Abstract

We design and numerically investigate the high Q-factor, high modulation depth, and multiple Fano resonances based on a periodical all-dielectric asymmetric nanorod dimer in the near-infrared regime. It is demonstrated that, due to the excitation of the subradiant hybrid modes, five sharp Fano resonances can be achieved by breaking the symmetry of the dimer and can be flexibly tuned by varying the geometrical parameters. All five Fano resonances have a narrow line width, the maximal Q-factor exceeds 9700, and even the minimal Q-factor also reaches about 1090 in magnitude. Particularly, the modulation depth can reach nearly 100%. In addition, the maximal figure of merit reaches 5045. Considering the narrow line-width and significant near-field enhancement, five Fano resonances with large modulation depths in the proposed array are useful for lasing, nonlinear optics, and multiwavelength biosensing.

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

1. Introduction

Engineering high Q-factor responses in metamaterials is generally associated with the low loss rate and large local field enhancement and offer surprisingly rich physics, spanning many areas of research including plasmonic lasers [1], nonlinear optics [2], optical sensors [3,4] and quantum optics [5]. Fano resonance, characterized by asymmetric spectral line profiles, provides an effective way to realize the high Q-factor in metamaterials and has attracted great attention [610]. Fano resonances are generally attributed to the interaction between a superradiant (highly radiative) mode and a subradiant (poorly radiative) mode [9,11]. Unfortunately, Fano resonance in plasmonic metamaterials typically suffers from low Q-factor due to the ohmic losses.

All-dielectric metamaterials can eliminate the ohmic losses and provide a promising alternative to achieve higher Q-factor Fano resonance due to the lower radiation loss of series of magnetic responses in the dielectric Fano structures [1215]. Recently, it has shown that the excited toroidal dipole (TD) resonance in felicitously designed all-dielectric metamaterial can be pictured as radiating fields generated by a solenoid bent into a torus and can be used to achieving a high Q-factor Fano resonance by taking advantage of the weak free-space coupling [1620]. In addition, the toroidal resonance in metamaterials is highly relevant to the engineering of a type of essentially non-radiating anapole mode [18,2124], which arises from the destructive interference of the toroidal and electric dipole moments in the far-field at all angles. Due to non-radiating nature and efficient field confinement, the higher Q-factor and larger near-field enhancements can be obtained with excitation of anapole modes. Although nonradiative losses can be weak for dielectric resonators, strong radiative losses are still challenges to further enlarge enlarge the Q-factor [2527]. In addition, breaking the symmetry transversely in the direction perpendicular to a metamaterial effectively controls appearance of the high Q-factor Fano resonances in metasurfaces associated with the bound states in the continuum [25,28,29]. Recently, the collective oscillation mediated by near-field interaction between the unit cells in metamaterials has been proposed to effectively suppress radiation loss [15,3032]. Due to the sharp surface lattice resonance in array, it has been shown that extremely high Q-factor can be realized for dielectric metasurface based on the weak non-radiative losses and suppressed radiative losses [33]. However, the modulation depths, defined as the transmission intensity differences between the Fano peaks and the Fano dips Tpeak − Tdip, always decrease in the presence of non-radiative losses with the increasing Q-factors [34].

Compared to a single Fano resonance, multiple Fano resonances can be adjusted simultaneously at several different spectral positions and have been reported in the past few years. Liu et al. reported that tunability of the modulation depth of multiple Fano resonance from the plasmonic heptamer clusters [35]. Arash Ahmadivand et al. showed that multiple coil-type Fano resonances in all-dielectric antisymmetric quadrumers [36]. Xia et al. showed that multiple Fano resonances in symmetry breaking silicon gives rise to 3 orders of magnitude enhancement [37]. However, there are two shortcomings in these reported multiple Fano resonances, which make them not suitable in practical applications, i.e., (1) the Q factor in multiple Fano resonances underpinning most devices are limited to rather small values and (2) the modulation depths, that is, one or more modulation depths of the multiple Fano resonances are small in the spectra. So far, there are few studies that can realize more than four Fano resonances with high Q-factors and high modulation depths at the same time.

In this letter, we design the periodic paired nanorods and realize multiple Fano resonances with high Q-factor and large modulation depths by introducing the unique degree of freedom beyond the in-plane symmetry. The maximal Q-factor of multiple Fano resonances exceeds 9700 and even the minimal Q-factor also reaches about 1090 in magnitude. Most importantly, the modulation depth of each Fano resonance reaches nearly 100% in the near-infrared regime. Considering the narrow linewidth with large near-field enhancement, we theoretically demonstrate that the refractive index sensitivity exceeds 361 nm/RIU and the maximal figure of merit (FoM = (Δλ/Δn)/line width) reaches 5045. Moreover, the spectral positions and modulation depths of the multiple Fano resonances can be flexibly tuned and controlled by varying the geometrical parameters. Five Fano resonances with high Q-factor, large modulation depth and strong field enhancement simultaneously make the array promising for multiwavelength biomedical sensing and nonlinear optics.

2. Structures description

The unit cell of proposed paired nanorods array is placed over silica substrate and shown in Figs. 1(a) and 1(b). The lattice constants along the x and y directions are px = py = 670 nm, respectively. The two rods in a unit cell have the same length and width a, and have the different height h1, h2. The parameter δ = |h1h2| is introduced to specify structural asymmetry of unit cell. The gap between two nanorods is denoted as g. In our simulations, the proposed array is illuminated by y-polarized (electric field E along the y axis) plane waves, as illustrated in Fig. 1. And the array is immersed in water with refractive index n = 1.33. Numerical simulations are conducted using finite element and finite-difference time-domain methods. In our simulations, the experimentally measured dielectric function is utilized for silicon and silica [38]. The proposed array can be fabricated by the following method: the paired holes are etched with the focused ion beam etching (FIB) in the PMMA (poly (methyl methacrylate)). Differing from the processing method of silicon dimer [39,40], such holes have the different height to introduce the structural asymmetry by controlling the etching process. The nanostructured PMMA was covered with the sufficient thick silicon by the ion beam sputtering coating so that the thick film can form a plane [41]. Then such silicon film is etched via reactive ion etching. Subsequent the silicon dimer is transferred to the silica substrate and the PMMA is removed by a lift-off process in acetone.

 

Fig. 1. (a) Schematics of the unit cell for asymmetric paired silicon nanorods placed on the silica substrate. (b) Side view and geometric parameters of a unit cell.

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3. Simulation results and discussions

Figure 2(a) shows the transmission spectrum of a symmetric paired nanorods array with δ = 0 nm. The parameters width a, height h1, gap g, and period p have initially been set to be 280 nm, 565 nm, 35 nm, and 670 nm, respectively. In the symmetric design, it is shown that there are two Fano peaks occur at the wavelengths of 1232.7 nm and 1410.9 nm, marked as the M1 and TD resonances. And the transmission intensity at two resonances reaches nearly 100%. To quantitatively evaluate the contributions of multipoles in forming the resonant responses, the cartesian multipole moment analysis are applied and the radiating powers of the induced electric dipole (Py), magnetic dipole (Mx), toroidal dipole (Ty), electric quadrupole (Qyz) and magnetic quadrupole (Mxz) were calculated according to the the current density ${\boldsymbol J} = -i{\omega}{{\varepsilon }_{0}}{(}{{n}^{2}}{-1){\boldsymbol E}({\boldsymbol r})}$ by integrating spatially distributed fields in nanorods [20]. As shown in Fig. 2(b), in addition to conventional multipole resonances, there is very strong contribution of the toroidal dipole excitation at 1232.7 nm and 1410.9 nm, which is, actually, dominant over the whole spectrum. The scattering of the magnetic quadrupole Mxz shows a similar frequency dependence on the toroidal dipole Ty; however, the radiating intensity of the toroidal dipole Ty is larger than that of the Mxz. We note that the radiating powers of components of the Py and Qyz are lower in comparison with the three mainly contributed multipoles. Once we introduce the asymmetry δ = 40 nm (h1= 565 nm and h2= 525 nm), besides the resonances related to the previously discussed M1 and TD resonances at 1222.3 nm and 1406.9 nm, three additional resonances at 1293.5 nm (M2), 1312.4 nm (M3) and 1378.7 nm (M4) appear in the transmitted spectrum, as shown in Fig. 2(c). Breaking the symmetry transversely in the direction perpendicular to a metamaterial effectively control appearance of the high Q-factor Fano resonances. And these are associated with the physics of bound states in the continuum. [42]. Remarkably, such resonances produce the resonant spectral line having the Fano feature with narrow line widths and large modulation depths. In addition, one can see that as the fundamental resonances of the nanorods the M1 and TD modes have redshift with increasing δ. In order to improve contrast, the spectrum (δ = 0) has also been shown with blue line in Fig. 2(c).

 

Fig. 2. (a) Transmission spectrum of the symmetric array (δ = 0 nm). The inset represents the fitted spectrum near the resonances. (b) The radiating powers of various multipole moments. (c) Comparison results of transmission spectra between symmetric and asymmetric arrays. (d) Q factors for different δ.

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The Fano spectral feature of the proposed array can be reproduced accurately by a Fano model [43]. The transmittance spectrum in Fig. 2(a) can be fitted to a Fano line shape given by: ${\textrm{T}_{\textrm{Fano}}}\textrm{=}{\left|{{\textrm{a}_\textrm{1}}\textrm{+i}{\textrm{a}_\textrm{2}}\textrm{+}\frac{\textrm{b}}{{{\omega -}{{\omega }_\textrm{0}}{+i \gamma }}}} \right|^\textrm{2}},$ where ${\textrm{a}_\textrm{1}}$, ${\textrm{a}_\textrm{2}}$ and $\textrm{b}$ are constant numbers, ${{\omega }_\textrm{0}}$ is the oscillation frequency, and ${\gamma }$ is the damping factor. It can be seen clearly that the analytical derivation can reproduce well the result attained from the simulation, as shown in the inset of Fig. 2(a). Furthermore, the Q-factor of the spectral response can be extracted by such model and calculated by Q = (${{\omega }_{0}}/{2\gamma }$). The extracted Q-factors as a function of the asymmetry parameter δ are shown in Fig. 2(d). One can see that the Q-factors of the M1 and TD resonances are almost unaffected by asymmetry parameter δ. However, it is evident that the Q-factors of the M2, M3, and M4 resonances depend crucially on the δ and increase by decreasing the δ, which defines the degree of the introduced asymmetry. When δ = 40 nm, the corresponding Q-factors of the M1, M2, M3, M4 and TD resonances reach 2697 (${{\omega }_\textrm{0}}$ = 1.014 eV and ${\gamma}\,$  0.1880×10−3 eV), 1094 (${{\omega }_\textrm{0}}$ = 0.9587 eV and ${\gamma }$ = 0.4380×10−3 eV), 4723 (${{\omega }_\textrm{0}}$ = 0.9447 eV and ${\gamma}$  0.1000×10−3 eV), 6575 (${{\omega }_\textrm{0}}$ = 0.8993 eV and ${\gamma }$ = 0.0550×10−3 eV), and 1546 (${{\omega }_\textrm{0}}$ = 0.8815 eV and ${\gamma }$ = 0.2850×10−3 eV), respectively. In particular, the Q-factors of M3 and M4 resonances reach 8277 and 9766 when δ = 25 nm, respectively. Further, it can be seen that multiple Fano resonances all have large modulation depths. The modulation depths reach nearly 100% at M1 and TD resonances, while at M2, M3 and M4 the modulation depths also reaches 92%, 69% and 93%, respectively. Comparing with the Q factors in the range of a few hundreds in ref. [37], the quality factor has been increased by at least 35 times, and the modulation depth is also significantly better than the modulation depth in ref. [37]. Therefore, breaking symmetry can effectively excite multiple Fano resonances with the high Q-factors and high modulation depths while keeping the remaining dimensions of the dimers unchanged.

In order to further illustrate the subradiant properties related to multiple Fano resonances, the magnetic field enhancement |H/H0| as well as the field vector distributions on different center cross sections of the asymmetric array (δ = 40 nm) are represented in Fig. 3. One can see that the magnetic field can be firmly constrained within the nanorods and no radiation energy transmits outward at 1406.9 nm, where electric field in the x − y plane indicate two peculiar reversed swirls and the magnetic field in the x − z plane forms a swirl, indicating a typical TD feature [17,33,44,45], as shown in Fig. 3. The electric field at 1312.4 nm and 1378.7 nm forms two swirls rotating in the same direction in the xy plane, while the magnetic field in the two nanorods has the same direction and is almost linearly polarized along the z axis in the xz plane. As a result, the resonances at 1312.4 nm and 1378.7 nm can radiate like two parallel magnetic dipoles oriented along the z axis. According to the magnetic field vector distributions at 1293.5 nm, the magnetic field in the two nanorods oriented along the x axis and have opposite direction in the xy plane, and the magnetic field in single nanorod forms two reversed swirls in the xz plane, indicating a magnetic quadrupole resonance at 1293.5 nm. The magnetic field of a single nanorod at 1222.3 nm have opposite direction oriented along the x axis in the xy plane or the z axis in the xz plane, as shown in Fig. 3(a) and 3(b), which proves the presence of a magnetic quadrupole resonance in a single nanorod and provides a coupling pathway between magnetic quadrupole resonances in two nanorods through magnetic field interaction, ultimately leading to Fano resonance at 1222.3 nm. In addition, thanks to the high quality factors of Fano resonances, the maximum magnetic field can be enhanced by more than 75 times, comparable to plasmonic nanostructures.

 

Fig. 3. (a) Normalized magnetic field amplitudes |H/H0| in the middle xy plane of the unit cell at characteristic wavelengths. The white arrows at 1222.3 nm and 1293.5 nm (1312.4 nm, 1378.7 nm and 1406.9 nm) indicate the magnetic (electric) field directions. (b) The z-component of H-field intensity at 1222.3 nm, 1312.4 nm, 1378.7 nm and 1406.9 nm, the z-component of E-field intensity at 1293.5 nm. The black and white arrows show the magnetic field directions.

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In the following, we investigate transmission spectra of the asymmetric paired nanorods array at different geometric parameters shown in Fig. 4. Other parameters are the same as that used in Fig. 2(c). As shown in Figs. 4, the M1 and TD resonances are virtually unaffected by the parameters p, g and δ. In Fig. 4(a), the M2 and M3 are not sensitive to the parameters p and only generate a slight redshift, however, the M4 is sensitive to the array periodicity p. In Fig. 4(b), it can be seen clearly that the all Fano peaks are very sensitive to width a and experience a significant redshift as the width increases, altogether resulting in the easily traceable tuning characteristics of Fano resonances. It can be found that the reduced interaction with the increasing gap g causes a slight redshift of the M2 and M3, as shown in Fig. 4(c), while the M4 can be readily tuned and undergoes an obvious blueshift. Meanwhile, the M4 has a relatively large redshift compared to the M3 and is enhanced with the weaken interaction. As shown in Fig. 4(d), the resonant frequencies of Fano resonances remain nearly unchanged with increasing asymmetry because the symmetry breaking along the z axis of the dimer does not change the excitation energy of the resonances. Meanwhile, the line-width of the M2 is clearly broadened with increasing asymmetry, and the corresponding Q-factor dramatically decreases. The reduction of Q-factor with increasing δ is due to the increase of radiation loss.

 

Fig. 4. Transmission spectra at different parameters. (a)Period p, (b) side a, (c) Gap g and (d) Asymmetric parameter δ. Other parameters are the same as that used in Fig. 2(c).

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Due to high Q-factor and large field enhancement of multiple Fano resonances, one can expect that the proposed nanorod dimer array can be used for sensing applications. The spectral shift per refractive index (RI) unit (RIU) and FoM are two good indicators for the local sensitivity. Figure 5(a) shows the shift in transmission spectra of the asymmetric array (δ = 40 nm), whose surface is covered by water with a refractive index from 1.32 to 1.34. It can be seen that a clear redshift of the multiple Fano resonances is visible as the refractive index increases. The spectral shift sensitivity of the M1, M2, M3, M4 and TD resonances reaches 117 nm/RIU, 131 nm/RIU, 361 nm/RIU, 344 nm/RIU and 162 nm/RIU, respectively. The extracted line width from the Fano model is 0.2331 nm, 0.5431 nm, 0.1240 nm, 0.0682 nm and 0.3534 nm, and the corresponding FoM reaches 502, 241, 2912, 5045 and 459, respectively. Although the sensitivity 361 nm/RIU is even less than sensitivity demonstrated experimentally for plasmonic sensors, the largest FoM exceeds 5000 due to the high quality factor [46]. The differences in the sensitivity of multiple Fano resonances are mainly due to the different near-field distributions. Thus, the proposed array offers a good platform to design high-performance multichannel bio-sensing devices.

 

Fig. 5. Wavelength shifts as a function of the refractive index of the background. The geometry parameters of the array are the same as that used in Fig. 2(c).

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4. Conclusion

In conclusion, we have shown that multiple Fano resonances with high Q-factor and large modulation depth can be realized by a periodical all-dielectric asymmetric nanorod dimer in the near-infrared regime. Due to the formation of the subradiant hybrid modes by breaking the symmetry of dimer in array, five Fano resonances (M1, M2, M3, M4 and TD) all have the high Q-factors, the maximal Q-factor exceeds 9700 and even the minimal Q-factor also reaches 1090. The higher Q-factor can be obtained by adjusting the asymmetry. And the modulation depths reach nearly 100% at M1 and TD, while at M2, M3 and M4 the modulation depths also reach 92%, 69% and 93%, respectively. Moreover, the Q-factors and modulation depths can be flexibly tuned by varying the geometrical parameters. In addition, five Fano resonances with the strongly enhanced magnetic field make the proposed array suitable for refractive index sensing. The bulk refractive index sensitivity reaches 361 nm/RIU, the maximal FoM reaches 5045 and can be further improved by reducing the asymmetry. Such sharp multiple Fano resonances, high Q-factors, large modulation depths and FoM values supported by the proposed design make it more adaptable to numerous potential applications ranging from nonlinear optics and multiwavelength biosensing to the realization of new types of optical modulation and low-loss slow-light devices.

Funding

Dalian Polytechnic University (71600160); National Natural Science Foundation of China (11647102, 12785604).

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References

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  1. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
    [Crossref]
  2. J. Butet and O. J. Martin, “Fano resonances in the nonlinear optical response of coupled plasmonic nanostructures,” Opt. Express 22(24), 29693 (2014).
    [Crossref]
  3. M. Gupta, Y. K. Srivastava, M. Manjappa, and R. Singh, “Sensing with toroidal metamaterial,” Appl. Phys. Lett. 110(12), 121108 (2017).
    [Crossref]
  4. A. A. Siraji and Y. Zhao, “High-sensitivity and high-q-factor glass photonic crystal cavity and its applications as sensors,” Opt. Lett. 40(7), 1508 (2015).
    [Crossref]
  5. D. Finkelsteinshapiro, I. Urdaneta, M. Calatayud, O. Atabek, V. Mujica, and A. Keller, “Fano-Liouville Spectral Signatures in Open Quantum Systems,” Phys. Rev. Lett. 115(11), 113006 (2015).
    [Crossref]
  6. Y. Moritake, Y. Kanamori, and K. Hane, “Enhanced quality factor of fano resonance in optical metamaterials by manipulating configuration of unit cells,” Appl. Phys. Lett. 107(21), 211108 (2015).
    [Crossref]
  7. Z. Liu, W. Li, J. Li, and C. Gu, “Fano resonance rabi splitting of surface plasmons,” Sci. Rep. 7(1), 8010 (2017).
    [Crossref]
  8. A. E. Miroshnichenko and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
    [Crossref]
  9. B. Luk’Yanchuk, P. Nordlander, and H. Giessen, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
    [Crossref]
  10. X. B. W. Liu, X. Yao, L. Zhang, H. X. Lin, S. Chen, J. H. Zhong, and B. Ren, “Efficient Platform for Flexible Engineering of Superradiant, Fano-Type, and Subradiant Resonances,” ACS Photonics 2(12), 1725–1731 (2015).
    [Crossref]
  11. S. Bakhti, N. Bonod, S. D. Dhuey, P. J. Schuck, and N. Destouches, “Fano-like resonance emerging from magnetic and electric plasmon mode coupling in small arrays of gold particles,” Sci. Rep. 6(1), 32061 (2016).
    [Crossref]
  12. C. S. Sui, X. J. Li, T. T. Lang, X. F. Jing, and Z. Hong, “High Q-Factor Resonance in a Symmetric Array of All-Dielectric Bars,” Appl. Sci. 8(2), 161 (2018).
    [Crossref]
  13. Y. Tsuchimoto, T. A. Yano, T. Hayashi, and M. Hara, “Fano resonant all-dielectric core/shell nanoparticles with ultrahigh scattering directionality in the visible region,” Opt. Express 24(13), 14451 (2016).
    [Crossref]
  14. S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11(1), 23–36 (2016).
    [Crossref]
  15. D. J. Cai, Y. H. Huang, W. J. Wang, W. B. Ji, Z. H. Chen, and S. D. Liu, “Fano Resonances Generated in a Single Dielectric Homogeneous Nanoparticle with High Structural Symmetry,” J. Phys. Chem. C 119(8), 4252–4260 (2015).
    [Crossref]
  16. 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]
  17. 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]
  18. S. Q. Li and K. B. Crozier, “Origin of the anapole condition as revealed by a simple expansion beyond the toroidal multipole,” Phys. Rev. B 97(24), 245423 (2018).
    [Crossref]
  19. N. Papasimakis, I. V. Fedotov, T. Kaelberer, D. P. Tsai, and N. I. Zheludev, “Toroidal Dipolar Response in a Metamaterial,” Science 330(6010), 1510–1512 (2010).
    [Crossref]
  20. I. V. Stenishchev and A. A. Basharin, “Toroidal response in all-dielectric metamaterials based on water,” Sci. Rep. 7(1), 9468 (2017).
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  21. A. K. Ospanova, L. Matekovits, and A. A. Basharin, “Multipolar passive cloaking by nonradiating anapole excitation,” Sci. Rep. 8(1), 12514 (2018).
    [Crossref]
  22. N. A. Nemkov and A. A. Basharin, “Nontrivial nonradiating alldielectric anapole,” Sci. Rep. 7(1), 1064 (2017).
    [Crossref]
  23. A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, and A. I. Kuznetsov, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
    [Crossref]
  24. Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-Assisted Strong Field Enhancement in Individual All-Dielectric Nanostructures,” ACS Photonics 5(5), 1960–1966 (2018).
    [Crossref]
  25. A. A. Bogdanov, K. L. Koshelev, P. V. Kapitanova, M. V. Rybin, S. A. Gladyshev, and Z. F. Sadrieva, “Bound states in the continuum and fano resonances in the strong mode coupling regime,” Adv. Photonics 1(01), 1 (2019).
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  26. K. Koshelev, G. Favraud, A. Bogdanov, Y. Kivshar, and A. Fratalocchi, “Nonradiating photonics with resonant dielectric nanostructures,” Nanophotonics 8(5), 725–745 (2019).
    [Crossref]
  27. M. V. Rybin, K. L. Koshelev, Z. F. Sadrieva, K. B. Samusev, A. A. Bogdanov, M. F. Limonov, and Y. S. Kivshar, “High-Q Supercavity Modes in Subwavelength Dielectric Resonators,” Phys. Rev. Lett. 119(24), 243901 (2017).
    [Crossref]
  28. A. S. Kupriianov, Y. Xu, A. Sayanskiy, V. Dmitriev, Y. S. Kivshar, and V. R. Tuz, “Metasurface engineering through bound states in the continuum,” Phys. Rev. Appl. 12(1), 014024 (2019).
    [Crossref]
  29. K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric Metasurfaces with High- Q Resonances Governed by Bound States in the Continuum,” Phys. Rev. Lett. 121(19), 193903 (2018).
    [Crossref]
  30. S. Campione, S. Liu, L. I. Basilio, L. K. Warne, W. L. Langston, and T. S. Luk, “Broken symmetry dielectric resonators for high quality-factor fano metasurfaces,” ACS Photonics 3(12), 2362–2367 (2016).
    [Crossref]
  31. Y. Liu, Y. Luo, X. Jin, X. Zhou, K. Song, and X. Zhao, “High-Q Fano Resonances in Asymmetric and Symmetric All-Dielectric Metasurfaces,” Plasmonics 12(5), 1431–1438 (2017).
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  32. G. Sun, L. Yuan, Y. Zhang, X. Zhang, and Y. Zhu, “Q-factor enhancement of Fano resonance in all-dielectric metasurfaces by modulating metaatom interactions,” Sci. Rep. 7(1), 8128 (2017).
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  33. Y. Zhang, W. Liu, Z. Li, Z. Li, H. Cheng, and S. Chen, “High-quality-factor multiple fano resonances for refractive index sensing,” Opt. Lett. 43(8), 1842 (2018).
    [Crossref]
  34. W. Zhao, H. Jiang, B. Liu, Y. Jiang, C. Tang, and J. Li, “Fano resonance based optical modulator reaching 85% modulation depth,” Appl. Phys. Lett. 107(17), 171109 (2015).
    [Crossref]
  35. S. D. Liu, J. Deng, and J. H. Teng, “Polarization-Independent Multiple Fano Resonances in Plasmonic Nonamers for Multimode-Matching Enhanced Multiband Second-Harmonic Generation,” ACS Nano 10(1), 1442–1453 (2016).
    [Crossref]
  36. A. Ahmadivand and N. Pala, “Multiple coil-type fano resonances in all-dielectric antisymmetric quadrumers,” Opt. Quantum Electron. 47(7), 2055–2064 (2015).
    [Crossref]
  37. C. Cui, C. Zhou, S. Yuan, X. Qiu, L. Zhu, Y. Wang, and J. Xia, “Multiple Fano Resonances in Symmetry-Breaking Silicon Metasurface for Manipulating Light Emission,” ACS Photonics 5(10), 4074–4080 (2018).
    [Crossref]
  38. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985). Vol. I.
  39. T. Shibanuma, S. A. Maier, and P. Albella, “Polarization control of high transmission/reflection switching by all-dielectric metasurfaces,” Appl. Phys. Lett. 112(6), 063103 (2018).
    [Crossref]
  40. T. Shibanuma, T. Matsui, T. Roschuk, J. Wojcik, P. Mascher, and P. Albella, “Experimental demonstration of tunable directional scattering of visible light from all-dielectric asymmetric dimers,” ACS Photonics 4(3), 489–494 (2017).
    [Crossref]
  41. J. Qi, Y. Xiang, W. Yan, M. Li, and Z. Chen, “The excitation of the tunable longitudinal higher-order multipole SPR modes by strong coupling in large-area metal sub-10nm-gap array structures and its application,” J. Phys. Chem. C 120(43), 24932–24940 (2016).
    [Crossref]
  42. Z. Sadrieva, K. Frizyuk, M. Petrov, Y. Kivshar, and A. Bogdanov, “Multipolar origin of bound states in the continuum”, arXiv:1903.00309 (2019)
  43. Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
    [Crossref]
  44. 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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  45. M. Gupta, Y. K. Srivastava, and R. Singh, “A Toroidal Metamaterial Switch,” Adv. Mater. 30(4), 1704845 (2018).
    [Crossref]
  46. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators, B 54(1–2), 3–15 (1999).
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2019 (3)

A. S. Kupriianov, Y. Xu, A. Sayanskiy, V. Dmitriev, Y. S. Kivshar, and V. R. Tuz, “Metasurface engineering through bound states in the continuum,” Phys. Rev. Appl. 12(1), 014024 (2019).
[Crossref]

K. Koshelev, G. Favraud, A. Bogdanov, Y. Kivshar, and A. Fratalocchi, “Nonradiating photonics with resonant dielectric nanostructures,” Nanophotonics 8(5), 725–745 (2019).
[Crossref]

A. A. Bogdanov, K. L. Koshelev, P. V. Kapitanova, M. V. Rybin, S. A. Gladyshev, and Z. F. Sadrieva, “Bound states in the continuum and fano resonances in the strong mode coupling regime,” Adv. Photonics 1(01), 1 (2019).
[Crossref]

2018 (11)

S. Q. Li and K. B. Crozier, “Origin of the anapole condition as revealed by a simple expansion beyond the toroidal multipole,” Phys. Rev. B 97(24), 245423 (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]

C. S. Sui, X. J. Li, T. T. Lang, X. F. Jing, and Z. Hong, “High Q-Factor Resonance in a Symmetric Array of All-Dielectric Bars,” Appl. Sci. 8(2), 161 (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]

K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric Metasurfaces with High- Q Resonances Governed by Bound States in the Continuum,” Phys. Rev. Lett. 121(19), 193903 (2018).
[Crossref]

Y. Zhang, W. Liu, Z. Li, Z. Li, H. Cheng, and S. Chen, “High-quality-factor multiple fano resonances for refractive index sensing,” Opt. Lett. 43(8), 1842 (2018).
[Crossref]

C. Cui, C. Zhou, S. Yuan, X. Qiu, L. Zhu, Y. Wang, and J. Xia, “Multiple Fano Resonances in Symmetry-Breaking Silicon Metasurface for Manipulating Light Emission,” ACS Photonics 5(10), 4074–4080 (2018).
[Crossref]

M. Gupta, Y. K. Srivastava, and R. Singh, “A Toroidal Metamaterial Switch,” Adv. Mater. 30(4), 1704845 (2018).
[Crossref]

T. Shibanuma, S. A. Maier, and P. Albella, “Polarization control of high transmission/reflection switching by all-dielectric metasurfaces,” Appl. Phys. Lett. 112(6), 063103 (2018).
[Crossref]

Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-Assisted Strong Field Enhancement in Individual All-Dielectric Nanostructures,” ACS Photonics 5(5), 1960–1966 (2018).
[Crossref]

A. K. Ospanova, L. Matekovits, and A. A. Basharin, “Multipolar passive cloaking by nonradiating anapole excitation,” Sci. Rep. 8(1), 12514 (2018).
[Crossref]

2017 (8)

I. V. Stenishchev and A. A. Basharin, “Toroidal response in all-dielectric metamaterials based on water,” Sci. Rep. 7(1), 9468 (2017).
[Crossref]

M. Gupta, Y. K. Srivastava, M. Manjappa, and R. Singh, “Sensing with toroidal metamaterial,” Appl. Phys. Lett. 110(12), 121108 (2017).
[Crossref]

Y. Liu, Y. Luo, X. Jin, X. Zhou, K. Song, and X. Zhao, “High-Q Fano Resonances in Asymmetric and Symmetric All-Dielectric Metasurfaces,” Plasmonics 12(5), 1431–1438 (2017).
[Crossref]

Z. Liu, W. Li, J. Li, and C. Gu, “Fano resonance rabi splitting of surface plasmons,” Sci. Rep. 7(1), 8010 (2017).
[Crossref]

G. Sun, L. Yuan, Y. Zhang, X. Zhang, and Y. Zhu, “Q-factor enhancement of Fano resonance in all-dielectric metasurfaces by modulating metaatom interactions,” Sci. Rep. 7(1), 8128 (2017).
[Crossref]

N. A. Nemkov and A. A. Basharin, “Nontrivial nonradiating alldielectric anapole,” Sci. Rep. 7(1), 1064 (2017).
[Crossref]

T. Shibanuma, T. Matsui, T. Roschuk, J. Wojcik, P. Mascher, and P. Albella, “Experimental demonstration of tunable directional scattering of visible light from all-dielectric asymmetric dimers,” ACS Photonics 4(3), 489–494 (2017).
[Crossref]

M. V. Rybin, K. L. Koshelev, Z. F. Sadrieva, K. B. Samusev, A. A. Bogdanov, M. F. Limonov, and Y. S. Kivshar, “High-Q Supercavity Modes in Subwavelength Dielectric Resonators,” Phys. Rev. Lett. 119(24), 243901 (2017).
[Crossref]

2016 (7)

S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11(1), 23–36 (2016).
[Crossref]

J. Qi, Y. Xiang, W. Yan, M. Li, and Z. Chen, “The excitation of the tunable longitudinal higher-order multipole SPR modes by strong coupling in large-area metal sub-10nm-gap array structures and its application,” J. Phys. Chem. C 120(43), 24932–24940 (2016).
[Crossref]

S. Campione, S. Liu, L. I. Basilio, L. K. Warne, W. L. Langston, and T. S. Luk, “Broken symmetry dielectric resonators for high quality-factor fano metasurfaces,” ACS Photonics 3(12), 2362–2367 (2016).
[Crossref]

S. Bakhti, N. Bonod, S. D. Dhuey, P. J. Schuck, and N. Destouches, “Fano-like resonance emerging from magnetic and electric plasmon mode coupling in small arrays of gold particles,” Sci. Rep. 6(1), 32061 (2016).
[Crossref]

Y. Tsuchimoto, T. A. Yano, T. Hayashi, and M. Hara, “Fano resonant all-dielectric core/shell nanoparticles with ultrahigh scattering directionality in the visible region,” Opt. Express 24(13), 14451 (2016).
[Crossref]

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]

S. D. Liu, J. Deng, and J. H. Teng, “Polarization-Independent Multiple Fano Resonances in Plasmonic Nonamers for Multimode-Matching Enhanced Multiband Second-Harmonic Generation,” ACS Nano 10(1), 1442–1453 (2016).
[Crossref]

2015 (8)

Y. Moritake, Y. Kanamori, and K. Hane, “Enhanced quality factor of fano resonance in optical metamaterials by manipulating configuration of unit cells,” Appl. Phys. Lett. 107(21), 211108 (2015).
[Crossref]

W. Zhao, H. Jiang, B. Liu, Y. Jiang, C. Tang, and J. Li, “Fano resonance based optical modulator reaching 85% modulation depth,” Appl. Phys. Lett. 107(17), 171109 (2015).
[Crossref]

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, and A. I. Kuznetsov, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref]

X. B. W. Liu, X. Yao, L. Zhang, H. X. Lin, S. Chen, J. H. Zhong, and B. Ren, “Efficient Platform for Flexible Engineering of Superradiant, Fano-Type, and Subradiant Resonances,” ACS Photonics 2(12), 1725–1731 (2015).
[Crossref]

D. J. Cai, Y. H. Huang, W. J. Wang, W. B. Ji, Z. H. Chen, and S. D. Liu, “Fano Resonances Generated in a Single Dielectric Homogeneous Nanoparticle with High Structural Symmetry,” J. Phys. Chem. C 119(8), 4252–4260 (2015).
[Crossref]

A. A. Siraji and Y. Zhao, “High-sensitivity and high-q-factor glass photonic crystal cavity and its applications as sensors,” Opt. Lett. 40(7), 1508 (2015).
[Crossref]

A. Ahmadivand and N. Pala, “Multiple coil-type fano resonances in all-dielectric antisymmetric quadrumers,” Opt. Quantum Electron. 47(7), 2055–2064 (2015).
[Crossref]

D. Finkelsteinshapiro, I. Urdaneta, M. Calatayud, O. Atabek, V. Mujica, and A. Keller, “Fano-Liouville Spectral Signatures in Open Quantum Systems,” Phys. Rev. Lett. 115(11), 113006 (2015).
[Crossref]

2014 (2)

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
[Crossref]

J. Butet and O. J. Martin, “Fano resonances in the nonlinear optical response of coupled plasmonic nanostructures,” Opt. Express 22(24), 29693 (2014).
[Crossref]

2010 (3)

B. Luk’Yanchuk, P. Nordlander, and H. Giessen, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref]

N. Papasimakis, I. V. Fedotov, T. Kaelberer, D. P. Tsai, and N. I. Zheludev, “Toroidal Dipolar Response in a Metamaterial,” Science 330(6010), 1510–1512 (2010).
[Crossref]

A. E. Miroshnichenko and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[Crossref]

2008 (1)

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[Crossref]

1999 (1)

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators, B 54(1–2), 3–15 (1999).
[Crossref]

Ahmadivand, A.

A. Ahmadivand and N. Pala, “Multiple coil-type fano resonances in all-dielectric antisymmetric quadrumers,” Opt. Quantum Electron. 47(7), 2055–2064 (2015).
[Crossref]

Albella, P.

T. Shibanuma, S. A. Maier, and P. Albella, “Polarization control of high transmission/reflection switching by all-dielectric metasurfaces,” Appl. Phys. Lett. 112(6), 063103 (2018).
[Crossref]

T. Shibanuma, T. Matsui, T. Roschuk, J. Wojcik, P. Mascher, and P. Albella, “Experimental demonstration of tunable directional scattering of visible light from all-dielectric asymmetric dimers,” ACS Photonics 4(3), 489–494 (2017).
[Crossref]

Atabek, O.

D. Finkelsteinshapiro, I. Urdaneta, M. Calatayud, O. Atabek, V. Mujica, and A. Keller, “Fano-Liouville Spectral Signatures in Open Quantum Systems,” Phys. Rev. Lett. 115(11), 113006 (2015).
[Crossref]

Bakhti, S.

S. Bakhti, N. Bonod, S. D. Dhuey, P. J. Schuck, and N. Destouches, “Fano-like resonance emerging from magnetic and electric plasmon mode coupling in small arrays of gold particles,” Sci. Rep. 6(1), 32061 (2016).
[Crossref]

Bakker, R. M.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, and A. I. Kuznetsov, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref]

Basharin, A. A.

A. K. Ospanova, L. Matekovits, and A. A. Basharin, “Multipolar passive cloaking by nonradiating anapole excitation,” Sci. Rep. 8(1), 12514 (2018).
[Crossref]

N. A. Nemkov and A. A. Basharin, “Nontrivial nonradiating alldielectric anapole,” Sci. Rep. 7(1), 1064 (2017).
[Crossref]

I. V. Stenishchev and A. A. Basharin, “Toroidal response in all-dielectric metamaterials based on water,” Sci. Rep. 7(1), 9468 (2017).
[Crossref]

Basilio, L. I.

S. Campione, S. Liu, L. I. Basilio, L. K. Warne, W. L. Langston, and T. S. Luk, “Broken symmetry dielectric resonators for high quality-factor fano metasurfaces,” ACS Photonics 3(12), 2362–2367 (2016).
[Crossref]

Bogdanov, A.

K. Koshelev, G. Favraud, A. Bogdanov, Y. Kivshar, and A. Fratalocchi, “Nonradiating photonics with resonant dielectric nanostructures,” Nanophotonics 8(5), 725–745 (2019).
[Crossref]

K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric Metasurfaces with High- Q Resonances Governed by Bound States in the Continuum,” Phys. Rev. Lett. 121(19), 193903 (2018).
[Crossref]

Z. Sadrieva, K. Frizyuk, M. Petrov, Y. Kivshar, and A. Bogdanov, “Multipolar origin of bound states in the continuum”, arXiv:1903.00309 (2019)

Bogdanov, A. A.

A. A. Bogdanov, K. L. Koshelev, P. V. Kapitanova, M. V. Rybin, S. A. Gladyshev, and Z. F. Sadrieva, “Bound states in the continuum and fano resonances in the strong mode coupling regime,” Adv. Photonics 1(01), 1 (2019).
[Crossref]

M. V. Rybin, K. L. Koshelev, Z. F. Sadrieva, K. B. Samusev, A. A. Bogdanov, M. F. Limonov, and Y. S. Kivshar, “High-Q Supercavity Modes in Subwavelength Dielectric Resonators,” Phys. Rev. Lett. 119(24), 243901 (2017).
[Crossref]

Bonod, N.

S. Bakhti, N. Bonod, S. D. Dhuey, P. J. Schuck, and N. Destouches, “Fano-like resonance emerging from magnetic and electric plasmon mode coupling in small arrays of gold particles,” Sci. Rep. 6(1), 32061 (2016).
[Crossref]

Bozhevolnyi, S. I.

Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-Assisted Strong Field Enhancement in Individual All-Dielectric Nanostructures,” ACS Photonics 5(5), 1960–1966 (2018).
[Crossref]

Briggs, D. P.

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
[Crossref]

Butet, J.

Cai, D. J.

D. J. Cai, Y. H. Huang, W. J. Wang, W. B. Ji, Z. H. Chen, and S. D. Liu, “Fano Resonances Generated in a Single Dielectric Homogeneous Nanoparticle with High Structural Symmetry,” J. Phys. Chem. C 119(8), 4252–4260 (2015).
[Crossref]

Calatayud, M.

D. Finkelsteinshapiro, I. Urdaneta, M. Calatayud, O. Atabek, V. Mujica, and A. Keller, “Fano-Liouville Spectral Signatures in Open Quantum Systems,” Phys. Rev. Lett. 115(11), 113006 (2015).
[Crossref]

Campione, S.

S. Campione, S. Liu, L. I. Basilio, L. K. Warne, W. L. Langston, and T. S. Luk, “Broken symmetry dielectric resonators for high quality-factor fano metasurfaces,” ACS Photonics 3(12), 2362–2367 (2016).
[Crossref]

Chen, S.

Y. Zhang, W. Liu, Z. Li, Z. Li, H. Cheng, and S. Chen, “High-quality-factor multiple fano resonances for refractive index sensing,” Opt. Lett. 43(8), 1842 (2018).
[Crossref]

X. B. W. Liu, X. Yao, L. Zhang, H. X. Lin, S. Chen, J. H. Zhong, and B. Ren, “Efficient Platform for Flexible Engineering of Superradiant, Fano-Type, and Subradiant Resonances,” ACS Photonics 2(12), 1725–1731 (2015).
[Crossref]

Chen, Z.

J. Qi, Y. Xiang, W. Yan, M. Li, and Z. Chen, “The excitation of the tunable longitudinal higher-order multipole SPR modes by strong coupling in large-area metal sub-10nm-gap array structures and its application,” J. Phys. Chem. C 120(43), 24932–24940 (2016).
[Crossref]

Chen, Z. H.

D. J. Cai, Y. H. Huang, W. J. Wang, W. B. Ji, Z. H. Chen, and S. D. Liu, “Fano Resonances Generated in a Single Dielectric Homogeneous Nanoparticle with High Structural Symmetry,” J. Phys. Chem. C 119(8), 4252–4260 (2015).
[Crossref]

Cheng, H.

Chipouline, A.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, and A. I. Kuznetsov, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref]

Crozier, K. B.

S. Q. Li and K. B. Crozier, “Origin of the anapole condition as revealed by a simple expansion beyond the toroidal multipole,” Phys. Rev. B 97(24), 245423 (2018).
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Cui, C.

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S. Bakhti, N. Bonod, S. D. Dhuey, P. J. Schuck, and N. Destouches, “Fano-like resonance emerging from magnetic and electric plasmon mode coupling in small arrays of gold particles,” Sci. Rep. 6(1), 32061 (2016).
[Crossref]

Shibanuma, T.

T. Shibanuma, S. A. Maier, and P. Albella, “Polarization control of high transmission/reflection switching by all-dielectric metasurfaces,” Appl. Phys. Lett. 112(6), 063103 (2018).
[Crossref]

T. Shibanuma, T. Matsui, T. Roschuk, J. Wojcik, P. Mascher, and P. Albella, “Experimental demonstration of tunable directional scattering of visible light from all-dielectric asymmetric dimers,” ACS Photonics 4(3), 489–494 (2017).
[Crossref]

Singh, R.

M. Gupta, Y. K. Srivastava, and R. Singh, “A Toroidal Metamaterial Switch,” Adv. Mater. 30(4), 1704845 (2018).
[Crossref]

M. Gupta, Y. K. Srivastava, M. Manjappa, and R. Singh, “Sensing with toroidal metamaterial,” Appl. Phys. Lett. 110(12), 121108 (2017).
[Crossref]

Siraji, A. A.

Song, K.

Y. Liu, Y. Luo, X. Jin, X. Zhou, K. Song, and X. Zhao, “High-Q Fano Resonances in Asymmetric and Symmetric All-Dielectric Metasurfaces,” Plasmonics 12(5), 1431–1438 (2017).
[Crossref]

Srivastava, Y. K.

M. Gupta, Y. K. Srivastava, and R. Singh, “A Toroidal Metamaterial Switch,” Adv. Mater. 30(4), 1704845 (2018).
[Crossref]

M. Gupta, Y. K. Srivastava, M. Manjappa, and R. Singh, “Sensing with toroidal metamaterial,” Appl. Phys. Lett. 110(12), 121108 (2017).
[Crossref]

Stenishchev, I. V.

I. V. Stenishchev and A. A. Basharin, “Toroidal response in all-dielectric metamaterials based on water,” Sci. Rep. 7(1), 9468 (2017).
[Crossref]

Sui, C. S.

C. S. Sui, X. J. Li, T. T. Lang, X. F. Jing, and Z. Hong, “High Q-Factor Resonance in a Symmetric Array of All-Dielectric Bars,” Appl. Sci. 8(2), 161 (2018).
[Crossref]

Sun, G.

G. Sun, L. Yuan, Y. Zhang, X. Zhang, and Y. Zhu, “Q-factor enhancement of Fano resonance in all-dielectric metasurfaces by modulating metaatom interactions,” Sci. Rep. 7(1), 8128 (2017).
[Crossref]

Talebi, N.

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]

Tang, C.

W. Zhao, H. Jiang, B. Liu, Y. Jiang, C. Tang, and J. Li, “Fano resonance based optical modulator reaching 85% modulation depth,” Appl. Phys. Lett. 107(17), 171109 (2015).
[Crossref]

Teng, J. H.

S. D. Liu, J. Deng, and J. H. Teng, “Polarization-Independent Multiple Fano Resonances in Plasmonic Nonamers for Multimode-Matching Enhanced Multiband Second-Harmonic Generation,” ACS Nano 10(1), 1442–1453 (2016).
[Crossref]

Tsai, D. P.

N. Papasimakis, I. V. Fedotov, T. Kaelberer, D. P. Tsai, and N. I. Zheludev, “Toroidal Dipolar Response in a Metamaterial,” Science 330(6010), 1510–1512 (2010).
[Crossref]

Tsuchimoto, Y.

Tuz, V. R.

A. S. Kupriianov, Y. Xu, A. Sayanskiy, V. Dmitriev, Y. S. Kivshar, and V. R. Tuz, “Metasurface engineering through bound states in the continuum,” Phys. Rev. Appl. 12(1), 014024 (2019).
[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]

Urdaneta, I.

D. Finkelsteinshapiro, I. Urdaneta, M. Calatayud, O. Atabek, V. Mujica, and A. Keller, “Fano-Liouville Spectral Signatures in Open Quantum Systems,” Phys. Rev. Lett. 115(11), 113006 (2015).
[Crossref]

Valentine, J.

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
[Crossref]

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, W. J.

D. J. Cai, Y. H. Huang, W. J. Wang, W. B. Ji, Z. H. Chen, and S. D. Liu, “Fano Resonances Generated in a Single Dielectric Homogeneous Nanoparticle with High Structural Symmetry,” J. Phys. Chem. C 119(8), 4252–4260 (2015).
[Crossref]

Wang, Y.

C. Cui, C. Zhou, S. Yuan, X. Qiu, L. Zhu, Y. Wang, and J. Xia, “Multiple Fano Resonances in Symmetry-Breaking Silicon Metasurface for Manipulating Light Emission,” ACS Photonics 5(10), 4074–4080 (2018).
[Crossref]

Warne, L. K.

S. Campione, S. Liu, L. I. Basilio, L. K. Warne, W. L. Langston, and T. S. Luk, “Broken symmetry dielectric resonators for high quality-factor fano metasurfaces,” ACS Photonics 3(12), 2362–2367 (2016).
[Crossref]

Wojcik, J.

T. Shibanuma, T. Matsui, T. Roschuk, J. Wojcik, P. Mascher, and P. Albella, “Experimental demonstration of tunable directional scattering of visible light from all-dielectric asymmetric dimers,” ACS Photonics 4(3), 489–494 (2017).
[Crossref]

Xia, J.

C. Cui, C. Zhou, S. Yuan, X. Qiu, L. Zhu, Y. Wang, and J. Xia, “Multiple Fano Resonances in Symmetry-Breaking Silicon Metasurface for Manipulating Light Emission,” ACS Photonics 5(10), 4074–4080 (2018).
[Crossref]

Xiang, Y.

J. Qi, Y. Xiang, W. Yan, M. Li, and Z. Chen, “The excitation of the tunable longitudinal higher-order multipole SPR modes by strong coupling in large-area metal sub-10nm-gap array structures and its application,” J. Phys. Chem. C 120(43), 24932–24940 (2016).
[Crossref]

Xu, Y.

A. S. Kupriianov, Y. Xu, A. Sayanskiy, V. Dmitriev, Y. S. Kivshar, and V. R. Tuz, “Metasurface engineering through bound states in the continuum,” Phys. Rev. Appl. 12(1), 014024 (2019).
[Crossref]

Yan, W.

J. Qi, Y. Xiang, W. Yan, M. Li, and Z. Chen, “The excitation of the tunable longitudinal higher-order multipole SPR modes by strong coupling in large-area metal sub-10nm-gap array structures and its application,” J. Phys. Chem. C 120(43), 24932–24940 (2016).
[Crossref]

Yang, Y.

Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-Assisted Strong Field Enhancement in Individual All-Dielectric Nanostructures,” ACS Photonics 5(5), 1960–1966 (2018).
[Crossref]

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
[Crossref]

Yano, T. A.

Yao, X.

X. B. W. Liu, X. Yao, L. Zhang, H. X. Lin, S. Chen, J. H. Zhong, and B. Ren, “Efficient Platform for Flexible Engineering of Superradiant, Fano-Type, and Subradiant Resonances,” ACS Photonics 2(12), 1725–1731 (2015).
[Crossref]

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J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators, B 54(1–2), 3–15 (1999).
[Crossref]

Yu, Y. F.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, and A. I. Kuznetsov, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref]

Yuan, L.

G. Sun, L. Yuan, Y. Zhang, X. Zhang, and Y. Zhu, “Q-factor enhancement of Fano resonance in all-dielectric metasurfaces by modulating metaatom interactions,” Sci. Rep. 7(1), 8128 (2017).
[Crossref]

Yuan, S.

C. Cui, C. Zhou, S. Yuan, X. Qiu, L. Zhu, Y. Wang, and J. Xia, “Multiple Fano Resonances in Symmetry-Breaking Silicon Metasurface for Manipulating Light Emission,” ACS Photonics 5(10), 4074–4080 (2018).
[Crossref]

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Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-Assisted Strong Field Enhancement in Individual All-Dielectric Nanostructures,” ACS Photonics 5(5), 1960–1966 (2018).
[Crossref]

Zhang, L.

X. B. W. Liu, X. Yao, L. Zhang, H. X. Lin, S. Chen, J. H. Zhong, and B. Ren, “Efficient Platform for Flexible Engineering of Superradiant, Fano-Type, and Subradiant Resonances,” ACS Photonics 2(12), 1725–1731 (2015).
[Crossref]

Zhang, X.

G. Sun, L. Yuan, Y. Zhang, X. Zhang, and Y. Zhu, “Q-factor enhancement of Fano resonance in all-dielectric metasurfaces by modulating metaatom interactions,” Sci. Rep. 7(1), 8128 (2017).
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Y. Zhang, W. Liu, Z. Li, Z. Li, H. Cheng, and S. Chen, “High-quality-factor multiple fano resonances for refractive index sensing,” Opt. Lett. 43(8), 1842 (2018).
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G. Sun, L. Yuan, Y. Zhang, X. Zhang, and Y. Zhu, “Q-factor enhancement of Fano resonance in all-dielectric metasurfaces by modulating metaatom interactions,” Sci. Rep. 7(1), 8128 (2017).
[Crossref]

Zhao, W.

W. Zhao, H. Jiang, B. Liu, Y. Jiang, C. Tang, and J. Li, “Fano resonance based optical modulator reaching 85% modulation depth,” Appl. Phys. Lett. 107(17), 171109 (2015).
[Crossref]

Zhao, X.

Y. Liu, Y. Luo, X. Jin, X. Zhou, K. Song, and X. Zhao, “High-Q Fano Resonances in Asymmetric and Symmetric All-Dielectric Metasurfaces,” Plasmonics 12(5), 1431–1438 (2017).
[Crossref]

Zhao, Y.

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]

N. Papasimakis, I. V. Fedotov, T. Kaelberer, D. P. Tsai, and N. I. Zheludev, “Toroidal Dipolar Response in a Metamaterial,” Science 330(6010), 1510–1512 (2010).
[Crossref]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[Crossref]

Zhong, J. H.

X. B. W. Liu, X. Yao, L. Zhang, H. X. Lin, S. Chen, J. H. Zhong, and B. Ren, “Efficient Platform for Flexible Engineering of Superradiant, Fano-Type, and Subradiant Resonances,” ACS Photonics 2(12), 1725–1731 (2015).
[Crossref]

Zhou, C.

C. Cui, C. Zhou, S. Yuan, X. Qiu, L. Zhu, Y. Wang, and J. Xia, “Multiple Fano Resonances in Symmetry-Breaking Silicon Metasurface for Manipulating Light Emission,” ACS Photonics 5(10), 4074–4080 (2018).
[Crossref]

Zhou, X.

Y. Liu, Y. Luo, X. Jin, X. Zhou, K. Song, and X. Zhao, “High-Q Fano Resonances in Asymmetric and Symmetric All-Dielectric Metasurfaces,” Plasmonics 12(5), 1431–1438 (2017).
[Crossref]

Zhu, L.

C. Cui, C. Zhou, S. Yuan, X. Qiu, L. Zhu, Y. Wang, and J. Xia, “Multiple Fano Resonances in Symmetry-Breaking Silicon Metasurface for Manipulating Light Emission,” ACS Photonics 5(10), 4074–4080 (2018).
[Crossref]

Zhu, Y.

G. Sun, L. Yuan, Y. Zhang, X. Zhang, and Y. Zhu, “Q-factor enhancement of Fano resonance in all-dielectric metasurfaces by modulating metaatom interactions,” Sci. Rep. 7(1), 8128 (2017).
[Crossref]

ACS Nano (1)

S. D. Liu, J. Deng, and J. H. Teng, “Polarization-Independent Multiple Fano Resonances in Plasmonic Nonamers for Multimode-Matching Enhanced Multiband Second-Harmonic Generation,” ACS Nano 10(1), 1442–1453 (2016).
[Crossref]

ACS Photonics (6)

S. Campione, S. Liu, L. I. Basilio, L. K. Warne, W. L. Langston, and T. S. Luk, “Broken symmetry dielectric resonators for high quality-factor fano metasurfaces,” ACS Photonics 3(12), 2362–2367 (2016).
[Crossref]

Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-Assisted Strong Field Enhancement in Individual All-Dielectric Nanostructures,” ACS Photonics 5(5), 1960–1966 (2018).
[Crossref]

X. B. W. Liu, X. Yao, L. Zhang, H. X. Lin, S. Chen, J. H. Zhong, and B. Ren, “Efficient Platform for Flexible Engineering of Superradiant, Fano-Type, and Subradiant Resonances,” ACS Photonics 2(12), 1725–1731 (2015).
[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]

C. Cui, C. Zhou, S. Yuan, X. Qiu, L. Zhu, Y. Wang, and J. Xia, “Multiple Fano Resonances in Symmetry-Breaking Silicon Metasurface for Manipulating Light Emission,” ACS Photonics 5(10), 4074–4080 (2018).
[Crossref]

T. Shibanuma, T. Matsui, T. Roschuk, J. Wojcik, P. Mascher, and P. Albella, “Experimental demonstration of tunable directional scattering of visible light from all-dielectric asymmetric dimers,” ACS Photonics 4(3), 489–494 (2017).
[Crossref]

Adv. Mater. (1)

M. Gupta, Y. K. Srivastava, and R. Singh, “A Toroidal Metamaterial Switch,” Adv. Mater. 30(4), 1704845 (2018).
[Crossref]

Adv. Photonics (1)

A. A. Bogdanov, K. L. Koshelev, P. V. Kapitanova, M. V. Rybin, S. A. Gladyshev, and Z. F. Sadrieva, “Bound states in the continuum and fano resonances in the strong mode coupling regime,” Adv. Photonics 1(01), 1 (2019).
[Crossref]

Appl. Phys. Lett. (4)

M. Gupta, Y. K. Srivastava, M. Manjappa, and R. Singh, “Sensing with toroidal metamaterial,” Appl. Phys. Lett. 110(12), 121108 (2017).
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Y. Moritake, Y. Kanamori, and K. Hane, “Enhanced quality factor of fano resonance in optical metamaterials by manipulating configuration of unit cells,” Appl. Phys. Lett. 107(21), 211108 (2015).
[Crossref]

W. Zhao, H. Jiang, B. Liu, Y. Jiang, C. Tang, and J. Li, “Fano resonance based optical modulator reaching 85% modulation depth,” Appl. Phys. Lett. 107(17), 171109 (2015).
[Crossref]

T. Shibanuma, S. A. Maier, and P. Albella, “Polarization control of high transmission/reflection switching by all-dielectric metasurfaces,” Appl. Phys. Lett. 112(6), 063103 (2018).
[Crossref]

Appl. Sci. (1)

C. S. Sui, X. J. Li, T. T. Lang, X. F. Jing, and Z. Hong, “High Q-Factor Resonance in a Symmetric Array of All-Dielectric Bars,” Appl. Sci. 8(2), 161 (2018).
[Crossref]

J. Phys. Chem. C (2)

D. J. Cai, Y. H. Huang, W. J. Wang, W. B. Ji, Z. H. Chen, and S. D. Liu, “Fano Resonances Generated in a Single Dielectric Homogeneous Nanoparticle with High Structural Symmetry,” J. Phys. Chem. C 119(8), 4252–4260 (2015).
[Crossref]

J. Qi, Y. Xiang, W. Yan, M. Li, and Z. Chen, “The excitation of the tunable longitudinal higher-order multipole SPR modes by strong coupling in large-area metal sub-10nm-gap array structures and its application,” J. Phys. Chem. C 120(43), 24932–24940 (2016).
[Crossref]

Nanophotonics (2)

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]

K. Koshelev, G. Favraud, A. Bogdanov, Y. Kivshar, and A. Fratalocchi, “Nonradiating photonics with resonant dielectric nanostructures,” Nanophotonics 8(5), 725–745 (2019).
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Nat. Commun. (2)

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, and A. I. Kuznetsov, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref]

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
[Crossref]

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).
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B. Luk’Yanchuk, P. Nordlander, and H. Giessen, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
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Nat. Nanotechnol. (1)

S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11(1), 23–36 (2016).
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Nat. Photonics (1)

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
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Opt. Express (2)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

A. Ahmadivand and N. Pala, “Multiple coil-type fano resonances in all-dielectric antisymmetric quadrumers,” Opt. Quantum Electron. 47(7), 2055–2064 (2015).
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Phys. Rev. Appl. (1)

A. S. Kupriianov, Y. Xu, A. Sayanskiy, V. Dmitriev, Y. S. Kivshar, and V. R. Tuz, “Metasurface engineering through bound states in the continuum,” Phys. Rev. Appl. 12(1), 014024 (2019).
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Phys. Rev. B (1)

S. Q. Li and K. B. Crozier, “Origin of the anapole condition as revealed by a simple expansion beyond the toroidal multipole,” Phys. Rev. B 97(24), 245423 (2018).
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Phys. Rev. Lett. (3)

D. Finkelsteinshapiro, I. Urdaneta, M. Calatayud, O. Atabek, V. Mujica, and A. Keller, “Fano-Liouville Spectral Signatures in Open Quantum Systems,” Phys. Rev. Lett. 115(11), 113006 (2015).
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K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric Metasurfaces with High- Q Resonances Governed by Bound States in the Continuum,” Phys. Rev. Lett. 121(19), 193903 (2018).
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Plasmonics (1)

Y. Liu, Y. Luo, X. Jin, X. Zhou, K. Song, and X. Zhao, “High-Q Fano Resonances in Asymmetric and Symmetric All-Dielectric Metasurfaces,” Plasmonics 12(5), 1431–1438 (2017).
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Z. Liu, W. Li, J. Li, and C. Gu, “Fano resonance rabi splitting of surface plasmons,” Sci. Rep. 7(1), 8010 (2017).
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S. Bakhti, N. Bonod, S. D. Dhuey, P. J. Schuck, and N. Destouches, “Fano-like resonance emerging from magnetic and electric plasmon mode coupling in small arrays of gold particles,” Sci. Rep. 6(1), 32061 (2016).
[Crossref]

G. Sun, L. Yuan, Y. Zhang, X. Zhang, and Y. Zhu, “Q-factor enhancement of Fano resonance in all-dielectric metasurfaces by modulating metaatom interactions,” Sci. Rep. 7(1), 8128 (2017).
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I. V. Stenishchev and A. A. Basharin, “Toroidal response in all-dielectric metamaterials based on water,” Sci. Rep. 7(1), 9468 (2017).
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A. K. Ospanova, L. Matekovits, and A. A. Basharin, “Multipolar passive cloaking by nonradiating anapole excitation,” Sci. Rep. 8(1), 12514 (2018).
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Science (1)

N. Papasimakis, I. V. Fedotov, T. Kaelberer, D. P. Tsai, and N. I. Zheludev, “Toroidal Dipolar Response in a Metamaterial,” Science 330(6010), 1510–1512 (2010).
[Crossref]

Sens. Actuators, B (1)

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators, B 54(1–2), 3–15 (1999).
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Z. Sadrieva, K. Frizyuk, M. Petrov, Y. Kivshar, and A. Bogdanov, “Multipolar origin of bound states in the continuum”, arXiv:1903.00309 (2019)

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematics of the unit cell for asymmetric paired silicon nanorods placed on the silica substrate. (b) Side view and geometric parameters of a unit cell.
Fig. 2.
Fig. 2. (a) Transmission spectrum of the symmetric array (δ = 0 nm). The inset represents the fitted spectrum near the resonances. (b) The radiating powers of various multipole moments. (c) Comparison results of transmission spectra between symmetric and asymmetric arrays. (d) Q factors for different δ.
Fig. 3.
Fig. 3. (a) Normalized magnetic field amplitudes |H/H0| in the middle xy plane of the unit cell at characteristic wavelengths. The white arrows at 1222.3 nm and 1293.5 nm (1312.4 nm, 1378.7 nm and 1406.9 nm) indicate the magnetic (electric) field directions. (b) The z-component of H-field intensity at 1222.3 nm, 1312.4 nm, 1378.7 nm and 1406.9 nm, the z-component of E-field intensity at 1293.5 nm. The black and white arrows show the magnetic field directions.
Fig. 4.
Fig. 4. Transmission spectra at different parameters. (a)Period p, (b) side a, (c) Gap g and (d) Asymmetric parameter δ. Other parameters are the same as that used in Fig. 2(c).
Fig. 5.
Fig. 5. Wavelength shifts as a function of the refractive index of the background. The geometry parameters of the array are the same as that used in Fig. 2(c).

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