Abstract

We present a tunable metamodulator to work at terahertz frequencies by employing the dependency of toroidal dipolar resonance on the conductivity of vanadium dioxide. Numerical results show that toroidal dipolar resonance in the proposed planar structure can be observed around 0.288 THz in transmission spectrum. From the distribution of the anti-phase current flowing in the symmetric split ring resonator, the formation of toroidal dipole is validated. Our design may have potential applications in advanced terahertz devices, such as filter, plasmonic sensor, and fast switch.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Metamaterials consisting of periodic arrays of artificially designed blocks have been extensively studied for numerous novel phenomena not readily available in nature, such as electromagnetically induced transparency [1–3], perfect absorption [4–6], and polarization conversion [7–9]. Generally, they are represented by an expansion of electric and magnetic multipoles. Recently, a new nonradiative resonant mode-toroidal dipole is introduced [10–13]. The excitation of toroidal dipole can be visualized as a vortex of closed-loop magnetic field flowing around the surface of a torus along the corresponding meridian. Historically, the contribution of toroidal dipole is always neglected, because it is weakly coupled to free space and the corresponding far-field radiation is much smaller than that of electric dipole and magnetic dipole. Now toroidal dipole is considered as a higher-order correction in multipole expansion. Besides, the detection of toroidal dipole is challenging. Hence, designing an artificial structure is a useful way to significantly enhance the response of toroidal dipole. It seems that using metamaterials to design toroidal dipole becomes very necessary [14–25]. But most of previous works are static. So it is deserved to achieve tunable toroidal dipole for developing sensitive optical devices. In 2017, M. V. Cojocari et al. proposed a tunable terahertz metamaterial. Its main advantage is the blueshift of resonance and phase tunability caused by the change of semiconductor conductivity [26]. In 2018, B. Gerislioglu et al. developed a dynamic plasmonic metamodulator to operate at terahertz frequencies using the dependency of the hybrid toroidal dipolar mode on the incident beam power [27]. Phase change materials (PCMs) are capable of providing great variations in material properties during the phase transition [28,29]. As a representative of PCMs, vanadium dioxide (VO2) has been widely studied because of its potential applications in photodetector, rewritable optical data storage, and sensors with ultrafast response [30–35]. During the transition process at the critical temperature around 340 K, it undergoes a transformation from an insulating dielectric state to a conductive metallic state. Meanwhile, there is an approximately three orders of magnitude change in the conductivity. Therefore, VO2 is able to support a strong resonance that can be used to achieve tunable devices. In this paper, we present a planar metamodulator based on split ring resonators (SRRs) to realize a tunable spectra of toroidal dipole.

2. Designed scheme and discussion of calculated result

The unit cell of the proposed toroidal dipole is illustrated in Fig. 1, which consists of four parts: a top gold pattern layer with two SRRs, a middle dielectric spacer (SiO2), a VO2 layer, and a dielectric substrate (SiO2) on the bottom. Structure parameters are obtained as Px=190μm, Py=115μm, lx=150μm, ly=75μm, g=20μm, and w=5μm. All metamolecules are periodically arranged in the directions of X and Y, and separated from each other with 2a=40μm distance. The thicknesses of metallic pattern, dielectric spacer, and VO2 is chosen to be 0.2μm, 30μm, and 1.0μm. The permittivity of VO2 in terahertz range can be expressed by Drude model, and it is usually written by ε(ω)=εωp2(σ)(ω2+iγω), where ε and γ are 12 and 5.75×1013rad/s [35]. The plasma frequency ωp at conductivity σ can be approximately described as ωp2(σ)=σσ0ωp2(σ0) with σ0=3×103Ω1cm1 andωp(σ0)=1.4×1015rad/s. Gold is also modeled with the Drude model εAu=1ωp2/ω(ω+iΓ), where plasma frequency is ωp=1.37×1016rad/s and collision frequency are set to Γ=1.2×1014rad/s [36]. The permittivity of dielectric spacer and substrate (SiO2) is 3.8 [37,38].

 

Fig. 1 Schematic of the designed toroidal metamaterial.

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To demonstrate the response, full wave electromagnetic simulations are performed based on the standard finite-element-method (FEM). In simulations, two-dimensional unit cell boundary conditions are used in X and Y directions, and incident wave is modeled as a Floquet port above the unit cell. Incident plane wave with electric field along the central wire excites the conductive current in each loop of the metamolecule. Figure 2(a) shows simulated transmission spectrum, and toroidal dipolar resonance is observed around 0.288 THz. With the increasing of conductivity, the amplitude of toroidal dipolar resonance decreases, because the metallic properties increase with the increasing of conductivity. The resonance almost disappears when conductivity is2000Ω-1cm-1. Therefore, the impact of VO2 on transmission is significant. By adjusting the conductivity, the designed toroidal dipolar resonance does not show any geometric change. In order to study the resonant characteristic of toroidal dipole, the current of toroidal dipole is numerically simulated in Fig. 2(b). When incident electric field is parallel to the center line, incident wave makes electric current flow on each SRR surface, and then generates a magnetic dipole in each SRR. According to the concept of toroidization, the localized plasmon in structures with gaps plays an important role in determining the current direction. As shown in Fig. 2(b), the inductive current of two circuits is basically opposite. The inverse phase oscillation of the current leads to the ring-like profile of magnetic field, and suppresses the generation of magnetic dipole. The magnetic field, shown in Fig. 2(c), is distributed with opposite directions around the central wire in the unit cell. The spatial localization of magnetic field and closed magnetic vortex indicates the excitation of toroidal dipole.

 

Fig. 2 (a) Simulated transmission spectra of the proposed toroidal dipole. Simulated electric current (b) and magnetic field (c) distributions at the resonant frequency of 0.288 THz, when the conductivity of VO2 is10Ω-1cm-1.

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In order to determine the sensitivity of toroidal dipole on the variation of two geometrical parameters, SiO2 thickness (t1) and VO2 thickness (t2), the influence of these two parameters on the response of toroidal dipole is numerically investigated in Fig. 3 when the conductivity of VO2 is 10Ω-1cm-1. Figure 3(a) shows simulated transmission as a function of frequency and the thickness of SiO2 while other structure parameters are kept unchanged. When distance between metallic structure and VO2 increases gradually with the increasing of t1 from 5 μm to 50 μm, the resonance becomes gradually sharper. The larger the distance between metallic structure and VO2, the sharper the transmission, the smaller the influence on toroidal dipole. SiO2 plays the role of cavity, and different thicknesses mean different field distributions. When the thickness of SiO2 is small, the interaction between metallic structure and VO2 is very strong. A little change in the thickness of SiO2 will have an obvious influence on the transmission spectrum. When the thickness of SiO2 is enough large, the interaction between metallic structure and VO2 becomes weak. So transmission will experience little change. These results confirm the role of structure parameter to improve the performance of toroidal dipole. In Fig. 3(b), because dielectric permittivity of VO2 is positive (ε10.6) under the condition of conductivity 10Ω-1cm-1 [2,6,35], transmission dip change little with the increasing of t2 from 0.2 μm to 1.2 μm.

 

Fig. 3 (a) Simulated transmission spectra as a function of frequency and thicknesses of SiO2 (a) and VO2 (b), when the conductivity of VO2 is 10Ω-1cm-1.

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The toroidal dipolar resonance at different polarization angles is shown in Fig. 4(a). From simulated results under normal incidence, it can be seen that the phenomenon of toroidal dipolar resonance disappear when polarization angle between electric field and Y axis is larger than 45°, because the structure is anisotropic. For practical applications, toroidal design is required not only to work well under normal incidence but also be insensitive to oblique incidence. Therefore, the performance of the system are simulated at various incident angles for transverse electric (TE, kx, kz, Ey, Hx, Hz) and transverse magnetic (TM, ky, kz, Ey, Ez, Hx) polarizations, and the corresponding results are shown in Figs. 4(b)-4(c) as a function of frequency and incident angle. At the smaller incident angle, both polarizations show strong resonance around 0.288 THz. When incident angle is more than 60°, the performance of TE-polarized wave still work well. But working intensity for TM-polarized wave becomes weaker.

 

Fig. 4 Simulated transmission spectra of the proposed toroidal dipole for polarization angle under normal incidence (a), TE oblique incidence (b), and TM oblique incidence (c), when the conductivity of VO2 is 10Ω-1cm-1.

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3. Summary

A tunable toroidal dipolar response in two SRRs is proposed in the terahertz frequency range. Toroidal dipole is obtained and verified by electric current distribution. The excitation of tunable toroidal dipole can help to develop functional plasmonic and nanophotonic devices. The proposed system may have a key role in toroidal resonance-based active filter, subtle sensing, and ultrafast switching device.

Funding

National Natural Science Foundation of China (NSFC) (11504305).

References

1. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008). [CrossRef]   [PubMed]  

2. Q. Chu, Z. Song, and Q. H. Liu, “Omnidirectional tunable terahertz analog of electromagnetically induced transparency realized by isotropic vanadium dioxide metasurfaces,” Appl. Phys. Express 11(8), 082203 (2018). [CrossRef]  

3. Z. Song, Q. Chu, and Q. H. Liu, “Isotropic wide-angle analog of electromagnetically induced transparency in a terahertz metasurface,” Mater. Lett. 223, 90–92 (2018). [CrossRef]  

4. J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96(25), 251104 (2010). [CrossRef]  

5. Z. Song, Z. Wang, and M. Wei, “Broadband tunable absorber for terahertz waves based on isotropic silicon metasurfaces,” Mater. Lett. 234, 138–141 (2019). [CrossRef]  

6. Z. Song, K. Wang, J. Li, and Q. H. Liu, “Broadband tunable terahertz absorber based on vanadium dioxide metamaterials,” Opt. Express 26(6), 7148–7154 (2018). [CrossRef]   [PubMed]  

7. N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013). [CrossRef]   [PubMed]  

8. Z. Song, Q. Chu, X. Shen, and Q. H. Liu, “Wideband high-efficient linear polarization rotators,” Front. Phys. 13(5), 137803 (2018). [CrossRef]  

9. Z. Song, L. Zhang, and Q. H. Liu, “High-efficiency broadband cross polarization converter for near-infrared light based on anisotropic plasmonic meta-surfaces,” Plasmonics 11(1), 61–64 (2016). [CrossRef]  

10. T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010). [CrossRef]   [PubMed]  

11. Z. G. Dong, P. Ni, J. Zhu, X. Yin, and X. Zhang, “Toroidal dipole response in a multifold double-ring metamaterial,” Opt. Express 20(12), 13065–13070 (2012). [CrossRef]   [PubMed]  

12. A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015). [CrossRef]  

13. N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016). [CrossRef]   [PubMed]  

14. A. Sayanskiy, M. Danaeifar, P. Kapitanova, and A. E. Miroshnichenko, “All-dielectric metalattice with enhanced toroidal dipole response,” Adv. Opt. Mater. 6(19), 1800302 (2018). [CrossRef]  

15. V. R. Tuz, V. V. Khardikov, and Y. S. Kivshar, “All-dielectric resonant metasurfaces with a strong toroidal response,” ACS Photonics 5(5), 1871–1876 (2018). [CrossRef]  

16. B. Gerislioglu, A. Ahmadivand, and N. Pala, “Tunable plasmonic toroidal terahertz metamodulator,” Phys. Rev. B 97(16), 161405(R) (2018).

17. M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016). [CrossRef]   [PubMed]  

18. M. Gupta, Y. K. Srivastava, and R. Singh, “A toroidal metamaterial switch,” Adv. Mater. 30(4), 1704845 (2018). [CrossRef]   [PubMed]  

19. Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017). [CrossRef]   [PubMed]  

20. A. K. Ospanova, I. V. Stenishchev, and A. A. Basharin, “Anapole mode sustaining silicon metamaterials in visible spectral range,” Laser Photonics Rev. 12(7), 1800005 (2018). [CrossRef]  

21. N. Talebi, S. Guo, and P. A. van Aken, “Theory and applications of toroidal moments in electrodynamics: their emergence, characteristics, and technological relevance,” Nanophotonics 7(1), 93–110 (2018). [CrossRef]  

22. P. Qin, Y. Yang, M. Y. Musa, B. Zheng, Z. Wang, R. Hao, W. Yin, H. Chen, and E. Li, “Toroidal localized spoof plasmons on compact metadisks,” Adv. Sci. (Weinh.) 5(3), 1700487 (2018). [CrossRef]   [PubMed]  

23. L. Cong, Y. K. Srivastava, and R. Singh, “Tailoring the multipoles in THz toroidal metamaterials,” Appl. Phys. Lett. 111(8), 081108 (2017). [CrossRef]  

24. J. Li, J. Shao, Y. H. Wang, M. J. Zhu, J. Q. Li, and Z. G. Dong, “Toroidal dipolar response by a dielectric microtube metamaterial in the terahertz regime,” Opt. Express 23(22), 29138–29144 (2015). [CrossRef]   [PubMed]  

25. X. Chen and W. Fan, “Study of the interaction between graphene and planar terahertz metamaterial with toroidal dipolar resonance,” Opt. Lett. 42(10), 2034–2037 (2017). [CrossRef]   [PubMed]  

26. M. V. Cojocari, K. I. Schegoleva, and A. A. Basharin, “Blueshift and phase tunability in planar THz metamaterials: the role of losses and toroidal dipole contribution,” Opt. Lett. 42(9), 1700–1703 (2017). [CrossRef]   [PubMed]  

27. B. Gerislioglu, A. Ahmadivand, and N. Pala, “Tunable plasmonic toroidal terahertz metamodulator,” Phys. Rev. B 97(16), 161405(R) (2018).

28. M. Wei, Z. Song, Y. Deng, Y. Liu, and Q. Chen, “Large-angle mid-infrared absorption switch enabled by polarization-independent GST metasurfaces,” Mater. Lett. 236, 350–353 (2019). [CrossRef]  

29. M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012). [CrossRef]   [PubMed]  

30. N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018). [CrossRef]  

31. D. J. Park, J. H. Shin, K. H. Park, and H. C. Ryu, “Electrically controllable THz asymmetric split-loop resonator with an outer square loop based on VO2,” Opt. Express 26(13), 17397–17406 (2018). [CrossRef]   [PubMed]  

32. H. Liu, J. Lu, and X. R. Wang, “Metamaterials based on the phase transition of VO2,” Nanotechnology 29(2), 024002 (2018). [CrossRef]   [PubMed]  

33. H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional hybrid metasurfaces for dynamic tuning of terahertz waves,” Adv. Opt. Mater. 6(14), 1800257 (2018). [CrossRef]  

34. S. Song, X. Ma, M. Pu, X. Li, Y. Guo, P. Gao, and X. Luo, “Tailoring active color rendering and multiband photodetection in a vanadium-dioxide-based metamaterial absorber,” Photon. Res. 6(6), 492–497 (2018). [CrossRef]  

35. S. Wang, L. Kang, and D. H. Werner, “Hybrid resonators and highly tunable terahertz metamaterials enabled by vanadium dioxide (VO2),” Sci. Rep. 7(1), 4326 (2017). [CrossRef]   [PubMed]  

36. N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009). [CrossRef]   [PubMed]  

37. M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties,” J. Appl. Phys. 102(4), 043517 (2007). [CrossRef]  

38. R. Malureanu, M. Zalkovskij, Z. Song, C. Gritti, A. Andryieuski, Q. He, L. Zhou, P. U. Jepsen, and A. V. Lavrinenko, “A new method for obtaining transparent electrodes,” Opt. Express 20(20), 22770–22782 (2012). [CrossRef]   [PubMed]  

References

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  1. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
    [Crossref] [PubMed]
  2. Q. Chu, Z. Song, and Q. H. Liu, “Omnidirectional tunable terahertz analog of electromagnetically induced transparency realized by isotropic vanadium dioxide metasurfaces,” Appl. Phys. Express 11(8), 082203 (2018).
    [Crossref]
  3. Z. Song, Q. Chu, and Q. H. Liu, “Isotropic wide-angle analog of electromagnetically induced transparency in a terahertz metasurface,” Mater. Lett. 223, 90–92 (2018).
    [Crossref]
  4. J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96(25), 251104 (2010).
    [Crossref]
  5. Z. Song, Z. Wang, and M. Wei, “Broadband tunable absorber for terahertz waves based on isotropic silicon metasurfaces,” Mater. Lett. 234, 138–141 (2019).
    [Crossref]
  6. Z. Song, K. Wang, J. Li, and Q. H. Liu, “Broadband tunable terahertz absorber based on vanadium dioxide metamaterials,” Opt. Express 26(6), 7148–7154 (2018).
    [Crossref] [PubMed]
  7. N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
    [Crossref] [PubMed]
  8. Z. Song, Q. Chu, X. Shen, and Q. H. Liu, “Wideband high-efficient linear polarization rotators,” Front. Phys. 13(5), 137803 (2018).
    [Crossref]
  9. Z. Song, L. Zhang, and Q. H. Liu, “High-efficiency broadband cross polarization converter for near-infrared light based on anisotropic plasmonic meta-surfaces,” Plasmonics 11(1), 61–64 (2016).
    [Crossref]
  10. T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
    [Crossref] [PubMed]
  11. Z. G. Dong, P. Ni, J. Zhu, X. Yin, and X. Zhang, “Toroidal dipole response in a multifold double-ring metamaterial,” Opt. Express 20(12), 13065–13070 (2012).
    [Crossref] [PubMed]
  12. A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
    [Crossref]
  13. N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
    [Crossref] [PubMed]
  14. A. Sayanskiy, M. Danaeifar, P. Kapitanova, and A. E. Miroshnichenko, “All-dielectric metalattice with enhanced toroidal dipole response,” Adv. Opt. Mater. 6(19), 1800302 (2018).
    [Crossref]
  15. V. R. Tuz, V. V. Khardikov, and Y. S. Kivshar, “All-dielectric resonant metasurfaces with a strong toroidal response,” ACS Photonics 5(5), 1871–1876 (2018).
    [Crossref]
  16. B. Gerislioglu, A. Ahmadivand, and N. Pala, “Tunable plasmonic toroidal terahertz metamodulator,” Phys. Rev. B 97(16), 161405(R) (2018).
  17. M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
    [Crossref] [PubMed]
  18. M. Gupta, Y. K. Srivastava, and R. Singh, “A toroidal metamaterial switch,” Adv. Mater. 30(4), 1704845 (2018).
    [Crossref] [PubMed]
  19. Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
    [Crossref] [PubMed]
  20. A. K. Ospanova, I. V. Stenishchev, and A. A. Basharin, “Anapole mode sustaining silicon metamaterials in visible spectral range,” Laser Photonics Rev. 12(7), 1800005 (2018).
    [Crossref]
  21. N. Talebi, S. Guo, and P. A. van Aken, “Theory and applications of toroidal moments in electrodynamics: their emergence, characteristics, and technological relevance,” Nanophotonics 7(1), 93–110 (2018).
    [Crossref]
  22. P. Qin, Y. Yang, M. Y. Musa, B. Zheng, Z. Wang, R. Hao, W. Yin, H. Chen, and E. Li, “Toroidal localized spoof plasmons on compact metadisks,” Adv. Sci. (Weinh.) 5(3), 1700487 (2018).
    [Crossref] [PubMed]
  23. L. Cong, Y. K. Srivastava, and R. Singh, “Tailoring the multipoles in THz toroidal metamaterials,” Appl. Phys. Lett. 111(8), 081108 (2017).
    [Crossref]
  24. J. Li, J. Shao, Y. H. Wang, M. J. Zhu, J. Q. Li, and Z. G. Dong, “Toroidal dipolar response by a dielectric microtube metamaterial in the terahertz regime,” Opt. Express 23(22), 29138–29144 (2015).
    [Crossref] [PubMed]
  25. X. Chen and W. Fan, “Study of the interaction between graphene and planar terahertz metamaterial with toroidal dipolar resonance,” Opt. Lett. 42(10), 2034–2037 (2017).
    [Crossref] [PubMed]
  26. M. V. Cojocari, K. I. Schegoleva, and A. A. Basharin, “Blueshift and phase tunability in planar THz metamaterials: the role of losses and toroidal dipole contribution,” Opt. Lett. 42(9), 1700–1703 (2017).
    [Crossref] [PubMed]
  27. B. Gerislioglu, A. Ahmadivand, and N. Pala, “Tunable plasmonic toroidal terahertz metamodulator,” Phys. Rev. B 97(16), 161405(R) (2018).
  28. M. Wei, Z. Song, Y. Deng, Y. Liu, and Q. Chen, “Large-angle mid-infrared absorption switch enabled by polarization-independent GST metasurfaces,” Mater. Lett. 236, 350–353 (2019).
    [Crossref]
  29. M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
    [Crossref] [PubMed]
  30. N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
    [Crossref]
  31. D. J. Park, J. H. Shin, K. H. Park, and H. C. Ryu, “Electrically controllable THz asymmetric split-loop resonator with an outer square loop based on VO2,” Opt. Express 26(13), 17397–17406 (2018).
    [Crossref] [PubMed]
  32. H. Liu, J. Lu, and X. R. Wang, “Metamaterials based on the phase transition of VO2,” Nanotechnology 29(2), 024002 (2018).
    [Crossref] [PubMed]
  33. H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional hybrid metasurfaces for dynamic tuning of terahertz waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
    [Crossref]
  34. S. Song, X. Ma, M. Pu, X. Li, Y. Guo, P. Gao, and X. Luo, “Tailoring active color rendering and multiband photodetection in a vanadium-dioxide-based metamaterial absorber,” Photon. Res. 6(6), 492–497 (2018).
    [Crossref]
  35. S. Wang, L. Kang, and D. H. Werner, “Hybrid resonators and highly tunable terahertz metamaterials enabled by vanadium dioxide (VO2),” Sci. Rep. 7(1), 4326 (2017).
    [Crossref] [PubMed]
  36. N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
    [Crossref] [PubMed]
  37. M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties,” J. Appl. Phys. 102(4), 043517 (2007).
    [Crossref]
  38. R. Malureanu, M. Zalkovskij, Z. Song, C. Gritti, A. Andryieuski, Q. He, L. Zhou, P. U. Jepsen, and A. V. Lavrinenko, “A new method for obtaining transparent electrodes,” Opt. Express 20(20), 22770–22782 (2012).
    [Crossref] [PubMed]

2019 (2)

Z. Song, Z. Wang, and M. Wei, “Broadband tunable absorber for terahertz waves based on isotropic silicon metasurfaces,” Mater. Lett. 234, 138–141 (2019).
[Crossref]

M. Wei, Z. Song, Y. Deng, Y. Liu, and Q. Chen, “Large-angle mid-infrared absorption switch enabled by polarization-independent GST metasurfaces,” Mater. Lett. 236, 350–353 (2019).
[Crossref]

2018 (15)

M. Gupta, Y. K. Srivastava, and R. Singh, “A toroidal metamaterial switch,” Adv. Mater. 30(4), 1704845 (2018).
[Crossref] [PubMed]

N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
[Crossref]

D. J. Park, J. H. Shin, K. H. Park, and H. C. Ryu, “Electrically controllable THz asymmetric split-loop resonator with an outer square loop based on VO2,” Opt. Express 26(13), 17397–17406 (2018).
[Crossref] [PubMed]

H. Liu, J. Lu, and X. R. Wang, “Metamaterials based on the phase transition of VO2,” Nanotechnology 29(2), 024002 (2018).
[Crossref] [PubMed]

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional hybrid metasurfaces for dynamic tuning of terahertz waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

S. Song, X. Ma, M. Pu, X. Li, Y. Guo, P. Gao, and X. Luo, “Tailoring active color rendering and multiband photodetection in a vanadium-dioxide-based metamaterial absorber,” Photon. Res. 6(6), 492–497 (2018).
[Crossref]

Z. Song, K. Wang, J. Li, and Q. H. Liu, “Broadband tunable terahertz absorber based on vanadium dioxide metamaterials,” Opt. Express 26(6), 7148–7154 (2018).
[Crossref] [PubMed]

Q. Chu, Z. Song, and Q. H. Liu, “Omnidirectional tunable terahertz analog of electromagnetically induced transparency realized by isotropic vanadium dioxide metasurfaces,” Appl. Phys. Express 11(8), 082203 (2018).
[Crossref]

Z. Song, Q. Chu, and Q. H. Liu, “Isotropic wide-angle analog of electromagnetically induced transparency in a terahertz metasurface,” Mater. Lett. 223, 90–92 (2018).
[Crossref]

Z. Song, Q. Chu, X. Shen, and Q. H. Liu, “Wideband high-efficient linear polarization rotators,” Front. Phys. 13(5), 137803 (2018).
[Crossref]

A. Sayanskiy, M. Danaeifar, P. Kapitanova, and A. E. Miroshnichenko, “All-dielectric metalattice with enhanced toroidal dipole response,” Adv. Opt. Mater. 6(19), 1800302 (2018).
[Crossref]

V. R. Tuz, V. V. Khardikov, and Y. S. Kivshar, “All-dielectric resonant metasurfaces with a strong toroidal response,” ACS Photonics 5(5), 1871–1876 (2018).
[Crossref]

A. K. Ospanova, I. V. Stenishchev, and A. A. Basharin, “Anapole mode sustaining silicon metamaterials in visible spectral range,” Laser Photonics Rev. 12(7), 1800005 (2018).
[Crossref]

N. Talebi, S. Guo, and P. A. van Aken, “Theory and applications of toroidal moments in electrodynamics: their emergence, characteristics, and technological relevance,” Nanophotonics 7(1), 93–110 (2018).
[Crossref]

P. Qin, Y. Yang, M. Y. Musa, B. Zheng, Z. Wang, R. Hao, W. Yin, H. Chen, and E. Li, “Toroidal localized spoof plasmons on compact metadisks,” Adv. Sci. (Weinh.) 5(3), 1700487 (2018).
[Crossref] [PubMed]

2017 (5)

L. Cong, Y. K. Srivastava, and R. Singh, “Tailoring the multipoles in THz toroidal metamaterials,” Appl. Phys. Lett. 111(8), 081108 (2017).
[Crossref]

S. Wang, L. Kang, and D. H. Werner, “Hybrid resonators and highly tunable terahertz metamaterials enabled by vanadium dioxide (VO2),” Sci. Rep. 7(1), 4326 (2017).
[Crossref] [PubMed]

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref] [PubMed]

X. Chen and W. Fan, “Study of the interaction between graphene and planar terahertz metamaterial with toroidal dipolar resonance,” Opt. Lett. 42(10), 2034–2037 (2017).
[Crossref] [PubMed]

M. V. Cojocari, K. I. Schegoleva, and A. A. Basharin, “Blueshift and phase tunability in planar THz metamaterials: the role of losses and toroidal dipole contribution,” Opt. Lett. 42(9), 1700–1703 (2017).
[Crossref] [PubMed]

2016 (3)

M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
[Crossref] [PubMed]

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref] [PubMed]

Z. Song, L. Zhang, and Q. H. Liu, “High-efficiency broadband cross polarization converter for near-infrared light based on anisotropic plasmonic meta-surfaces,” Plasmonics 11(1), 61–64 (2016).
[Crossref]

2015 (2)

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

J. Li, J. Shao, Y. H. Wang, M. J. Zhu, J. Q. Li, and Z. G. Dong, “Toroidal dipolar response by a dielectric microtube metamaterial in the terahertz regime,” Opt. Express 23(22), 29138–29144 (2015).
[Crossref] [PubMed]

2013 (1)

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

2012 (3)

Z. G. Dong, P. Ni, J. Zhu, X. Yin, and X. Zhang, “Toroidal dipole response in a multifold double-ring metamaterial,” Opt. Express 20(12), 13065–13070 (2012).
[Crossref] [PubMed]

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
[Crossref] [PubMed]

R. Malureanu, M. Zalkovskij, Z. Song, C. Gritti, A. Andryieuski, Q. He, L. Zhou, P. U. Jepsen, and A. V. Lavrinenko, “A new method for obtaining transparent electrodes,” Opt. Express 20(20), 22770–22782 (2012).
[Crossref] [PubMed]

2010 (2)

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
[Crossref] [PubMed]

J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96(25), 251104 (2010).
[Crossref]

2009 (1)

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref] [PubMed]

2008 (1)

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref] [PubMed]

2007 (1)

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties,” J. Appl. Phys. 102(4), 043517 (2007).
[Crossref]

Andryieuski, A.

Averitt, R. D.

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
[Crossref] [PubMed]

Azad, A. K.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Basharin, A. A.

A. K. Ospanova, I. V. Stenishchev, and A. A. Basharin, “Anapole mode sustaining silicon metamaterials in visible spectral range,” Laser Photonics Rev. 12(7), 1800005 (2018).
[Crossref]

M. V. Cojocari, K. I. Schegoleva, and A. A. Basharin, “Blueshift and phase tunability in planar THz metamaterials: the role of losses and toroidal dipole contribution,” Opt. Lett. 42(9), 1700–1703 (2017).
[Crossref] [PubMed]

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Butakov, N. A.

N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
[Crossref]

Cai, H.

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional hybrid metasurfaces for dynamic tuning of terahertz waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

Chen, H.

P. Qin, Y. Yang, M. Y. Musa, B. Zheng, Z. Wang, R. Hao, W. Yin, H. Chen, and E. Li, “Toroidal localized spoof plasmons on compact metadisks,” Adv. Sci. (Weinh.) 5(3), 1700487 (2018).
[Crossref] [PubMed]

Chen, H. T.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Chen, Q.

M. Wei, Z. Song, Y. Deng, Y. Liu, and Q. Chen, “Large-angle mid-infrared absorption switch enabled by polarization-independent GST metasurfaces,” Mater. Lett. 236, 350–353 (2019).
[Crossref]

Chen, S.

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional hybrid metasurfaces for dynamic tuning of terahertz waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref] [PubMed]

Chen, X.

Chorsi, H. T.

N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
[Crossref]

Chowdhury, D. R.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Chu, Q.

Q. Chu, Z. Song, and Q. H. Liu, “Omnidirectional tunable terahertz analog of electromagnetically induced transparency realized by isotropic vanadium dioxide metasurfaces,” Appl. Phys. Express 11(8), 082203 (2018).
[Crossref]

Z. Song, Q. Chu, and Q. H. Liu, “Isotropic wide-angle analog of electromagnetically induced transparency in a terahertz metasurface,” Mater. Lett. 223, 90–92 (2018).
[Crossref]

Z. Song, Q. Chu, X. Shen, and Q. H. Liu, “Wideband high-efficient linear polarization rotators,” Front. Phys. 13(5), 137803 (2018).
[Crossref]

Cojocari, M. V.

Cong, L.

L. Cong, Y. K. Srivastava, and R. Singh, “Tailoring the multipoles in THz toroidal metamaterials,” Appl. Phys. Lett. 111(8), 081108 (2017).
[Crossref]

M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
[Crossref] [PubMed]

Cui, A.

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref] [PubMed]

Dalvit, D. A. R.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Danaeifar, M.

A. Sayanskiy, M. Danaeifar, P. Kapitanova, and A. E. Miroshnichenko, “All-dielectric metalattice with enhanced toroidal dipole response,” Adv. Opt. Mater. 6(19), 1800302 (2018).
[Crossref]

Dayal, G.

M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
[Crossref] [PubMed]

Del Valle Granda, J.

N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
[Crossref]

Deng, Y.

M. Wei, Z. Song, Y. Deng, Y. Liu, and Q. Chen, “Large-angle mid-infrared absorption switch enabled by polarization-independent GST metasurfaces,” Mater. Lett. 236, 350–353 (2019).
[Crossref]

Dong, Z. G.

Du, S.

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref] [PubMed]

Economou, E. N.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Fan, K.

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
[Crossref] [PubMed]

Fan, W.

Fan, Y.

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref] [PubMed]

Fedotov, V. A.

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref] [PubMed]

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
[Crossref] [PubMed]

Fleischhauer, M.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref] [PubMed]

Fu, Z.

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional hybrid metasurfaces for dynamic tuning of terahertz waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

Gao, P.

Genov, D. A.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref] [PubMed]

Giessen, H.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref] [PubMed]

Grady, N. K.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Gritti, C.

Gu, C.

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref] [PubMed]

Guo, S.

N. Talebi, S. Guo, and P. A. van Aken, “Theory and applications of toroidal moments in electrodynamics: their emergence, characteristics, and technological relevance,” Nanophotonics 7(1), 93–110 (2018).
[Crossref]

Guo, Y.

Gupta, M.

M. Gupta, Y. K. Srivastava, and R. Singh, “A toroidal metamaterial switch,” Adv. Mater. 30(4), 1704845 (2018).
[Crossref] [PubMed]

M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
[Crossref] [PubMed]

Hao, J. M.

J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96(25), 251104 (2010).
[Crossref]

Hao, R.

P. Qin, Y. Yang, M. Y. Musa, B. Zheng, Z. Wang, R. Hao, W. Yin, H. Chen, and E. Li, “Toroidal localized spoof plasmons on compact metadisks,” Adv. Sci. (Weinh.) 5(3), 1700487 (2018).
[Crossref] [PubMed]

He, H.

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional hybrid metasurfaces for dynamic tuning of terahertz waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

He, Q.

Heyes, J. E.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Higgs, D.

N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
[Crossref]

Hon, P. W. C.

N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
[Crossref]

Hu, X.

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional hybrid metasurfaces for dynamic tuning of terahertz waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

Huang, Q.

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional hybrid metasurfaces for dynamic tuning of terahertz waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

Hwang, H. Y.

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
[Crossref] [PubMed]

Iyer, P. P.

N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
[Crossref]

Jepsen, P. U.

Kaelberer, T.

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
[Crossref] [PubMed]

Kafesaki, M.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Kalcheim, Y.

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S. Wang, L. Kang, and D. H. Werner, “Hybrid resonators and highly tunable terahertz metamaterials enabled by vanadium dioxide (VO2),” Sci. Rep. 7(1), 4326 (2017).
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N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
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V. R. Tuz, V. V. Khardikov, and Y. S. Kivshar, “All-dielectric resonant metasurfaces with a strong toroidal response,” ACS Photonics 5(5), 1871–1876 (2018).
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M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
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V. R. Tuz, V. V. Khardikov, and Y. S. Kivshar, “All-dielectric resonant metasurfaces with a strong toroidal response,” ACS Photonics 5(5), 1871–1876 (2018).
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N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
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Lewi, T.

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Li, E.

P. Qin, Y. Yang, M. Y. Musa, B. Zheng, Z. Wang, R. Hao, W. Yin, H. Chen, and E. Li, “Toroidal localized spoof plasmons on compact metadisks,” Adv. Sci. (Weinh.) 5(3), 1700487 (2018).
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Li, J. Q.

Li, W.

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
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Li, Z.

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
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H. Liu, J. Lu, and X. R. Wang, “Metamaterials based on the phase transition of VO2,” Nanotechnology 29(2), 024002 (2018).
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M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
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S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
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N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
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Liu, Q. H.

Q. Chu, Z. Song, and Q. H. Liu, “Omnidirectional tunable terahertz analog of electromagnetically induced transparency realized by isotropic vanadium dioxide metasurfaces,” Appl. Phys. Express 11(8), 082203 (2018).
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Z. Song, Q. Chu, and Q. H. Liu, “Isotropic wide-angle analog of electromagnetically induced transparency in a terahertz metasurface,” Mater. Lett. 223, 90–92 (2018).
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Z. Song, K. Wang, J. Li, and Q. H. Liu, “Broadband tunable terahertz absorber based on vanadium dioxide metamaterials,” Opt. Express 26(6), 7148–7154 (2018).
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Z. Song, Q. Chu, X. Shen, and Q. H. Liu, “Wideband high-efficient linear polarization rotators,” Front. Phys. 13(5), 137803 (2018).
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Z. Song, L. Zhang, and Q. H. Liu, “High-efficiency broadband cross polarization converter for near-infrared light based on anisotropic plasmonic meta-surfaces,” Plasmonics 11(1), 61–64 (2016).
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Liu, X. L.

J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96(25), 251104 (2010).
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Liu, Y.

M. Wei, Z. Song, Y. Deng, Y. Liu, and Q. Chen, “Large-angle mid-infrared absorption switch enabled by polarization-independent GST metasurfaces,” Mater. Lett. 236, 350–353 (2019).
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H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional hybrid metasurfaces for dynamic tuning of terahertz waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
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Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
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Lu, J.

H. Liu, J. Lu, and X. R. Wang, “Metamaterials based on the phase transition of VO2,” Nanotechnology 29(2), 024002 (2018).
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M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
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P. Qin, Y. Yang, M. Y. Musa, B. Zheng, Z. Wang, R. Hao, W. Yin, H. Chen, and E. Li, “Toroidal localized spoof plasmons on compact metadisks,” Adv. Sci. (Weinh.) 5(3), 1700487 (2018).
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M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties,” J. Appl. Phys. 102(4), 043517 (2007).
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M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
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Ni, P.

Omenetto, F. G.

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
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Ospanova, A. K.

A. K. Ospanova, I. V. Stenishchev, and A. A. Basharin, “Anapole mode sustaining silicon metamaterials in visible spectral range,” Laser Photonics Rev. 12(7), 1800005 (2018).
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Padilla, W. J.

J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96(25), 251104 (2010).
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Papasimakis, N.

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
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T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
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Park, D. J.

Park, K. H.

Pfau, T.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref] [PubMed]

Pu, M.

Qin, P.

P. Qin, Y. Yang, M. Y. Musa, B. Zheng, Z. Wang, R. Hao, W. Yin, H. Chen, and E. Li, “Toroidal localized spoof plasmons on compact metadisks,” Adv. Sci. (Weinh.) 5(3), 1700487 (2018).
[Crossref] [PubMed]

Qiu, M.

J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96(25), 251104 (2010).
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Raybould, T. A.

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
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N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
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Savinov, V.

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
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M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
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A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
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A. Sayanskiy, M. Danaeifar, P. Kapitanova, and A. E. Miroshnichenko, “All-dielectric metalattice with enhanced toroidal dipole response,” Adv. Opt. Mater. 6(19), 1800302 (2018).
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Schegoleva, K. I.

Schuller, I. K.

N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
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Schuller, J. A.

N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
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Shao, J.

Shen, X.

Z. Song, Q. Chu, X. Shen, and Q. H. Liu, “Wideband high-efficient linear polarization rotators,” Front. Phys. 13(5), 137803 (2018).
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Singh, R.

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L. Cong, Y. K. Srivastava, and R. Singh, “Tailoring the multipoles in THz toroidal metamaterials,” Appl. Phys. Lett. 111(8), 081108 (2017).
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M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
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Song, S.

Song, Z.

M. Wei, Z. Song, Y. Deng, Y. Liu, and Q. Chen, “Large-angle mid-infrared absorption switch enabled by polarization-independent GST metasurfaces,” Mater. Lett. 236, 350–353 (2019).
[Crossref]

Z. Song, Z. Wang, and M. Wei, “Broadband tunable absorber for terahertz waves based on isotropic silicon metasurfaces,” Mater. Lett. 234, 138–141 (2019).
[Crossref]

Z. Song, Q. Chu, and Q. H. Liu, “Isotropic wide-angle analog of electromagnetically induced transparency in a terahertz metasurface,” Mater. Lett. 223, 90–92 (2018).
[Crossref]

Q. Chu, Z. Song, and Q. H. Liu, “Omnidirectional tunable terahertz analog of electromagnetically induced transparency realized by isotropic vanadium dioxide metasurfaces,” Appl. Phys. Express 11(8), 082203 (2018).
[Crossref]

Z. Song, Q. Chu, X. Shen, and Q. H. Liu, “Wideband high-efficient linear polarization rotators,” Front. Phys. 13(5), 137803 (2018).
[Crossref]

Z. Song, K. Wang, J. Li, and Q. H. Liu, “Broadband tunable terahertz absorber based on vanadium dioxide metamaterials,” Opt. Express 26(6), 7148–7154 (2018).
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Z. Song, L. Zhang, and Q. H. Liu, “High-efficiency broadband cross polarization converter for near-infrared light based on anisotropic plasmonic meta-surfaces,” Plasmonics 11(1), 61–64 (2016).
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R. Malureanu, M. Zalkovskij, Z. Song, C. Gritti, A. Andryieuski, Q. He, L. Zhou, P. U. Jepsen, and A. V. Lavrinenko, “A new method for obtaining transparent electrodes,” Opt. Express 20(20), 22770–22782 (2012).
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A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Srivastava, Y. K.

M. Gupta, Y. K. Srivastava, and R. Singh, “A toroidal metamaterial switch,” Adv. Mater. 30(4), 1704845 (2018).
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L. Cong, Y. K. Srivastava, and R. Singh, “Tailoring the multipoles in THz toroidal metamaterials,” Appl. Phys. Lett. 111(8), 081108 (2017).
[Crossref]

Stenishchev, I. V.

A. K. Ospanova, I. V. Stenishchev, and A. A. Basharin, “Anapole mode sustaining silicon metamaterials in visible spectral range,” Laser Photonics Rev. 12(7), 1800005 (2018).
[Crossref]

Sternbach, A. J.

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
[Crossref] [PubMed]

Strikwerda, A. C.

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
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N. Talebi, S. Guo, and P. A. van Aken, “Theory and applications of toroidal moments in electrodynamics: their emergence, characteristics, and technological relevance,” Nanophotonics 7(1), 93–110 (2018).
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Tao, H.

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
[Crossref] [PubMed]

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N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Trastoy, J.

N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
[Crossref]

Tsai, D. P.

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
[Crossref] [PubMed]

Tuz, V. R.

V. R. Tuz, V. V. Khardikov, and Y. S. Kivshar, “All-dielectric resonant metasurfaces with a strong toroidal response,” ACS Photonics 5(5), 1871–1876 (2018).
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N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
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N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
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van Aken, P. A.

N. Talebi, S. Guo, and P. A. van Aken, “Theory and applications of toroidal moments in electrodynamics: their emergence, characteristics, and technological relevance,” Nanophotonics 7(1), 93–110 (2018).
[Crossref]

Wang, J.

J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96(25), 251104 (2010).
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Wang, K.

Wang, P. Y.

N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
[Crossref]

Wang, S.

S. Wang, L. Kang, and D. H. Werner, “Hybrid resonators and highly tunable terahertz metamaterials enabled by vanadium dioxide (VO2),” Sci. Rep. 7(1), 4326 (2017).
[Crossref] [PubMed]

M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
[Crossref] [PubMed]

Wang, X. R.

H. Liu, J. Lu, and X. R. Wang, “Metamaterials based on the phase transition of VO2,” Nanotechnology 29(2), 024002 (2018).
[Crossref] [PubMed]

Wang, Y.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref] [PubMed]

Wang, Y. H.

Wang, Z.

Z. Song, Z. Wang, and M. Wei, “Broadband tunable absorber for terahertz waves based on isotropic silicon metasurfaces,” Mater. Lett. 234, 138–141 (2019).
[Crossref]

P. Qin, Y. Yang, M. Y. Musa, B. Zheng, Z. Wang, R. Hao, W. Yin, H. Chen, and E. Li, “Toroidal localized spoof plasmons on compact metadisks,” Adv. Sci. (Weinh.) 5(3), 1700487 (2018).
[Crossref] [PubMed]

Wei, M.

M. Wei, Z. Song, Y. Deng, Y. Liu, and Q. Chen, “Large-angle mid-infrared absorption switch enabled by polarization-independent GST metasurfaces,” Mater. Lett. 236, 350–353 (2019).
[Crossref]

Z. Song, Z. Wang, and M. Wei, “Broadband tunable absorber for terahertz waves based on isotropic silicon metasurfaces,” Mater. Lett. 234, 138–141 (2019).
[Crossref]

Weiss, T.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref] [PubMed]

Werner, D. H.

S. Wang, L. Kang, and D. H. Werner, “Hybrid resonators and highly tunable terahertz metamaterials enabled by vanadium dioxide (VO2),” Sci. Rep. 7(1), 4326 (2017).
[Crossref] [PubMed]

West, K. G.

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
[Crossref] [PubMed]

Wolf, S. A.

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
[Crossref] [PubMed]

Xu, N.

M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
[Crossref] [PubMed]

Yang, Y.

P. Qin, Y. Yang, M. Y. Musa, B. Zheng, Z. Wang, R. Hao, W. Yin, H. Chen, and E. Li, “Toroidal localized spoof plasmons on compact metadisks,” Adv. Sci. (Weinh.) 5(3), 1700487 (2018).
[Crossref] [PubMed]

Yin, W.

P. Qin, Y. Yang, M. Y. Musa, B. Zheng, Z. Wang, R. Hao, W. Yin, H. Chen, and E. Li, “Toroidal localized spoof plasmons on compact metadisks,” Adv. Sci. (Weinh.) 5(3), 1700487 (2018).
[Crossref] [PubMed]

Yin, X.

Zalkovskij, M.

Zeng, Y.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Zhang, L.

Z. Song, L. Zhang, and Q. H. Liu, “High-efficiency broadband cross polarization converter for near-infrared light based on anisotropic plasmonic meta-surfaces,” Plasmonics 11(1), 61–64 (2016).
[Crossref]

Zhang, S.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref] [PubMed]

Zhang, W.

M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
[Crossref] [PubMed]

Zhang, X.

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
[Crossref] [PubMed]

Z. G. Dong, P. Ni, J. Zhu, X. Yin, and X. Zhang, “Toroidal dipole response in a multifold double-ring metamaterial,” Opt. Express 20(12), 13065–13070 (2012).
[Crossref] [PubMed]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref] [PubMed]

Zhao, Y.

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional hybrid metasurfaces for dynamic tuning of terahertz waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

Zheludev, N. I.

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref] [PubMed]

M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
[Crossref] [PubMed]

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
[Crossref] [PubMed]

Zheng, B.

P. Qin, Y. Yang, M. Y. Musa, B. Zheng, Z. Wang, R. Hao, W. Yin, H. Chen, and E. Li, “Toroidal localized spoof plasmons on compact metadisks,” Adv. Sci. (Weinh.) 5(3), 1700487 (2018).
[Crossref] [PubMed]

Zhou, L.

R. Malureanu, M. Zalkovskij, Z. Song, C. Gritti, A. Andryieuski, Q. He, L. Zhou, P. U. Jepsen, and A. V. Lavrinenko, “A new method for obtaining transparent electrodes,” Opt. Express 20(20), 22770–22782 (2012).
[Crossref] [PubMed]

J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96(25), 251104 (2010).
[Crossref]

Zhu, J.

Zhu, M. J.

Zou, C.

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional hybrid metasurfaces for dynamic tuning of terahertz waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

ACS Photonics (2)

V. R. Tuz, V. V. Khardikov, and Y. S. Kivshar, “All-dielectric resonant metasurfaces with a strong toroidal response,” ACS Photonics 5(5), 1871–1876 (2018).
[Crossref]

N. A. Butakov, M. W. Knight, T. Lewi, P. P. Iyer, D. Higgs, H. T. Chorsi, J. Trastoy, J. Del Valle Granda, I. Valmianski, C. Urban, Y. Kalcheim, P. Y. Wang, P. W. C. Hon, I. K. Schuller, and J. A. Schuller, “Broadband electrically tunable dielectric resonators using metal-insulator transitions,” ACS Photonics 5(10), 4056–4060 (2018).
[Crossref]

Adv. Mater. (3)

M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
[Crossref] [PubMed]

M. Gupta, Y. K. Srivastava, and R. Singh, “A toroidal metamaterial switch,” Adv. Mater. 30(4), 1704845 (2018).
[Crossref] [PubMed]

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).
[Crossref] [PubMed]

Adv. Opt. Mater. (2)

A. Sayanskiy, M. Danaeifar, P. Kapitanova, and A. E. Miroshnichenko, “All-dielectric metalattice with enhanced toroidal dipole response,” Adv. Opt. Mater. 6(19), 1800302 (2018).
[Crossref]

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional hybrid metasurfaces for dynamic tuning of terahertz waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

Adv. Sci. (Weinh.) (1)

P. Qin, Y. Yang, M. Y. Musa, B. Zheng, Z. Wang, R. Hao, W. Yin, H. Chen, and E. Li, “Toroidal localized spoof plasmons on compact metadisks,” Adv. Sci. (Weinh.) 5(3), 1700487 (2018).
[Crossref] [PubMed]

Appl. Phys. Express (1)

Q. Chu, Z. Song, and Q. H. Liu, “Omnidirectional tunable terahertz analog of electromagnetically induced transparency realized by isotropic vanadium dioxide metasurfaces,” Appl. Phys. Express 11(8), 082203 (2018).
[Crossref]

Appl. Phys. Lett. (2)

J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96(25), 251104 (2010).
[Crossref]

L. Cong, Y. K. Srivastava, and R. Singh, “Tailoring the multipoles in THz toroidal metamaterials,” Appl. Phys. Lett. 111(8), 081108 (2017).
[Crossref]

Front. Phys. (1)

Z. Song, Q. Chu, X. Shen, and Q. H. Liu, “Wideband high-efficient linear polarization rotators,” Front. Phys. 13(5), 137803 (2018).
[Crossref]

J. Appl. Phys. (1)

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties,” J. Appl. Phys. 102(4), 043517 (2007).
[Crossref]

Laser Photonics Rev. (1)

A. K. Ospanova, I. V. Stenishchev, and A. A. Basharin, “Anapole mode sustaining silicon metamaterials in visible spectral range,” Laser Photonics Rev. 12(7), 1800005 (2018).
[Crossref]

Mater. Lett. (3)

Z. Song, Q. Chu, and Q. H. Liu, “Isotropic wide-angle analog of electromagnetically induced transparency in a terahertz metasurface,” Mater. Lett. 223, 90–92 (2018).
[Crossref]

Z. Song, Z. Wang, and M. Wei, “Broadband tunable absorber for terahertz waves based on isotropic silicon metasurfaces,” Mater. Lett. 234, 138–141 (2019).
[Crossref]

M. Wei, Z. Song, Y. Deng, Y. Liu, and Q. Chen, “Large-angle mid-infrared absorption switch enabled by polarization-independent GST metasurfaces,” Mater. Lett. 236, 350–353 (2019).
[Crossref]

Nanophotonics (1)

N. Talebi, S. Guo, and P. A. van Aken, “Theory and applications of toroidal moments in electrodynamics: their emergence, characteristics, and technological relevance,” Nanophotonics 7(1), 93–110 (2018).
[Crossref]

Nanotechnology (1)

H. Liu, J. Lu, and X. R. Wang, “Metamaterials based on the phase transition of VO2,” Nanotechnology 29(2), 024002 (2018).
[Crossref] [PubMed]

Nat. Mater. (2)

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref] [PubMed]

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref] [PubMed]

Nature (1)

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012).
[Crossref] [PubMed]

Opt. Express (5)

Opt. Lett. (2)

Photon. Res. (1)

Phys. Rev. Lett. (1)

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref] [PubMed]

Phys. Rev. X (1)

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Plasmonics (1)

Z. Song, L. Zhang, and Q. H. Liu, “High-efficiency broadband cross polarization converter for near-infrared light based on anisotropic plasmonic meta-surfaces,” Plasmonics 11(1), 61–64 (2016).
[Crossref]

Sci. Rep. (1)

S. Wang, L. Kang, and D. H. Werner, “Hybrid resonators and highly tunable terahertz metamaterials enabled by vanadium dioxide (VO2),” Sci. Rep. 7(1), 4326 (2017).
[Crossref] [PubMed]

Science (2)

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
[Crossref] [PubMed]

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Other (2)

B. Gerislioglu, A. Ahmadivand, and N. Pala, “Tunable plasmonic toroidal terahertz metamodulator,” Phys. Rev. B 97(16), 161405(R) (2018).

B. Gerislioglu, A. Ahmadivand, and N. Pala, “Tunable plasmonic toroidal terahertz metamodulator,” Phys. Rev. B 97(16), 161405(R) (2018).

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Figures (4)

Fig. 1
Fig. 1 Schematic of the designed toroidal metamaterial.
Fig. 2
Fig. 2 (a) Simulated transmission spectra of the proposed toroidal dipole. Simulated electric current (b) and magnetic field (c) distributions at the resonant frequency of 0.288 THz, when the conductivity of V O 2 is 10 Ω -1 c m -1 .
Fig. 3
Fig. 3 (a) Simulated transmission spectra as a function of frequency and thicknesses of SiO 2 (a) and V O 2 (b), when the conductivity of V O 2 is 10 Ω -1 c m -1 .
Fig. 4
Fig. 4 Simulated transmission spectra of the proposed toroidal dipole for polarization angle under normal incidence (a), TE oblique incidence (b), and TM oblique incidence (c), when the conductivity of V O 2 is 10 Ω -1 c m -1 .

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