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Abstract
Active control of induced reflection is crucial for many potential applications ranging from slowing light to biosensing devices. However, most previous approaches require patterned nanostructures to achieve controllable induced reflection, which hinders their further applications due to complicated architectures. Herein, we propose a lithography-free multilayered structure to achieve the induced reflection through the coupling of dual-topological-interface-states. The multilayers consist of two one-dimensional (1D) photonic crystals (PCs) and an Ag film separated by a Spacer, topological edge state (TES) and topological Tamm state (TTS) can be excited simultaneously and their coupling induces the reflection window. The coupled-oscillator model is proposed to mimic the coupling between the TES and TTS, and the analytical results are in good agreement with finite element method (FEM). In addition, the TES-TTS induced reflection is robust to the variation of structural parameters. By integrating an ultra-thin phase-change film of Ge2Sb2Te5 (GST) into the multilayers, the induced reflection can be switched through the phase transition of the GST film. The multipole decomposition reveals that the vanished reflection window is arising from the disappearance of TTS associated with the toroidal dipole (TD) mode.
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1. Introduction
Electromagnetically induced transparency (EIT) is a coherent coupling between a broad and a narrow band resonance due to the quantum interference, which was originally proposed in atomic system [1,2]. In photonic system, EIT exhibits near-zero reflection and near-perfect transmission window within a relatively broadband wavelength region, resulting in significantly slowed photons and enhanced nonlinearities [3,4]. An EIT-like effect known as plasmon-induced transparency (PIT), which is originated from the constructive and destructive interferences between several resonances in the artificial plasmon molecules, can also be used to regulate and control the transmission spectra of the plasmonic metamaterials [5–7]. However, optical devices based on the EIT or PIT effects can only work in the transmission space, which limits their further applications such as slow-light and optical sensing in the reflection space.
To overcome these issues, similar as EIT and PIT, electromagnetically induced reflection (EIR) and plasmon-induced reflection (PIR), which are originated from the interferences of the resonant modes in optical metamaterials, are proposed to modulate the reflection responses of the optoelectronic devices [8]. For example, by using the hybridization between the magnetic and electric modes in polymeric nanospheres, selective reflection and structural colors can be achieved in the nanosphere-aggregation system [9]. By exciting the resonant modes of the hybrid metal-dielectric metasurfaces, versatile functions such as large group delay [10–12] and high-quality optical sensing [13,14] can be realized based on the EIR and PIR effects. In addition, to dynamical control the resonance features of the induced reflection, active media such as Dirac semimetal metamaterials [15] and monolayer graphene [16–18] are integrated into the metasurfaces, where their conductivity can be tuned by changing the Fermi levels through doping or applying external voltage [19]. However, these approaches mentioned above require patterned nanostructures to achieve the controllable induced reflection, which increases the fabrication difficulty in application. Therefore, it has significant importance to achieve the induced reflection within the comparably simple architectures, and their induced reflection windows can be switched as well.
In this work, configurable induced reflection is demonstrated by using the lithography-free hybrid multilayers based on dual-topological-interface-states. The multilayered structure consists of two one-dimensional (1D) photonic crystals (PCs) and an Ag film separated by a Spacer, topological edge state (TES) and topological Tamm state (TTS) can be excited simultaneously and their coupling results in the induced reflection window. The coupled-oscillator model is proposed to evaluate the induced reflection performances, and the predicted results are in good agreement with the finite element method (FEM). In addition, the TES-TTS induced reflection can be maintained even if the structural parameters are significantly altered. By inserting an ultra-thin phase-change film of Ge2Sb2Te5 (GST) between the Spacer and Ag film, the induced reflection can be switched through the phase transition of the GST film. According to the multipolar decomposition, the vanished reflection window is arising from the disappearance of TTS associated with the toroidal dipole (TD) mode.
2. Design principle
The optical properties of the proposed multilayers under the normal illumination of the TM-polarized plane wave (magnetic -field along z-axis) are shown in Fig. 1. Figure 1(a) shows the schematic diagram of the hybrid multilayers, which consists of two pairs of 1D PCs (PC 1 and PC 2) with alternately stacked SiO2/Si layers (the period for both the two PCs are 4), a Spacer, and an Ag film. In principle, the hybrid PC 1-PC 2 structure can support the TES at the interface of the two PCs if their topological properties of bulk dispersion are different [20,21]; similarly, it is possible to excite the TTS at the interface of the PC 2 and Ag film if they have opposite reflection phase [22]. Here the Spacer can be utilized to achieve phase matching between the PC 2 and the Ag film, as well as to tune the resonant wavelength. As our proposed structure consists of two 1D PCs, a Spacer and Ag film, the TES and TTS may be excited simultaneously in the hybrid multilayers at the specific structural parameters, thus it is possible to achieve induced reflection through the coupling of TES and TTS.
Fig. 1. Optical properties of the multilayer-based structures under the normal illumination of TM wave. The structural parameters are: dA = 297 nm, dB = 125 nm, dC = 98 nm, dD = 232 nm, d0 = 100 nm, ds = 150 nm. (a) Schematic diagram of the proposed hybrid multilayers, which consists of two pairs of 1D PCs and an Ag film separated by a Spacer. (b) Band structures of PC 1 and PC 2 (left) and reflection spectrum of the hybrid PC 1-PC 2 structure (right). (c) Reflection phases of PC 2, Spacer, Ag film, and the hybrid structure of PC 2-Spacer-Ag film (left); reflection spectrum of the total structure (right). (d) Schematic diagram of the PC 1-PC 2 structure (top), and normalized electric field distributions |E/E0| at the resonance wavelength of TES at 1553 nm (bottom). (e) Schematic diagram of the hybrid structure of PC 2-Spacer-Ag film (top), normalized electric field distributions |E/E0| at the resonance wavelength of TTS at 1545 nm (bottom).
For the PC 1 and PC 2 with finite period, their band properties can be approximately estimated by using the dispersion of the PCs with infinite period, in the case of the TM-polarized wave illumination, the dispersion relation can be written as [23]:
To facilitate the analysis of the two different PCs with opposite topological properties, we construct PC 1 and PC 2 according to the Bragg condition so that they can obtain bandgaps with similar wavelength range, the Bragg condition for the two 1D PCs can be written as:
where na and nb are the refractive indices of the da and db layers, respectively; m1 is an integer, and λ is the Bragg wavelength.To better evaluate the band properties of PC 1 and PC 2, we investigate the Zak phase of the bands of the 1D PCs, where the nth isolated energy band defined as [24,25]:
The topological property (i.e., band property) for nth bandgap can be further defined by summing the Zak phase of all the passbands below it [20]:
On the other hand, for the hybrid structure of PC 2-Spacer-Ag film, the propagation of light in it can be represented by the transfer matrix:
In simulation, the refractive indices of Si and SiO2 are 3.48 and 1.47, respectively; the relative permittivity of Ag film is described by using Drude model according to experimental data [26]. The structural parameters of the hybrid multilayers are: dA = 297 nm, dB = 125 nm, dC = 98 nm, dD = 232 nm, d0 = 100 nm. The thickness of the Ag film (ds = 150 nm) is large enough to block the light transmission. The optical properties of the multilayers are calculated by using Comsol Multiphsics based on the FEM. Floquet periodic boundary conditions (PBC) are set along the y axis to simulate infinite films, perfectly matched layers (PML) are placed at the top and bottom boundaries, and the whole structure is divided into refined meshes to ensure the accuracy of the results.
Figure 1(b) shows the band structures of PC 1 and PC 2 as well as the reflection spectrum of the hybrid PC 1-PC 2 structure. As shown in the left of Fig. 1(b), the band gaps of PC 1 and PC 2 calculated by using Eq. (1) are overlapped in the region centered at 193 THz (1550 nm). According to Eqs. (3–5), the signs of the band gaps of PC 1 and PC 2 are negative (ζ<0) and positive (ζ>0), respectively; indicating their opposite topological properties. Therefore, the cascading PC 1-PC 2 structure can support the excitation of the TES. In the right of Fig. 1(b), for the hybrid PC 1-PC 2 structure, it can be seen that a reflection dip is occurred at 1553 nm in the overlapped band gap of the isolated PC 1 and PC 2, validating the excitation of TES. Figure 1(c) shows the reflection spectrum of the hybrid structure of PC 2-Spacer-Ag film as well as the reflection phases of PC 2, Spacer and Ag film. As shown in the left of Fig. 1(c), the sum of the reflection phase of PC 2, Spacer and Ag film is zero with φtotal = 0 at 1545 nm, indicating the existence of the TTS at this location. As direct evidence, in the right of Fig. 1(c), it can be seen that a reflection dip is appeared at 1545 nm in the structure of PC 2-Spacer-Ag film due to the excitation of the TTS. To vividly demonstrate the existence of the TES and TTS, the normalized electric field distributions at the resonant wavelengths are studied in Figs. 1(d) and 1(e). As shown in Fig. 1(d), the electric field is significantly enhanced at the interface between PC 1 and PC 2, indicating that the TES can be excited in the PC 1-PC 2 structure. Similarly, as shown in Fig. 1(e), the electric field is well trapped around the region of the Spacer, indicating the distinct features of TTS in the structure of PC 2-Spacer-Ag film. Therefore, it is possible to that excite the TES and TTS simultaneously in the hybrid multilayers of PC 1-PC 2-Spacer-Ag film.
3. Results and discussion
Figure 2 shows the optical properties of the hybrid multilayers of PC 1-PC 2-Spacer-Ag film. In Fig. 2(a), it can be seen that a reflection window is occurred between the resonance dips of the TES (1565 nm) and TTS (1533 nm), and the TES-TTS induced reflection with peak reflectivity of 95.7% can be obtained. To demonstrate the occurrence of the TES-TTS induced reflection, the normalized electric field distributions of the hybrid multilayers at the two reflection dips are studied. In Fig. 2(b), it can be seen that the electric field is significantly enhanced around the Spacer between the PC 2 and the Ag film, indicating the resonance at 1533 nm is excited by the TTS. Note the TTS exhibits the hybrid features, and its electric field is also slightly enhanced around the interface between the PC 1 and PC 2 due to the structural hybridization of the cascaded multilayers. While as shown in Fig. 2(c), beside the field enhancement around the Spacer between the PC 2 and the Ag film, a pronounced field enhancement is appeared around the interface between the PC 1 and PC 2, indicating the resonance at 1565 nm is dominated by the TES. Therefore, the induced reflection of the multilayered structures is originated from the resonant coupling between the TES and TTS.
Fig. 2. Optical properties of the hybrid multilayers of PC 1-PC 2-Spacer-Ag film, the parameters are the same as in Fig. 1. (a) Reflection spectrum of the hybrid multilayers, and the insert is the schematic diagram of the structure. (b) Normalized electric field distributions |E/E0| at resonant wavelength of λ1 = 1533 nm. (c) Normalized electric field distributions |E/E0| at resonant wavelength of λ2 = 1565 nm.
To better understand the TES-TTS induced reflection, we employed the coupled-oscillator model to mimic the resonant coupling process in the hybrid multilayers. In this model, TES and TTS are both regarded as the bright modes as shown in Fig. 3(a). In the bright-bright coupled system, $\tilde E$(ω)eiωt represents the incident plane wave; $\tilde M$1(ω)eiωt and $\tilde M$2(ω)eiωt denote the two bright mode resonators, respectively. The field amplitude of the two bright modes can be expressed as:
Fig. 3. Coupled-oscillator model of the hybrid multilayers and reflection spectra for different d0, other parameters are the same as Fig. 1. (a) Schematic diagram of the two coupled oscillators in the hybrid multilayers, where γ, ω and κ are damping factor, resonance frequency, and coupling coefficient, respectively. Reflection spectra of the hybrid multilayers at (b) d0 = 95 nm, (c) d0 = 98 nm, (c) d0 = 101 nm, and (d) d0 = 104 nm.
Therefore, the reflection of the hybrid multilayers can be calculated with the formula R=|$\tilde M$1/ $\tilde E$|2. Figures 3(b)-3(e) show the reflection spectra of proposed structure with different thickness d0 of the Spacer. As shown in Figs. 3(b)-3(e), although the resonant features of the TES-TTS induced reflection are different for different d0, the results of the coupled-oscillator model are agreed well with those of the FEM, validating that the coupled-oscillator model could provide a general strategy to evaluate the TES-TTS induced reflection in hybrid multilayers from the phenomenological perspective.
To evaluate the robustness of the TES-TTS induced reflection of the hybrid multilayers, influences of structural parameters (dA,dB,dC,dD) on reflection performances are analyzed. Figures 4(a) and 4(b) show reflection of the hybrid multilayers as functions of the thicknesses of PC 1 for SiO2 layer dA, and Si layer dB, respectively. In Figs. 4(a) and 4(b), it can be seen that the TES-TTS induced reflection is gradually red-shifted with the increase of dA or dB; this is because that an increase in layer thickness of PC 1 leads to an increase in Bragg wavelength according to Eq. (2). In addition, because the refractive index of the Si layer is larger than that of the SiO2 layer, the influence of dB on reflection spectra of the hybrid multilayers is more pronounced than that of dA. Figures. 4(c) and 4(d) show reflection as functions of the thicknesses of PC 2 for Si layer dC, and SiO2 layer dD, respectively. Similarly, as can be seen in Figs. 4(c) and 4(d), the TES-TTS induced reflection still exists and red-shifts with the increase of dC or dD. However, as the thickness of the unit cell of PC 2 is smaller than PC 1, the shift of the induced reflection band is smaller as dC or dD is varied comparing with those of dA and dB. Note the TES-TTS induced reflection can be robustly excited even if the structural parameters (dA,dB,dC,dD) deviate from the design value of ±10%, which is favorable in applications due to the large fabrication tolerance.
Fig. 4. Reflection spectra of the hybrid multilayers as function of (a) thicknesses of the SiO2 layer in PC 1 dA, (b) thicknesses of the Si layer in PC 1 dB, (c) thicknesses of the Si layer in PC 2 dC, (d) thicknesses of the SiO2 layer in PC 2 dD. Other parameters are the same as Fig. 1.
To realize the active control of the TES-TTS induced reflection, an ultra-thin GST film (10 nm) is integrated into the hybrid multilayers, as indicated in Fig. 5(a). As a typical phase-change material, GST is particularly fascinating due to its excellent phase transition properties. GST film can be switched from amorphous (a-GST) to crystalline (c-GST) state by thermal-conduction annealing [27,28], electrical pulse [29,30], or laser excitation [31,32], and its phase transition has the advantages of low optical loss, quick response and good reversibility between two structural phases [33]. Figures 5(b) and 5(c) show optical responses of the hybrid multilayers with a-GST and c-GST film, respectively; the thickness of PC 1 is slightly altered so as to keep the resonant coupling between the TES and TTS. In Fig. 5(b), it can be seen that the TES-TTS induced reflection can be maintained after the inserting of the ultra-thin GST film, and the absorption is increased due to the resonances arising from the two topological interface states. However, as shown in Fig. 5(c), the TES-TTS induced reflection window is disappeared after the GST film is transformed from a-GST to c-GST state, and the absorption associated with the TTS is significantly reduced as well. To vividly illustrate the switch of the TES-TTS induced reflection, the electric field distributions at the two resonance locations are studied in Figs. 5(d)-5(f). As shown in Figs. 5(d) and 5(e), for hybrid multilayers with a-GST film, the electric fields can be enhanced around the interface of PC 1-PC 2 and the GST film, indicating that the resonance at λ1 = 1606 nm is dominated by TES, and the resonance at λ2 = 1643 nm is mainly excited by TTS. For hybrid multilayers with c-GST film, as shown in Fig. 5(f), the electric field associated with the resonant dip is mainly enhanced at the interface between PC 1-PC 2, indicating that the resonance at λ3 = 1616 nm is excited by TES. Note the resonance location of the TES is slightly red-shifted due to the increased optical constant as the GST film is transformed from the a-GST to c-GST state. Therefore, the phase transition of the GST film from amorphous to crystalline state will cancel the TTS, resulting in the collapse of the TES-TTS induced reflection window. Different from the GST PCs [34] and GST-based plasmonic waveguide [35] whose reversible topological interface states are excited by the in-plane incident light, the configurable topological interface states of the proposed hybrid multilayers are excited by the out-of-plane incident light. Moreover, comparing with the graphene-functionalized EIR metasurfaces [36,37] and the graphene-semiconductor PIR metasurfaces [18] whose induced reflections can be dynamically controlled by changing the Fermi energy of graphene via extra voltages, the induced reflection of the hybrid multilayers can also be switched between the on and off states in the lithography-free architecture instead of in the patterned structure, indicating its promising role for versatile manipulation of light with robust performances in the compact platform.
Fig. 5. Optical properties of the hybrid multilayers consisting of an ultra-thin GST film with thickness h = 10 nm. dA = 321 nm, dB = 135 nm, other parameters are the same as in Fig. 1. (a) Schematic diagram of the hybrid multilayers containing the GST film. (b) Reflection and absorption of the hybrid multilayers with GST in amorphous state. (c) Reflection and absorption of the hybrid multilayers with GST in crystalline state. (d) and (e) are normalized electric field distributions |E/E0| at resonant wavelengths of λ1 = 1606 nm, and λ2 = 1643 nm, respectively. (f) Normalized electric field distributions |E/E0| at resonant wavelength of λ3 = 1616 nm.
In principle, the optical responses of nanostructures can be decomposed into radiating contributions from multipoles, including electric dipole (ED), magnetic dipole (MD), TD, electric quadrupole (EQ), and magnetic quadrupole (MQ) according to the multipole decomposition theory [38,39]. To better understand the resonant process of the configurable TES-TTS induced reflection, we perform a thorough multipole analysis on the hybrid multilayers with a-GST or c-GST film, as shown in Fig. 6. For the hybrid multilayers with a-GST film, as shown in Fig. 6(a), it can be seen that the dominate dipoles at λ1 = 1606 nm and λ2 = 1643 nm are EQ and TD, respectively; indicating that the EQ plays the dominant role for the excitation of the TES, and the TTS is mainly resulted from the TD. In Fig. 6(b), it can be seen that the far-field scattering power of EQ and TD are reduced simultaneously after the GST film is transformed from amorphous to crystalline state. In particular, the TD mode associated with the TTS tends to be disappeared, validating that the vanishment of the TES-TTS induced reflection is arising from the absence of the TTS.
Fig. 6. Scattering power of ED, MD, TD, EQ and MQ, the insert shows the schematic diagram of the structure, and the parameters are the same as Fig. 5. (a) Scattering power of different multipoles for hybrid multilayers with a-GST film. (d) Scattering power of different multipoles for hybrid multilayers with c-GST film.
4. Conclusions
In conclusion, we propose a lithography-free multilayered structure to achieve induced reflection based on dual-topological-interface-states. The multilayers consist of two 1D PCs and an Ag film separated by a Spacer, dual-topological states of TES and TTS can be excited simultaneously and their coupling induces the reflection window. The TES-TTS induced reflection can be evaluated by the coupled-oscillator model from the phenomenological perspective, and the predicted results are in good agreement with the FEM. Moreover, the TES-TTS induced reflection can be maintained even if the thickness of the two PCs deviates from the design value of ±10%. The integration of an ultra-thin GST film into the multilayers enables the dynamic modulation of the TES-TTS induced reflection, and the reflection window will be closed if the GST film is transformed from amorphous to crystalline state. The multipole decomposition reveals that the vanished reflection window is originated from the disappearance of TTS associated with the TD mode. Our work provides a design strategy to create the induced reflection within the comparably simple architectures, and the configurable dual-topological-interface-states may offer a platform for the reversible switching of induced reflection, which is promising for various potential applications including optical modulators, light manipulation, optical filtering and low-loss switching devices.
Funding
National Natural Science Foundation of China (62375113).
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.
References
1. R. Röhlsberger, H. C. Wille, K. Schlage, et al., “Electromagnetically induced transparency with resonant nuclei in a cavity,” Nature 482(7384), 199–203 (2012). [CrossRef]
2. Y. Yang, I. I. Kravchenko, D. P. Briggs, et al., “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014). [CrossRef]
3. I. Novikova, R. L. Walsworth, and Y. Xiao, “Electromagnetically induced transparency-based slow and stored light in warm atoms,” Laser Photonics Rev. 6(3), 333–353 (2012). [CrossRef]
4. S. Hu, W. He, M. Tong, et al., “Dual-dimensional EIT manipulation for angle-multiplexed ultrafast terahertz switching,” ACS Photonics 10(7), 2182–2191 (2023). [CrossRef]
5. Y. Ling, L. Huang, W. Hong, et al., “Polarization-controlled dynamically switchable plasmon-induced transparency in plasmonic metamaterial,” Nanoscale 10(41), 19517–19523 (2018). [CrossRef]
6. B. Tang, Z. Guo, and G. Jin, “Polarization-controlled and symmetry-dependent multiple plasmon-induced transparency in graphene-based metasurfaces,” Opt. Express 30(20), 35554–35566 (2022). [CrossRef]
7. N. Ichiji and A. Kubo, “Resonance-order-dependent plasmon-induced transparency in orthogonally arranged nanocavities,” Opt. Lett. 47(2), 265–268 (2022). [CrossRef]
8. Z. Vafapour, “Near-infrared biosensor based on classical electromagnetically induced reflectance (Cl-EIR) in a planar complementary metamaterial,” Opt. Commun. 387, 1–11 (2017). [CrossRef]
9. Y. Wu, J. Ren, S. Zhang, et al., “Nanosphere-aggregation-induced reflection and its application in large-area and high-precision panchromatic inkjet printing,” ACS Appl. Mater. Interfaces 12(9), 10867–10874 (2020). [CrossRef]
10. Z. Vafapour, “Large group delay in a microwave metamaterial analog of electromagnetically induced reflectance,” J. Opt. Soc. Am. A 35(3), 417–422 (2018). [CrossRef]
11. W. Liu, H. Li, C. Li, et al., “Simultaneous realization of electromagnetically induced transparency and electromagnetically induced reflectance in a metasurface,” Opt. Express 29(8), 12580–12589 (2021). [CrossRef]
12. Q. Ma, W. Hong, and L. Shui, “Polarization and incidence insensitive analogue of electromagnetically induced reflection metamaterial with high group delay,” Opt. Express 30(2), 3055–3065 (2022). [CrossRef]
13. A. H. Alipour and A. Mir, “Design and simulation of a high-selective plasmon-induced reflectance in coupled dielectric-metal-dielectric nano-structure for senor devices and slow light propagation,” Plasmonics 14(2), 511–521 (2019). [CrossRef]
14. J. Huang, W. Wang, X. Xu, et al., “Ultraviolet ultranarrow second-order magnetic plasmon induced reflection of lifted 3D metamaterials for slow light and optical sensing,” Results Phys. 47, 106354 (2023). [CrossRef]
15. S. Shen, Y. Liu, W. Liu, et al., “Tunable electromagnetically induced reflection with a high Q factor in complementary Dirac semimetal metamaterials,” Mater. Res. Express 5(12), 125804 (2018). [CrossRef]
16. M. Habib, M. Gokbayrak, E. Ozbay, et al., “Electrically controllable plasmon induced reflectance in hybrid metamaterials,” Appl. Phys. Lett. 113(22), 221105 (2018). [CrossRef]
17. M. Janfaza, M. A. Mansouri-Birjandi, and A. Tavousi, “Tunable plasmon-induced reflection based on graphene nanoribbon Fabry-Perot resonator and nanodisks,” Opt. Mater. 84, 675–680 (2018). [CrossRef]
18. Y. Yang, J. Li, J. Li, et al., “Plasmon-induced reflection metasurface with dual-mode modulation for multi-functional THz devices,” Opt. Lasers. Eng. 127, 105969 (2020). [CrossRef]
19. C. Yang, T. Sang, S. Li, et al., “Tailoring the light absorption of monolayer graphene via accidental quasi-bound states in the continuum,” J. Opt. Soc. Am. B 39(9), 2531–2539 (2022). [CrossRef]
20. M. Xiao, Z. Zhang, and C. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014). [CrossRef]
21. M. Li, Y. Wang, T. Sang, et al., “Experimental observation of multiple edge and corner states in photonic slabs heterostructures,” Photonics Res. 10(1), 197–204 (2022). [CrossRef]
22. Q. Wang, M. Xiao, H. Liu, et al., “Measurement of the Zak phase of photonic bands through the interface states of a metasurface/photonic crystal,” Phys. Rev. B 93(4), 041415 (2016). [CrossRef]
23. M. Gryga, D. Ciprian, and P. Hlubina, “Bloch surface wave resonance based sensors as an alternative to surface plasmon resonance sensors,” Sensors 20(18), 5119 (2020). [CrossRef]
24. R. Resta, “Manifestations of Berry’s phase in molecules and condensed matter,” J. Phys.: Condens. Matter 12(9), R107–R143 (2000). [CrossRef]
25. Z. Gu, J. Chen, B. Gao, et al., “Metasurfaces with high-Q resonances governed by topological edge state,” Opt. Lett. 47(7), 1822–1825 (2022). [CrossRef]
26. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
27. J. Tian, H. Luo, Y. Yang, et al., “Active control of anapole states by structuring the phase-change alloy Ge2Sb2Te5,” Nat. Commun. 10(1), 396 (2019). [CrossRef]
28. S. Li, T. Sang, C. Yang, et al., “Phase-change metasurfaces for dynamic control of chiral quasi-bound states in the continuum,” Opt. Lett. 48(24), 6488–6491 (2023). [CrossRef]
29. H. Zhang, L. Zhou, L. Lu, et al., “Miniature multilevel optical memristive switch using phase change material,” ACS Photonics 6(9), 2205–2212 (2019). [CrossRef]
30. S. Abdollahramezani, O. Hemmatyar, M. Taghinejad, et al., “Electrically driven reprogrammable phase-change metasurface reaching 80% efficiency,” Nat. Commun. 13(1), 1696 (2022). [CrossRef]
31. H. Zhang, L. Zhou, J. Xu, et al., “All-optical non-volatile tuning of an AMZI-coupled ring resonator with GST phase-change material,” Opt. Lett. 43(22), 5539–5542 (2018). [CrossRef]
32. C. R. de Galarreta, I. Sinev, A. M. Alexeev, et al., “Reconfigurable multilevel control of hybrid all-dielectric phase-change metasurfaces,” Optica 7(5), 476–484 (2020). [CrossRef]
33. C. Liu, Q. Tang, Y. Zheng, et al., “The origin of hexagonal phase and its evolution process in Ge2Sb2Te5 alloy,” APL Mater. 10(2), 021102 (2022). [CrossRef]
34. T. Cao, L. Fang, Y. Cao, et al., “Dynamically reconfigurable topological edge state in phase change photonic crystals,” Sci. Bull. 64(12), 814–822 (2019). [CrossRef]
35. Y. Huang, Y. Shen, and G. Veronis, “Switching between topological edge states in plasmonic systems using phase-change materials,” Opt. Express 30(25), 44594–44603 (2022). [CrossRef]
36. X. He, Y. Wang, M. Tao, et al., “Dynamical switching of electromagnetically induced reflectance in complementary terahertz metamaterials,” Opt. Commun. 448, 98–103 (2019). [CrossRef]
37. X. He, C. Sun, Y. Wang, et al., “Graphene-modulated terahertz metasurfaces for selective and active control of dual-band electromagnetic induced reflection (EIR) windows,” Nanomaterials 11(9), 2420 (2021). [CrossRef]
38. V. Savinov, V.A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014). [CrossRef]
39. Z. Ge, T. Sang, S. Li, et al., “Active control of resonant asymmetric transmission based on topological edge states in paired photonic crystals with a Ge2Sb2Te5 film,” Appl. Opt. 62(22), 5969–5975 (2023). [CrossRef]
