated not only in intensity but also in phase retardation, which induces asymmetric polarization state conversion. An approximately 14° asymmetric reflected polarization offset from the symmetry axis is achieved. Our research provides an effective new method for constructing huge asymmetric coupled systems to manipulate electromagnetic waves.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The properties of electromagnetic waves can be effectively manipulated by tailoring permittivity and permeability or transmission matrix of systems [1–10]. Based on this methodology, several novels and useful systems, such as non-Hermitian and nonreciprocal systems are developed for various applications such as optical diodes, optical isolators, unidirectional lasers, and ultrasensitive sensors. The coupling between modes plays a key role in these systems. Recently, a class of systems with asymmetric coupling has received extensive attention [11–20]. Asymmetric coupling systems can produce many important effects, such as asymmetric and nonreciprocal propagation, unidirectional light emission, topological lasers and non-Hermitian skin effect.
Asymmetric electromagnetic wave propagation is a very interesting and useful phenomenon, that can be achieved by asymmetric coupling. For example, optical diodes based on asymmetric propagation are important components in optical circuits for optical communication and optical computing. Fedotov et al. discovered asymmetric transmission (AT) based on asymmetric coupling between left-handed circularly polarized (LCP,-) and right-handed circularly polarized (RCP,+) electromagnetic waves in “2D (planar) chiral” metasurfaces [20]. The asymmetric coupling between LCP and RCP light is called circular conversion dichroism (ccd). However, the AT obtained in “2D chiral” metasurfaces is very small and has a theoretical limit of about 25% [21,22,23], because the asymmetric coupling of the transmission matrix for these “2D chiral” metasurfaces is very small. This becomes an obstacle for using the AT of “2D ultrathin chiral” metamaterials in optical diodes. Therefore, a variety of multilayer metamaterials were proposed to achieve giant asymmetric coupling and AT [22–30]. However, the fabrication of submicrometer-size multilayer metamaterials with precise design remains a great challenge for today's micromachining technology.
A very simple and effective method to achieve large asymmetric coupling has been overlooked, which is the reflection in extrinsic chiral metasurfaces at oblique incidence. Extrinsic chiral metasurfaces can show giant circular dichroism by breaking the mirror symmetry of the experimental arrangement via oblique illumination [31–35]. Similar to the AT in “2D chiral” metasurfaces for the oblique incidence setup, extrinsic chiral metasurfaces possess reversed chirality when observed from the direction of the reflected beam. This opens the door to massive asymmetric couplings based on extrinsic chirality. However, to the best of our knowledge, no research work on this topic has been reported.
In this article, we propose and experimentally demonstrate that giant AR of circularly polarized light in the near-infrared region based on asymmetric coupling can be achieved in single-layer extrinsic chiral metasurfaces at oblique incidence. The giant asymmetric coupling and AR in single-layer extrinsic chiral metasurfaces caused by extrinsic chirality have the same magnitude as the reflected circular dichroism. The measured AR is approximately 40%, which is much greater than the theoretical limit of the AT in “2D chiral” metasurfaces (25%). In addition, the polarization states of the reflected light are measured and analyzed. An asymmetry phase retardation between forward and backward incident, of about 28°, is achieved in the single-layer extrinsic chiral metasurfaces at 1550 nm. As a result, asymmetric polarization state conversion occurs, which means that the reflected polarization direction offsets from the symmetry axis differ for forward and backward incident (approximately 14°). Our study provides a new perspective for designing large asymmetric coupled systems.
2. Theoretical analysis
First, we discuss the transmission of 3D chirality and “2D chirality”. The transmission Jones matrix T for circular polarization [22,29] is described as
Here, we define: $cd = {T_{ +{+} }} - {T_{ -{-} }},ccd = {T_{ -{+} }} - {T_{ +{-} }}\; and\; CD = {T_ + } - {T_ - } = {T_{ +{+} }} + {T_{ -{+} }} - {T_{ +{-} }} - {T_{ -{-} }} = cd + ccd$
Because total circular dichroism (CD) is related to loss, the transmission Jones matrix T of chiral structures is generally a non-Hermitian matrix. For 3D chiral structures like a helix, the diagonal elements are different, resulting in a large cd, and the anti-diagonal elements are zero, implying no coupling between LCP and RCP lights. AT cannot be obtained in these 3D chiral structures. The above-mentioned “2D chiral” structures are marked with double quotation marks because they are actually 3D chiral structures, as the “2D chiral” structure consists of a dielectric substrate and a true 2D chiral structure. The diagonal elements of these “2D chiral” structures are equal to each other, but the anti-diagonal elements are different, implying the presence of asymmetric coupling between LCP and RCP lights. Thus, AT based on asymmetric coupling can be obtained. Since the properties of the “2D chiral” structures differ significantly from those of the 3D chiral structure, we continue to use the term “2D chiral” structure in this paper to distinguish the two chiral structures.
Now, we discuss the reflection of the single-layer extrinsic chiral metasurfaces. As shown in Fig. 1, the extrinsic chiral metasurface consists of an array of gold split ring resonators (SRRs) arranged in a rectangular lattice geometry supported by a glass substrate. The reflection Jones matrix R for circular polarization is described as
Fig. 1. Measurement setup of the reflected CD and AR of the extrinsic chiral SRRs arrays. The inset shows an SEM image of the extrinsic chiral SRRs arrays.
Here, the superscript f stands for forward incidence, and the superscript b stands for backward incidence. Similar to the transmission case, we can give some simple definitions:${R_ + } = {R_{ +{+} }} + {R_{ -{+} }}$, ${R_ - } = {R_{ -{-} }} + {R_{ +{-} }}$, $cd = {R_{ +{+} }} - {R_{ -{-} }}$, $ccd = {R_{ -{+} }} - {R_{ +{-} }}$ and $CD = {R_ + } - {R_ - } = cd + ccd$.
Because of the symmetry of the system, for the backward incidence cases, the reflections of the RCP and LCP light are reversed compared to the forward incidence cases. One can easily draw the following results for the oblique incidence: $r_{ +{+} }^f$=$r_{ -{-} }^b,\; r_{ -{-} }^f$=$r_{ +{+} }^b,r_{ +{-} }^f$=$r_{ -{+} }^b,r_{ -{+} }^f$=$r_{ +{-} }^b$ and $\varphi _{ +{+} }^f$=$\varphi _{ -{-} }^b,\; \varphi _{ -{-} }^f$=$\varphi _{ +{+} }^b,\varphi _{ +{-} }^f$=$\varphi _{ -{+} }^b,\varphi _{ -{+} }^f$=$\varphi _{ +{-} }^b$
Therefore,
Extrinsic chiral metasurfaces are expected to exhibit giant asymmetric coupling, reflected CD, and AR because their chirality is reversed when viewed from the direction of the reflected beam, as shown in Fig. 1.
3. Experimental and simulated setups and results
As shown in Fig. 1, the extrinsic chiral metasurface is made up of an array of gold split ring resonators (SRRs) arranged in a rectangular lattice geometry, which is supported by a glass substrate. These gold split ring resonators are fabricated by electron beam lithography (EBL) (Tianjin H-Chip Technology Group Corporation). The lattice spacings of the metasurface are Px = 1000 nm and Py = 650 nm. The metasurface extends over the (x, y) plane with the symmetry axis of the SRRs oriented along the y direction. The structure is illuminated from the metasurface side by circularly polarized light that propagates in the (x, z) plane, making an angle with the metasurface normal. The inset on the right side of Fig. 1 shows a scanning electron microscope (SEM) image of the fabricated structure. The SRRs have a U shape with R = 350 nm, w = 200 nm, and a thickness of ∼100 nm. Commercial software COMSOL Multiphysics based on the finite element method (FEM) is employed for model building and simulation calculations. The simulation model is established according to the experimental parameters. Here, the quartz constitutes the substrate and the U-shaped structure is set to gold, as in the Johnson and Christy’s model. Periodic boundary conditions were applied along the x- and y-directions.
The measurement setup is shown in Fig. 1. The reflection spectra were measured using an R1 spectrometer (Ideaoptics). The light beam from a white light source or a laser passes through a polarizer and a broadband 1/4 wave plate (Thorlabs) to form RCP or LCP light. Then, the RCP or LCP light beam is obliquely incident on the extrinsic chiral SRRs array sample. The reflected light is recorded with a spectrometer to obtain the reflection spectra.
Figure 2 shows the measured $R_{ +{+} }^f,\; R_{ -{+} }^f,R_{ +{-} }^f\textrm{and}\; R_{ -{-} }^f\; $ of the extrinsic chiral SRRs, for 45°incidence. There is a giant and broad peak at approximately 1120 nm in $R_{ -{+} }^f$ and two reflection peaks at approximately 1650 nm and 1075 nm in $R_{ +{-} }^f$. The behavior of $R_{ +{+} }^f$ and $R_{ -{-} }^f$ curves are quite similar, and both have reflection valleys at approximately 1060 nm and 1700nm. The huge difference between the anti-diagonal elements ($R_{ -{+} }^f$ and $R_{ +{-} }^f$) indicates the presence of giant asymmetric coupling. Next, the physical mechanism of forming these spectra is qualitatively examined.
Fig. 2. The measured ${\boldsymbol R}_{ +{+} }^{\boldsymbol f}\; ,{\boldsymbol R}_{ -{+} }^{\boldsymbol f}\; ,{\boldsymbol R}_{ +{-} }^{\boldsymbol f}{\boldsymbol \; and\; R}_{ -{-} }^{\boldsymbol f},{\boldsymbol \; }$ of the extrinsic chiral SRRs for 45° incidence
Extrinsic chiral SRRs can support local surface plasmon resonance (LSPR) modes and lattice surface modes (LSMs), which induced the reflection peaks. According to the electric field distribution shown in Fig. 3, the broad reflection peaks at approximately 1120 nm are induced by the quadrupole LSPR mode, which does not move with the variation in incident angle. The reflection peaks located at approximately 1650 nm and 1075 nm result from the (1,0) mode and (1,1) mode of the LSMs, respectively. As shown in Fig. 3, these peaks redshift with increasing incident angle.
Fig. 3. Simulated and measured reflection spectra of the extrinsic chiral SRRs arrays for incident angles of 30°, 35°, 40°, and 45°: (a), (c) simulated and measured reflection spectra for RCP light incident from the forward and backward directions, the insets are the intensity distributions of the z component of the electric field for 45° incidence at 1160 nm; (b), (d) simulated and measured reflection spectra for LCP light incident from the forward and backward directions.
First, we investigate the cases in which extrinsic chiral SRRs interact with light through LSPR. As shown in Fig. 1, if we observe the extrinsic chiral SRRs obliquely from the left side, the SRRs show left-handedness, with the same twist as the LCP light. When the extrinsic chiral SRRs are obliquely observed from the right side, the SRRs show right-handedness, with the same twist as the RCP light. Light and SRRs with opposite handedness exhibit stronger interaction through quadrupole LSPR modes than those with the same handedness, which means larger excitation efficiency and radiation efficiency of quadrupole LSPR modes [34]. In addition, since the extrinsic chiral SRRs do not have the chiral mirror effect, when circularly polarized light is incident, the rotation direction of the electric field vector of most electromagnetic waves remains unchanged, and a small number of electromagnetic waves are converted into the one with opposite rotation direction. When the RCP light is incident obliquely from the left side (forward) to the extrinsic chiral SRRs arrays, strong LSPR is excited in the extrinsic chiral SRRs. Figure 1 shows that the rotation direction of the electric vector of the forward incident RCP light is counter-clockwise. Both the dominant counter-clockwise LSPR modes and weak clockwise LSPR modes exist. Then, counter-clockwise LSPR radiates to the right side as LCP light high efficiently, while clockwise LSPR radiates to the right side as RCP light low efficiently. When LCP light is incident forward to the extrinsic chiral SRRs arrays, weak LSPR is excited in the extrinsic chiral SRRs. Then, similar to the RCP incident, counter-clockwise LSPR radiates to the right side as LCP light high efficiently, whereas clockwise LSPR radiates to the right side as RCP light low efficiently. It can be concluded from these analyses that $R_{ -{+} }^f$>$R_{ +{-} }^f$, $R_{ +{+} }^f$≈$R_{ -{-} }^f$.
When LSMs act as the primary mechanism, light and SRRs with the same handedness exhibit stronger interactions than those with opposite handedness [33,35]. Similar to the case of LSPR as the primary mechanism, we can obtain $R_{ -{+} }^f$<$R_{ +{-} }^f$, $R_{ +{+} }^f$≈$R_{ -{-} }^f$.
LSPR and LSMs act simultaneously to form the reflection spectra as shown in Fig. 2 and Fig. 3. The giant and broad peak at about 1120 nm in $R_{ -{+} }^f$ is induced by the quadrupole LSPR mode. The reflection peaks located at approximately 1650 nm and 1075 nm in $R_{ +{-} }^f$ are resulted from the LSMs. Since the excitation and emission efficiencies of LSMs are lower than those of LSPRs, LSMs exhibit reflection valleys in $R_{ -{+} }^f,R_{ +{+} }^f$ and $R_{ -{-} }^f\; $. In addition, $R_{ +{+} }^f$ and $R_{ -{-} }^f$ are far less than $R_{ -{+} }^f\; $ and $R_{ +{-} }^f$, because the conversion efficiency from incident rotation electromagnetic waves to opposite rotation electromagnetic waves is very low.
Thus, giant and broad asymmetric couplings (or ccd) originating from extrinsic chirality are obtained. Furthermore, the giant reflection CD and AR can be achieved in the single-layer extrinsic chiral SRRs arrays.
Figure 3 shows the simulated and measured reflection spectra of the extrinsic chiral SRRs for incident angles of 30°, 35°, 40°, and 45°. The simulated reflection spectra are very consistent with the measured spectra. Both RCP and LCP light incidence show clear broadband differences in reflection spectra between forward and backward incidence directions. The reflection spectra for forward RCP light incidence are similar to those for backward LCP light incidence, and the reflection spectra for backward RCP light incidence are similar to those for forward LCP light incidence. This result agrees well with our theoretical prediction based on Eq. (6). The insets of Fig. 3(a) and (c) show the intensity distributions of the z component of the electric field with the incident angle of 45° at the broad peak (1160 nm), which suggests that the broad reflection peaks are induced by the quadrupole LSPR modes.
Figure 4 shows the reflected CD and AR of the extrinsic chiral metasurface for incident angles of 30°, 35°, 40°, and 45°. The broadband large reflected CD and AR are obtained. All the reflected CD and AR spectra are similar in value and conform to Eq. (9). The absolute values of the reflected CD and AR change slightly as the incident angle increases from 30° to 45°. The maximum reflected CD and AR values of approximately 40% are achieved, which are much greater than the theoretical limit of the AT in 2D chiral metasurfaces of 25%. All of these findings are consistent with the theoretical analysis presented above.
Fig. 4. Reflected CD and AR of the extrinsic chiral SRRs arrays for incident angles of 30°, 35°, 40°, and 45°: (a) Forward incidence reflected CD; (b) backward incidence reflected CD; (c) AR for RCP incidence; (d) AR for LCP incidence.
The phase retardations of the reflection in extrinsic chiral metasurfaces are also studied. Figure 5 shows the polar plots of the polarization state for reflected light with an incident angle of 45°. For Figs. 5(a–b), the wavelength of the incident laser is 1064 nm, and for Figs. 5(c–d), it is 1550 nm. The 0°-180° direction is the symmetry axis direction of the SRRs, that is, the vertical direction of the incident surface, and is referred to as the symmetry axis in the following discussion. All of the reflected light is elliptically polarized. According to general rules, the long-axis direction of the polarization states is defined as the polarization direction of the reflected light. Since the reflected light contains both LCP light and RCP light with a single circularly polarized incident light, we define relative phase retardations between reflected LCP light and RCP light as follows: $\mathrm{\Delta }{\varphi _ + }$=${\varphi _{ +{+} }} - {\varphi _{ -{+} }}$ and $\mathrm{\Delta }{\varphi _ - }$=${\varphi _{ -{-} }} - {\varphi _{ +{-} }}$. As shown in Fig. 5, the polarization states of the four pairs of reflected light are highly symmetric about the symmetry axis. These results are consistent with Eq. (9). For the case of the incident laser wavelength of 1060 nm, the polarization direction of the reflected light is rotated by an angle of approximately 10$^\circ $ from the symmetry axis when RCP light is incident, and the rotation angle is approximately -10$^\circ $ when LCP light is incident, regardless of whether the incident is forward or backward (see Figs. 5(a) and 5(b)). These results are induced by the relative phase retardations between reflected LCP and RCP light and mean that: $({\mathrm{\Delta }\varphi_ +^f = \mathrm{\Delta }\varphi_ -^b} )\approx ({\mathrm{\Delta }\varphi_ -^f = \mathrm{\Delta }\varphi_ +^b} )\approx 20^\circ $. There are no asymmetric phase retardations or asymmetric polarization state conversions at this time. For the case of the incident laser wavelength of 1550 nm, the results are quite different. As shown in Fig. 5(c) and (d), when RCP light is incident from backward, the polarization direction of the reflected light is rotated by an angle of approximately 14$^\circ $ from the symmetry axis. Whereas, the rotation angle is almost zero when RCP light is incident from forward. Similarly, when LCP light is incident from forward, the rotation angle is approximately -14$^\circ $, and it is almost 0$^\circ $, when LCP light is incident from backward. These results imply that: $\textrm{}({\mathrm{\Delta }\varphi_ +^f = \mathrm{\Delta }\varphi_ -^b} )\approx 0^\circ \; \textrm{and}\; ({\mathrm{\Delta }\varphi_ -^f = \mathrm{\Delta }\varphi_ +^b} )\approx 28^\circ $ for the case of the incident laser wavelength of 1550 nm. Therefore, considerable asymmetry phase retardations and asymmetric polarization states conversions are obtained. It is well known that polarization conversion and regulation of light are critical for many optical applications [36–39]. Therefore, the proposed asymmetric polarization state conversion will be useful in optical communication, optical computing and other fields.
Fig. 5. Polar plots of the polarization state for reflected light with an incident angle of 45°.(a) and (b) 1064 nm laser incidence, (c) and (d) 1550 nm laser incidence; (a) and (c) RCP light incident from the backward direction (red), and LCP light incident from the forward direction (blue); (b) and (d) RCP light incident from the forward direction (red), and LCP light incident from backward direction (blue).
4. Conclusion
In conclusion, the AR of circularly polarized light based on giant asymmetric coupling in a single-layer extrinsic chiral metasurface at oblique incidence is proposed and experimentally demonstrated. We demonstrated that the AR and asymmetric coupling in the single-layer extrinsic chiral metasurfaces caused by extrinsic chirality can have extremely high values which is almost identical to the reflected CD. Consequently, a giant AR of approximately 40% is obtained. The AR of the extrinsic chiral metasurfaces is observed not only in intensity but also in phase retardation and polarization state. An asymmetry phase retardation of approximately 28° is obtained at 1550 nm. Consequently, an asymmetry polarization conversion between forward and backward incident is achieved. The asymmetric reflected polarization offset from the symmetry axis is approximately 14°. Our findings will open up new avenues for the designing of large asymmetric coupled systems. The proposed AR in extrinsic chiral metasurfaces can be used in reflective optical elements, which is a significant step toward the practical realization of on-chip optical asymmetric propagation devices.
Funding
National Natural Science Foundation of China (11874229, 62205158); China Postdoctoral Science Foundation (2022M711709); Natural Science Foundation of Tianjin City (06TXTJJC13500, 20JCQNJC01410); Science and Technology Commission of Tianjin Binhai New Area (BHXQKJXM-PT-ZJSHJ-2017003); 111 Project (B07013); Program for Changjiang Scholars and Innovative Research Team in Nankai University (IRT_13R29); Fundamental Research Funds for the Central Universities.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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.
References
1. D. R. Smith, J. B. Pendry, and M. C. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). [CrossRef]
2. H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science 336(6078), 205–209 (2012). [CrossRef]
3. A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013). [CrossRef]
4. T. Xu, A. Agrawal, M. Abashin, K. J. Chau, and H. J. Lezec, “All-angle negative refraction and active flat lensing of ultraviolet light,” Nature 497(7450), 470–474 (2013). [CrossRef]
5. A. M. Mahmoud, A. R. Davoyan, and N. Engheta, “All-passive nonreciprocal metastructure,” Nat. Commun. 6(1), 8359 (2015). [CrossRef]
6. F. Ruesink, M. A. Miri, A. Alu, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nat. Commun. 7(1), 13662 (2016). [CrossRef]
7. M. A. Miri and A. Alu, “Exceptional points in optics and photonics,” Science363(6422), (2019).
8. Y. Chen, W. Du, Q. Zhang, O. Ávalos-Ovando, J. Wu, Q.-H. Xu, N. Liu, H. Okamoto, A. O. Govorov, Q. Xiong, and C.-W. Qiu, “Multidimensional nanoscopic chiroptics,” Nat. Rev. Phys. 4(2), 113–124 (2021). [CrossRef]
9. Z. Jin, D. Janoschka, J. Deng, L. Ge, P. Dreher, B. Frank, G. Hu, J. Ni, Y. Yang, J. Li, C. Yu, D. Lei, G. Li, S. Xiao, S. Mei, H. Giessen, F. M. zu Heringdorf, and C.-W. Qiu, “Phyllotaxis-inspired nanosieves with multiplexed orbital angular momentum,” eLight 1(1), 5 (2021). [CrossRef]
10. Y. Chen, X. Yang, and J. Gao, “3D Janus plasmonic helical nanoapertures for polarization-encrypted data storage,” Light: Sci. Appl. 8(1), 45 (2019). [CrossRef]
11. C. Qin, B. Wang, Z. J. Wong, S. Longhi, and P. Lu, “Discrete diffraction and Bloch oscillations in non-Hermitian frequency lattices induced by complex photonic gauge fields,” Phys. Rev. B 101(6), 064303 (2020). [CrossRef]
12. T. E. Lee, “Anomalous Edge State in a Non-Hermitian Lattice,” Phys. Rev. Lett. 116(13), 133903 (2016). [CrossRef]
13. R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14(1), 11–19 (2018). [CrossRef]
14. Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, “Topological Phases of Non-Hermitian Systems,” Phys. Rev. X 8(3), 031079 (2018). [CrossRef]
15. S. Yao and Z. Wang, “Edge States and Topological Invariants of Non-Hermitian Systems,” Phys. Rev. Lett. 121(8), 086803 (2018). [CrossRef]
16. A. Rehemanjiang, M. Richter, U. Kuhl, and H. J. Stockmann, “Microwave Realization of the Chiral Orthogonal, Unitary, and Symplectic Ensembles,” Phys. Rev. Lett. 124(11), 116801 (2020). [CrossRef]
17. M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science359(6381), (2018).
18. W. E. Hayenga, M. Parto, J. Ren, F. O. Wu, M. P. Hokmabadi, C. Wolff, R. El-Ganainy, N. A. Mortensen, D. N. Christodoulides, and M. Khajavikhan, “Direct Generation of Tunable Orbital Angular Momentum Beams in Microring Lasers with Broadband Exceptional Points,” ACS Photonics 6(8), 1895–1901 (2019). [CrossRef]
19. Y. G. N. Liu, P. S. Jung, M. Parto, D. N. Christodoulides, and M. Khajavikhan, “Gain-induced topological response via tailored long-range interactions,” Nat. Phys. 17(6), 704–709 (2021). [CrossRef]
20. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006). [CrossRef]
21. A. B. Khanikaev, N. Arju, Z. Fan, D. Purtseladze, F. Lu, J. Lee, P. Sarriugarte, M. Schnell, R. Hillenbrand, M. A. Belkin, and G. Shvets, “Experimental demonstration of the microscopic origin of circular dichroism in two-dimensional metamaterials,” Nat. Commun. 7(1), 12045 (2016). [CrossRef]
22. C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, “High performance bianisotropic metasurfaces: asymmetric transmission of light,” Phys. Rev. Lett. 113(2), 023902 (2014). [CrossRef]
23. Z. Ma, Y. Li, Y. Li, Y. Gong, S. A. Maier, and M. Hong, “All-dielectric planar chiral metasurface with gradient geometric phase,” Opt. Express 26(5), 6067–6078 (2018). [CrossRef]
24. C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010). [CrossRef]
25. M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike Asymmetric Transmission of Linearly Polarized Waves Using Magnetoelectric Coupling and Electromagnetic Wave Tunneling,” Phys. Rev. Lett. 108(21), 213905 (2012). [CrossRef]
26. C. K. Amaljith, C. Venkateswaran, V. Subramanian, Z. Ouyang, and N. Yogesh, “Anisotropic asymmetric transmission of circularly polarized terahertz waves in a three-dimensional spline assembly,” Opt. Lett. 45(8), 2315–2318 (2020). [CrossRef]
27. R. Ji, S. W. Wang, X. Liu, and W. Lu, “Giant and broadband circular asymmetric transmission based on two cascading polarization conversion cavities,” Nanoscale 8(15), 8189–8194 (2016). [CrossRef]
28. Y. Zhao, M. A. Belkin, and A. Alu, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3(1), 870 (2012). [CrossRef]
29. Y. Wang, X. Wen, Y. Qu, L. Wang, R. Wan, and Z. Zhang, “Co-occurrence of circular dichroism and asymmetric transmission in twist nanoslit-nanorod Arrays,” Opt. Express 24(15), 16425–16433 (2016). [CrossRef]
30. L. Wu, Z. Yang, Y. Cheng, Z. Lu, P. Zhang, M. Zhao, R. Gong, X. Yuan, Y. Zheng, and J. Duan, “Electromagnetic manifestation of chirality in layer-by-layer chiral metamaterials,” Opt. Express 21(5), 5239–5246 (2013). [CrossRef]
31. E. Plum, V. A. Fedotov, and N. I. Zheludev, “Optical activity in extrinsically chiral metamaterial,” Appl. Phys. Lett. 93(19), 191911 (2008). [CrossRef]
32. E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009). [CrossRef]
33. I. De Leon, M. J. Horton, S. A. Schulz, J. Upham, P. Banzer, and R. W. Boyd, “Strong, spectrally-tunable chirality in diffractive metasurfaces,” Sci. Rep. 5(1), 13034 (2015). [CrossRef]
34. Y. Wang, J. Qi, C. Pan, Q. Wu, J. Yao, Z. Chen, J. Chen, Y. Li, X. Yu, Q. Sun, and J. Xu, “Giant circular dichroism of large-area extrinsic chiral metal nanocrecents,” Sci. Rep. 8(1), 3351 (2018). [CrossRef]
35. L. Cao, J. Qi, Q. Wu, Z. Li, R. Wang, J. Chen, Y. Lu, W. Zhao, J. Yao, X. Yu, Q. Sun, and J. Xu, “Giant Tunable Circular Dichroism of Large-Area Extrinsic Chiral Metal Nanocrescent Arrays,” Nanoscale Res. Lett. 14(1), 388 (2019). [CrossRef]
36. L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103(17), 171107 (2013). [CrossRef]
37. L. Cong, N. Xu, J. Gu, R. Singh, J. Han, and W. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photonics Rev. 8, 626–632 (2014). [CrossRef]
38. L. Cong, Y. K. Srivastava, and R. Singh, “Near-Field Inductive Coupling Induced Polarization Control in Metasurfaces,” Adv. Opt. Mater. 4(6), 848–852 (2016). [CrossRef]
39. L. Cong, Y. K. Srivastava, H. Zhang, X. Zhang, J. Han, and R. Singh, “All-optical active THz metasurfaces for ultrafast polarization switching and dynamic beam splitting,” Light: Sci. Appl. 7(1), 28 (2018). [CrossRef]
