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Abstract
Optical microcavities are capable of confining light to a small volume, which could dramatically enhance the light-matter interactions and hence improve the performances of photonic devices. However, in the previous works on the emergent properties with photonic molecules composed of multiple plasmonic microcavities, the underlying physical mechanism is unresolved, thereby imposing an inevitable restriction on manipulating degenerate modes in microcavity with outstanding performance. Here, we demonstrate the mode-mode interaction mechanism in photonic molecules composed of degenerate-mode cavity and single-mode cavity through utilizing the coupled mode theory. Numerical and analytical results further elucidate that the introduction of direct coupling between the degenerate-mode cavity and single-mode cavity can lift the mode degeneracy and give rise to the mode splitting, which contributes to single Fano resonance and dual EIT-like effects in the double-cavity photonic molecule structure. Four times the optical delay time compared to typical double-cavity photonic molecule are achieved after removing the mode degeneracy. Besides, with the preserved mode degeneracy, ultra-wide filtering bandwidth and high peak transmission is obtained in multiple-cavity photonic molecules. Our results provide a broad range of applications for ultra-compact and multifunction photonic devices in highly integrated optical circuits.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Molding the flow of light in nano-scale is one of the major pursuit in nanophotonics. Surface plasmon polaritons (SPPs), breaking the diffraction limit and allowing the deeply subwavelength confinement of light to even electron and molecule scale, have been long believed promising platforms for miniaturized on-chip photonic devices [1–5]. Among tremendous plasmonic architectures, optical microcavity coupled to metal-dielectric-metal (MDM) plasmonic waveguides is essential as it supports the mode within subwavelength volume, has zero bend losses and is easy to be fabricated [6–8]. One could further configure those microcavities, also known as artificial photonic molecules based on the close analog between the classical electromagnetics and quantum mechanics [9], to adjust the mode characteristics therein. With that, the resonance, dissipation, amplification and coupling of photonic molecules to plasmonic platforms can be easily engineered in an all-optical fashion [10–12], which has been of great interest for slow light, switch, sensing and many other applications [13–16].
To enable those high-performance photonic devices, it is critical to uncover the underlying mechanisms of interaction of plasmonic modes in artificial photonic molecules. For example, Fano resonance (FR) can be sustained in those photonic molecules, as a result of interference between a discrete state and a continuum state [17], which is instrumental for active optical switch [18], optical data storage [19], slow-light device [9], filter [20] and other applications. The electromagnetic-induced transparency (EIT) line shape could also evolve from the asymmetric Fano line shape [21–23]. In current state-of-the-art of theoretical analysis, the coupled oscillator model, transfer matrix method and coupled mode theory (CMT) have been widely exploited to elucidate the coupled systems [9,24–27]. Nevertheless, compared with those works that intensively study the simplest photonic molecules composed of single-mode cavities, multiple photonic molecules structure comprised of degenerate-mode cavity and single-mode cavity and related interaction physics behind are rarely involved. This in turn imposes a severe restriction on the multifunctional photonic devices applications.
In this paper, we demonstrate the dominating physics behind the interaction between degenerate mode and single mode in a plasmonic microcavity photonic molecule. Based on CMT, we propose a new theoretical model to identify the real physical parameters to manipulate and enhance the transmission characteristics. FR and dual EIT-like effects simultaneously occur in double-cavity system when the direct coupling is the main path, while there is only indirect coupling, the proposed multiple-cavity system can achieve higher transmission and wider bandwidth than double-cavity system, and its’ spectral responses are also different from traditional multiple-cavity system. Manipulating the mode degeneracy by control coupling distance enables the better optical features in double-cavity photonic molecule than that in multiple-cavity photonic molecule system. Our results open the way to novel on-chip optical buffers and many other multifunctional photonic devices.
2. Mode degeneracy preserved and broken
In atomic system, the electron cloud will overlap and hence results in energy level splitting as multiple atoms interact with each other [28]. This common phenomenon can also be realized in cavity photonic molecule systems. Degenerate modes in a cavity can be viewed as degenerate energy levels, which could split when perturbed by and directly coupled to other modes via, for example, evanescent field. In this case, mode degeneracy is broken, as shown in Fig. 1(a). In a contrast, the mode degeneracy preserves when degenerate-mode cavity couples to other cavities indirectly, as shown in Fig. 1(b). The physical illustration of mode degeneracy broken and preserved is shown in Figs. 1(c) and 1(d). Here, waveguide mode, single-mode cavity and degenerate-mode cavity represent ground state ($|1 \rangle$), non-degenerate state ($|2 \rangle$) and degenerate state ($|3 \rangle$). The degenerate state will split as degenerate-mode cavity directly couple with single-mode cavity (Fig. 1(c)), while the mode splitting is prevented when there are only indirect couplings (Fig. 1(d)). Therefore, based on the coupled mode theory (CMT), we could perform the theoretical study of interactions of degenerate-mode cavity and single-mode cavity, to better uncover the physics of spectral characteristics revealed in our structures. Assuming N modes in the whole system, the first cavity is the degenerate-mode cavity and it supports M modes (1<M < N), hence there are (N-M) single-mode cavities. Due to the orthogonality of degenerate resonant modes in a single cavity, the coupling coefficients between degenerate modes is zero. Thus, the theoretical model can be written as follows [24]
Fig. 1. Theoretical models and level diagrams of coupled microcavities. The schematics of interactions between optical modes correspond to the splitting (a) and no splitting (b) of degenerate modes in cavity. The level diagrams of microcavity photonic molecules with mode degeneracy broken (c) and preserved (d).
Here c represents the speed of light in vacuum, n0 is the effective refractive index, and ω is the frequency. d1 is the coupling distance between degenerate-mode cavity and the first single-mode cavity, and dq is the coupling distance between qth and (q+1)th single-mode cavity. When the light is only launched from the left port ($S_{ - ,{\rm{in}}}^{({\rm{N}} )} = 0$), the transmittance of the photonic molecule structure can be derived as
Obviously, once the values of N and M are confirmed, we can obtain the definite theoretical formula, thereby deriving the corresponding results of transmittance. Here, it is important to note that the removed mode degeneracy comes from the direct coupling in a mathematical form of non-zero values of coupling coefficients between different modes. However, the system with preserved mode degeneracy has zero-valued coupling coefficient (μ = 0), which fundamentally offers us the capability to configure the spectral characteristics in our system. The removal of mode degeneracy enables more degrees of freedom to create novel optical properties. In the following section, we will investigate the interactions between optical modes of double-cavity photonic molecule based on our theoretical analysis, which not only advances the understanding of mechanisms for spectral characteristics, but also serves as a guideline for enhancing the spectral responses and designing high-performance photonic devices.
3. Mode splitting and precise theoretical control
The photonic molecules interact with each other and create exciting optical properties, which provides impetus for integrated photonic devices. Our system is a double-cavity system, composed by two photonic molecules of one degenerate-mode cavity (nano-disk) and one single-mode cavity (rectangle), which couples to a plasmonic MDM bus waveguide as shown in Fig. 2(a). Based on the Drude model [29], the relative permittivity of sliver can be described by the relation εm = ε∞ – ωp2 / (ω2+jωγ) with ε∞ = 3.7, ωp = 9.1 eV, γ = 0.018 eV. The special spectral responses of photonic molecule are numerically simulated by the finite-difference time-domain method, in which the boundary conditions are set to be perfectly matched layers. In addition, other structural parameters are set as: w = w1 = w2 = 100 nm, L1 = 120 nm, L2 = 425 nm, and r = 200 nm. The SPPs will form on the metallic interfaces and is restricted in waveguide when TM polarized Gaussian beam is coupled into the bus waveguide. Figures 2(b)–2(d) display the transmission spectra of different individual photonic molecule structures, with the modal field distributions shown in insets. The red and blue line correspond to nano-disk cavity and rectangular cavity, respectively, which exhibit a symmetric Lorentzian line shape, while the green line corresponds to the double-cavity photonic molecule, which are composed by one Fano resonance and dual EIT-like resonance. Herein, the theoretical parameters can be extracted by the relationships Qa = λ/Δλ, 1/Qa = 1/Qw + 1/Qi and T = (Qw/ (Qi + Qw)) ^2, and Δλ is the full of half maximum (FHWM). According to Fig. 2(b) and 2(c), λ1=753.2 nm, λ2=751.2 nm, Δλ1=56 nm, Δλ2=56 nm, and T1=0.0005255, T2=0.0001802. Therefore, Qa1=13.45, Qi1=586.73, Qw1=13.77, and Qa2=5.78, Qi1=430.58, Qw1=5.86, all these parameters can be applied to the indirect coupling. Such complex spectra and splitting of the mode in double-cavity system results from the introduced direct coupling between two photonic molecules, that lift the mode degeneracy in the photonic molecules of cavity 1. The appearance of the coupled modes in our proposals reveals the promising opportunities and rich emerging properties in double-cavity photonic molecule system.
Fig. 2. Architecture and spectral responses. (a) The architecture schematic of double-cavity photonic molecule, comprised of degenerate-mode cavity (disk, cavity1) and single-mode cavity (rectangle, cavity2), w is the width of bus waveguide, w1 is the width of aperture, w2 is the width of the stub cavity, L1 is the length of gap, L2 is the stub depth, r is the radius of disk cavity, d1 is the coupling distance between adjacent cavity, the medium in waveguide and cavity is air (εd = 1.0), and the metal is chosen to be sliver. (b)-(d) The transmission spectra of different photonic molecules system. The insets depict the magnetic field distributions at the relevant resonant wavelength of degenerate-mode cavity and single-mode cavity.
To thoroughly exhibit the influences of mode degeneracy on spectral properties, we firstly study the case of double cavity on the same and opposite sides of bus waveguide, which render the splitting and absent splitting of degenerate modes, as illustrated in Figs. 3(a)-(h). The transmission spectra with different coupling distances of double cavities on the same side are shown in Figs. 3(b)-(d). Herein, the solid lines and circles denote numerical and theoretical results, respectively, which show an excellent consistence. For double-cavity photonic molecule, N=3, M=2, therefore, the transmittance of the photonic molecule structure can be derived as
Here,
Fig. 3. Spectral responses of mode degeneracy removed and preserved. (a) The schematic of double cavities on the same side of bus waveguide. (b)-(d) The transmission spectra of double-cavity photonic molecule, in Fig. 3(a), with direct coupling versus d1 = 255 nm, 260 nm and 265 nm, respectively. (e) The schematic of double cavities on the opposite side. (f)-(h) Transmission spectra of double-cavity photonic molecule, in Fig. 2(e), only with indirect coupling versus d1* = 255 nm, 260 nm and 265 nm, respectively. The inset depicts the transmission spectra versus coupling distance. The modified theoretical parameters are as follow: λ1=728∼740 nm, λ2=785∼815 nm, λ3 = 790∼846 nm, Qi1 = 130∼150, Qi2=200∼230, Qi3=210∼300, Qw1=80∼150, Qw2=3∼4, Qw3=250∼350, μ13=μ31=1*1013∼10*1013, μ23=μ32=5*1012∼7*1013.
In general, the N-cavity photonic molecule system has been typically identified to show N-1 Fano resonances [6,30,31], thus it is of particular interest that there are three peaks (P1, P2 and P3) and three dips (D1, D2 and D3) for our explored double-cavity structure. There is a critical coupling distance for the evolution of mode degeneracy when double cavities on the same side, and the critical coupling distance is 292 nm approximately. In contrast, we ingeniously construct the double cavities on the opposite side, as shown in Fig. 3(e), in which cases the direct coupling is absent. By disregarding the influence of direct coupling (μ = 0), the indirect coupling is the only coupling path and the degenerate-mode cavity acts as a single-mode cavity. Thus, the spectra of mode splitting with multiple Fano resonances features disappear, as reflected in Figs. 3(f)-(h). Nevertheless, to enrich our study, we show in the inset of Fig. 3(h) the transmission spectra of double-cavity photonic molecule with the coupling distance increasing from 270 nm to 295 nm, in which there is only one Fano resonance exhibiting a red shift as the coupling distance increases, which justifies the robustness of our method. To further investigate the mechanism and parameter sensitivity of the removal of mode degeneracy, it is critical to analyze the evolution of dip and peak versus different coupling distance. As shown in Fig. 4(a), increasing the coupling distance, D1 has a linear redshift, while D2 and D3 have a non-linear blueshift, similar to exponential line-shape. In the meanwhile, as plotted in Fig. 4(b), P1 presents linear redshift and P3 exhibits a non-linear blueshift as the coupling distance increases, while the position of P2 hardly changes. In order to distinguish the optical modes in the double-cavity photonic molecule more comprehensively, as shown in Figs. 4(c)-(e), we present the magnetic field distributions at the relevant wavelength of optical modes in Fig. 3(b). For D1, the optical modes in degenerate-mode cavity and single-mode cavity are in phase, while for D2, the optical modes in degenerate-mode cavity and single-mode cavity are out of phase. Comparing D3 with D1 and D2, the magnetic field distributions in the degenerate-mode cavity are significantly different. Moreover, D2 with broad bandwidth plays the role of quasi-continuum, while D1 and D3 with narrower bandwidth stand for discrete states. Figures 4(f) and 4(g) display the magnetic field distributions at the wavelengths of P2 and P3, which illustrate the distinctively different magnetic field distributions in the degenerate-mode cavity, arising from different coupling strength between the double cavities. For P2, the fields are only highly concentrated inside the degenerate-mode cavity, while the fields are both distributed in degenerate-mode cavity and the single-mode cavity for P3.
Fig. 4. Spectral Evolution and magnetic field distributions of peaks and dips. (a) The evolution of dip wavelength versus coupling distances. (b) The evolution of peak wavelength versus coupling distances. (c)-(g) Magnetic field distributions (Hz) at λ = 733.5 nm(D1), λ = 799.3 nm(D2), λ = 855.5 nm(D3), λ = 751.2 nm(P2) and λ = 839.5 nm(P3) in Fig. 2(b).
According to the Fig. 3 and Fig. 4, it is fundamentally important to reveal the formation mechanisms of spectral features and elucidate the influences of relevant system parameters. The high consistency between theoretical model and numerical simulations enables us to more accurately analyze the effects of each physical parameter and engineer the spectral characteristics. For direct coupling, the initial theoretical parameters of the mode need to be modified due to the strongly coupling between modes in different microcavities, and the corresponding parameters are listed at the illustration of Fig. 3. In the proposed theoretical model, the optical mode at ω2 indicates a new mode after removing the mode degeneracy of disk cavity in photonic molecule. The quality factors of each optical mode have great influences on the spectra. Qw1 primarily affects P1 and P2, and Qw2 shows important impacts on the P2 and P3, especially for P2, while Qw3 plays a vital role in modulating the intensity of P1. In addition, the coupling coefficients μ23 and μ32 play a key role in adjusting the intensity of P3, and μ13 and μ31 have a great influence on the intensity of P1. That is to say, the coupling coefficients could make significant differences on the transmission peaks. Combing the theoretical and numerical results, we can get that the P1 corresponding to the Fano resonance basically originates from indirect coupling between optical modes in degenerate-mode cavity and single-mode cavity, that P2 is attributed to the interactions of optical modes D1 and D2, and that P3 results from the interaction between optical modes D2 and D3 in photonic molecules. Therefore, the removal of mode degeneracy in degenerate-mode cavity results from the direct coupling between double cavities of photonic molecule, which opens the way for multifunctional optical devices with wide application prospects. Besides, the high consistency between theoretical model and simulation results provides a reliable basis for subsequent structural design and experimental implementation.
4. High transmission and wide bandwidth in multiple-cavity photonic molecules
To reveal the exciting opportunities of high-density integrated optics and miniaturization of nanodevices via mode engineering in complex photonic molecule system, we here further explore the multiple-cavity photonic molecule. Specifically, we study the spectra characteristics via increasing the number of the cavity from two (Fig. 5(a)) to three (Fig. 5(c)), four (Fig. 5(e)), five (Fig. 5(f)) and six (Fig. 5(g)) in photonic molecules. For double-cavity and three-cavity systems (N=4, M=2), as illustrated in Figs. 5(a) and 5(c), both the interesting results demonstrate only one Fano resonance in the spectra. Compared with double-cavity, triple-cavity photonic molecule introduces a single-mode cavity, of which the parameters are identical to the other single-mode cavity. Importantly, the transmittance of the Fano peak can reach 0.48 approximately, which is 30% higher than double-cavity photonic molecule system. The dynamics of the triple-cavity photonic molecule system can also be calculated by Eqs. (1)–(8), and the transmission ratio is given by
Here
To analyze more explicitly the transmission characteristics in double-cavity and triple-cavity photonic molecules, based on the Eqs. (9) and (10), we study the evolution of transmission spectra versus coupling distance and input wavelength λ, as illustrated in Figs. 5(b) and 5(d). Obviously, Fano line shape varies periodically as a function of coupling distance d1 and d3. For the double-cavity photonic molecule, the period and filtering bandwidth are approximately 310 nm and 60 nm respectively, while for the triple-cavity, the period and filtering bandwidth are approximately 300 nm and 120 nm, respectively, which presents a broad filtering bandwidth 100% broader than double-cavity photonic molecule structure. Besides, both two photonic molecules exhibit the linewidth vanishing at the certain coupling distance with high quality factors, which indicates that it is possible to realize narrow linewidths similar to the bound states in the continuum (BICs) in lossy system [32,33]. To further reveal the great promise brought by increasing the number of cavities, Figs. 5(e)–4(g) show the transmission spectra of four-cavity, five-cavity and six-cavity photonic molecules, respectively, where the coupling distance between two adjacent cavities are all 300 nm. It is apparent that the transmission ratio and the bandwidth can be further improved as the number of cavities increases, and a newly generated transmission peak exhibits in four-cavity photonic molecule system. Meanwhile, the intensity of Fano peak and a newly emerging transmission peak can be enhanced in the five-cavity photonic molecule structure, and another new transmission peak appears in the six-cavity photonic molecule. The results of previous sections have demonstrated that the first peak in the spectra is achieved by the disk cavity and the first rectangle cavity, while the magnetic field distributions in waveguide could be applied to provide credible insights into the produce of new peaks and the enhancement of peak intensity. It is obvious that a new peak appears when two resonant cavities are added. For the triple-cavity photonic molecule, the addition of a new rectangle cavity creates a resonance between the two rectangle cavities and hence increases the intensity of Fano peak (compared to Fig. 5(a)). For the four-cavity photonic molecule, as shown in Fig. 5(e), the new transmission peak is generated by the three rectangle cavities, which supports the symmetric mode in bus waveguide, while in Fig. 5(f), the four rectangle cavities form the new peak, which is marked by red arrow exhibit anti-symmetric mode distribution in bus waveguide. In addition, the inset in Fig. 5(g) explicitly illustrates that the resonant peak pointed by red arrow is strongly associated with the five rectangle cavities, which support the symmetric mode in the bus waveguide. Moreover, the magnetic field distributions, in Figs. 5(e)–5(g), definitely indicate that the enhancement of the optical performance of the system stems from the formation of the FP resonators between the rectangle cavities [34], and the constructed resonant design consisting of cascaded FP resonators produces new resonances [35]. Therefore, the proposed multiple-cavity photonic molecule structure can be designed as a feasible method to engineer the spectral line shape with high spectral contrast, small linewidth and preferable filtering performances.
Fig. 5. Spectral responses of multiple-cavity photonic molecules. (a) The transmission spectra of double-cavity photonic molecule system when d1 = 590 nm. (b) Evolution of the transmission spectrum versus d1 and λ for double-cavity photonic molecule. (c) The transmission spectrum of triple-cavity photonic molecule when d1* = 300 nm and d3 = 300 nm. (d) Evolution of the transmission spectra versus d3 and λ for triple-cavity photonic molecule. (e)-(f) The transmission spectra of four-cavity, five-cavity and six-cavity photonic molecules, respectively. The right and left insets are the magnetic field distributions of peak pointed by red arrows in transmission spectra and the corresponding schematics of structure diagram of cavity photonic molecules.
5. Enhancement for slow-light effect
Consistent with the spectral responses in atomic ensembles, the proposed plasmonic photonic molecule systems also sustain slow group velocities. Slowing down the light introduces the enhanced interaction between light and matter, which can evidently advance the performances of the nanoscale plasmonic structure. The slow-light effect can be described by the group index ng [30], which is defined as
Fig. 6. Slow light effects in photonic molecules systems. (a)-(c) The transmission phase shift for photonic molecules illustrated in Fig. 5(a) cavities with only indirect coupling, illustrated in Fig. 5(c) only with indirect coupling, and illustrated in Fig. 2(a) with direct coupling, respectively. (d)-(f) The corresponding optical delay time of three different photonic molecules, respectively.
6. Conclusion
We have investigated the physical mechanisms of mode-mode interaction in photonic molecule, composed of degenerate-mode cavity and single-mode cavity and elucidated the function of direct and indirect coupling in the microcavity photonic molecule structure. Utilizing the proposed theoretical model and subtly designed double-cavity photonic molecules, we can explicitly reveal the influences of physical parameters of system, and thus artificially engineer the spectral characteristics. The spectral performances enhancement in multi-cavity photonic molecules, such as transmission magnification, bandwidth expansion and delay extension, guides a categorical orientation for cavity photonic molecule on-chip. Meanwhile, the constructed photonic molecules consisting of cascaded FP resonators could enable diverse and exciting spectral responses. In particular, after removing the mode degeneracy, the optical delay time of double-cavity photonic molecule is increased by a factor of four, that indicates degenerate-mode cavity has an excellent potentiality in improving the optical performances of photonic molecules. These results could even be extended to other polaritonic systems [38–40], and may promote a great application prospect for ultra-compact optical buffers, ultra-wide bandwidth filters and multifunction optical switches in highly integrated optical circuits.
Funding
Natural Science Foundation of Hunan Province (2019JJ50481); Shanghai Municipal Science and Technology Major Project (2019SHZDZX01); Science and Technology Commission of Shanghai Municipality (18JC1420401, 20JC1416000); Education Department of Hunan Province (18B324); Shanghai Rising-Star Program (2019JJ50481); Strategic Priority Research Program of Chinese Academy of Sciences (XDB43010200); Key Research Project of Frontier Science of Chinese Academy of Sciences (QYZDJSSWJSC007); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2017285); National Natural Science Foundation of China (11564014, 11947017, 61705249, 61865006, 61874126, 61875218); National Key Research and Development Program of China (2017YFA0205800, 2018YFA0306200).
Disclosures
The authors declare no conflicts of interest.
References
1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef]
2. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]
3. G. Hu, A. Krasnok, Y. Mazor, C. W. Qiu, and A. Alu, “Moire Hyperbolic Metasurfaces,” Nano Lett. 20(5), 3217–3224 (2020). [CrossRef]
4. Y. Yang, L. Wu, Y. Liu, D. Xie, Z. Jin, J. Li, G. Hu, and C. W. Qiu, “Deuterogenic Plasmonic Vortices,” Nano Lett. 20(9), 6774–6779 (2020). [CrossRef]
5. S. Dong, Q. Zhang, G. Cao, J. Ni, T. Shi, S. Li, J. Duan, J. Wang, Y. Li, S. Sun, L. Zhou, G. Hu, and C.-W. Qiu, “On-chip trans-dimensional plasmonic router,” Nanophotonics 9(10), 3357–3365 (2020). [CrossRef]
6. G. Cao, H. Li, S. Zhan, H. Xu, Z. Liu, Z. He, and Y. Wang, “Formation and evolution mechanisms of plasmon-induced transparency in MDM waveguide with two stub resonators,” Opt. Express 21(8), 9198–9205 (2013). [CrossRef]
7. G. Cao, H. Li, Y. Deng, S. Zhan, Z. He, and B. Li, “Plasmon-induced transparency in a single multimode stub resonator,” Opt. Express 22(21), 25215–25223 (2014). [CrossRef]
8. J. Chen, F. Gan, Y. Wang, and G. Li, “Plasmonic Sensing and Modulation Based on Fano Resonances,” Adv. Opt. Mater. 6(9), 1701152 (2018). [CrossRef]
9. G. Cao, S. Dong, L. M. Zhou, Q. Zhang, Y. Deng, C. Wang, H. Zhang, Y. Chen, C. W. Qiu, and X. Liu, “Fano Resonance in Artificial Photonic Molecules,” Adv. Opt. Mater. 8(10), 1902153 (2020). [CrossRef]
10. D. Venkatakrishnarao, Y. S. L. V. Narayana, M. A. Mohaiddon, E. A. Mamonov, N. Mitetelo, I. A. Kolmychek, A. I. Maydykovskiy, V. B. Novikov, T. V. Murzina, and R. Chandrasekar, “Two-Photon Luminescence and Second-Harmonic Generation in Organic Nonlinear Surface Comprised of Self-Assembled Frustum Shaped Organic Microlasers,” Adv. Mater. 29(15), 1605260 (2017). [CrossRef]
11. T. Siegle, S. Schierle, S. Kraemmer, B. Richter, S. F. Wondimu, P. Schuch, C. Koos, and H. Kalt, “Photonic molecules with a tunable inter-cavity gap,” Light: Sci. Appl. 6(3), e16224 (2017). [CrossRef]
12. M. Zhang, C. Wang, Y. Hu, A. Shams-Ansari, T. Ren, S. Fan, and M. Lončar, “Electronically programmable photonic molecule,” Nat. Photonics 13(1), 36–40 (2019). [CrossRef]
13. S. Beaulieu, A. Comby, A. Clergerie, J. Caillat, D. Descamps, N. Dudovich, B. Fabre, R. Géneaux, F. Légaré, S. Petit, B. Pons, G. Porat, T. Ruchon, R. Taïeb, V. Blanchet, and Y. Mairesse, “Attosecond-resolved photoionization of chiral molecules,” Science 358(6368), 1288–1294 (2017). [CrossRef]
14. L. Chen, N. Xu, L. Singh, T. Cui, R. Singh, Y. Zhu, and W. Zhang, “Defect-Induced Fano Resonances in Corrugated Plasmonic Metamaterials,” Adv. Opt. Mater. 5(8), 1600960 (2017). [CrossRef]
15. N. H. Thakkar, M. T. Rea, K. C. Smith, K. D. Heylman, S. C. Quillin, K. A. Knapper, E. H. Horak, D. Masiello, and R. H. Goldsmith, “Sculpting Fano Resonances To Control Photonic-Plasmonic Hybridization,” Nano Lett. 17(11), 6927–6934 (2017). [CrossRef]
16. J. N. Liu, Q. Huang, K. K. Liu, S. Singamaneni, and B. T. Cunningham, “Nanoantenna-Microcavity Hybrids with Highly Cooperative Plasmonic-Photonic Coupling,” Nano Lett. 17(12), 7569–7577 (2017). [CrossRef]
17. M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11(9), 543–554 (2017). [CrossRef]
18. G. Dong, Y. Wang, and X. Zhang, “High-contrast and low-power all-optical switch using Fano resonance based on a silicon nanobeam cavity,” Opt. Lett. 43(24), 5977–5980 (2018). [CrossRef]
19. Y. Zheng, H. Liu, J. Li, J. Xiang, M. Panmai, Q. Dai, Y. Xu, S. Tie, and S. Lan, “Controllable Formation of Luminescent Carbon Quantum Dots Mediated by the Fano Resonances Formed in Oligomers of Gold Nanoparticles,” Adv. Mater. 31(30), 1901371 (2019). [CrossRef]
20. J. Xiang, J. Chen, S. Lan, and A. E. Miroshnichenko, “Nanoscale Optical Display and Sensing Based on the Modification of Fano Lineshape,” Adv. Opt. Mater. 8(16), 2000489 (2020). [CrossRef]
21. Y.-C. Liu, B.-B. Li, and Y.-F. Xiao, “Electromagnetically induced transparency in optical microcavities,” Nanophotonics 6(5), 789–811 (2017). [CrossRef]
22. G. Zhao, Ş. K. Özdemir, T. Wang, L. Xu, E. King, G.-L. Long, and L. Yang, “Raman lasing and Fano lineshapes in a packaged fiber-coupled whispering-gallery-mode microresonator,” Sci. Bull. 62(12), 875–878 (2017). [CrossRef]
23. R. Yahiaoui, M. Manjappa, Y. K. Srivastava, and R. Singh, “Active control and switching of broadband electromagnetically induced transparency in symmetric metadevices,” Appl. Phys. Lett. 111(2), 021101 (2017). [CrossRef]
24. S. Fan and W. Suh, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003). [CrossRef]
25. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010). [CrossRef]
26. C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, “Tailor the Functionalities of Metasurfaces Based on a Complete Phase Diagram,” Phys. Rev. Lett. 115(23), 235503 (2015). [CrossRef]
27. X. Liu, Z. Li, Z. Wen, M. Wu, J. Lu, X. Chen, X. Zhao, T. Wang, R. Ji, Y. Zhang, L. Sun, B. Zhang, H. Xu, J. Zhou, J. Hao, S. Wang, X. Chen, N. Dai, W. Lu, and X. Shen, “Large-area, lithography-free, narrow-band and highly directional thermal emitter,” Nanoscale 11(42), 19742–19750 (2019). [CrossRef]
28. M. Hussain, M. Rashid, F. Saeed, and A. S. Bhatti, “Spin–orbit coupling effect on energy level splitting and band structure inversion in CsPbBr3,” J. Mater. Sci. 56(1), 528–542 (2021). [CrossRef]
29. O. S. Heavens, “Handbook of Optical Constants of Solids II,” J. Mod. Opt. 39(1), 189 (1992). [CrossRef]
30. H. Lu, X. Liu, and D. Mao, “Plasmonic analog of electromagnetically induced transparency in multi-nanoresonator-coupled waveguide systems,” Phys. Rev. A 85(5), 053803 (2012). [CrossRef]
31. B. Wang, Q. Zeng, S. Xiao, C. Xu, L. Xiong, H. Lv, J. Du, and H. Yu, “Low-power, ultrafast, and dynamic all-optical tunable plasmon induced transparency in two stub resonators side-coupled with a plasmonic waveguide system,” J. Phys. D: Appl. Phys. 50(45), 455107 (2017). [CrossRef]
32. C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1(9), 16048 (2016). [CrossRef]
33. D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound States in the continuum in photonics,” Phys. Rev. Lett. 100(18), 183902 (2008). [CrossRef]
34. L. Gu, H. Fang, J. Li, L. Fang, S. J. Chua, J. Zhao, and X. Gan, “A compact structure for realizing Lorentzian, Fano, and electromagnetically induced transparency resonance lineshapes in a microring resonator,” Nanophotonics 8(5), 841–848 (2019). [CrossRef]
35. D. Zhao, L. Meng, H. Gong, X. Chen, Y. Chen, M. Yan, Q. Li, and M. Qiu, “Ultra-narrow-band light dissipation by a stack of lamellar silver and alumina,” Appl. Phys. Lett. 104(22), 221107 (2014). [CrossRef]
36. A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97(18), 181106 (2010). [CrossRef]
37. C. Yang, X. Jiang, Q. Hua, S. Hua, Y. Chen, J. Ma, and M. Xiao, “Realization of controllable photonic molecule based on three ultrahigh-Q microtoroid cavities,” Laser Photonics Rev. 11(2), 1600178 (2017). [CrossRef]
38. G. Hu, J. Shen, C. W. Qiu, A. Alù, and S. Dai, “Phonon Polaritons and Hyperbolic Response in van der Waals Materials,” Adv. Opt. Mater. 8(5), 1901393 (2020). [CrossRef]
39. G. Hu, Q. Ou, G. Si, Y. Wu, J. Wu, Z. Dai, A. Krasnok, Y. Mazor, Q. Zhang, Q. Bao, C. W. Qiu, and A. Alu, “Topological polaritons and photonic magic angles in twisted alpha-MoO3 bilayers,” Nature 582(7811), 209–213 (2020). [CrossRef]
40. Z. Dai, G. Hu, Q. Ou, L. Zhang, F. Xia, F. J. Garcia-Vidal, C. W. Qiu, and Q. Bao, “Artificial Metaphotonics Born Naturally in Two Dimensions,” Chem. Rev. 120(13), 6197–6246 (2020). [CrossRef]
