Open Access
Add to BibSonomy
Abstract
Bound states in the continuum (BICs) have become a new trend in the area of metaoptics and nanophotonics. Strong interactions in electromagnetic fields are analogous to electron transitions in atoms, giving rise to BICs with vanishing radiative losses. However, it is still a great challenge to realize BICs in the lossy plasmonic systems. For this problem, we propose a supercavity-like plasmonic nanocavity consisting of an Au nanorod deposited inside an Au symmetric split ring, and explore the possibility of exciting quasi-BICs that own finite but high quality (Q) factors. In such hybrid configuration, the excited resonances can be easily engineered by modifying the rotation angle or the length of the Au nanorod. With the integration of such nanocavity in silicon (Si) waveguides, sharp transmission spectra could be achieved with fiber-chip in-parallel excitations and detections. Besides, the ultracompact geometry of this plasmonic nanocavity provides a route to boost enhanced electric fields, thus improving sensing performances significantly. Our study not only offers a novel platform for the realization of chip-scale quasi-BICs, but extends functionalities of photonic-plasmonic hybrid circuits.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
It is possible to break the diffraction limit and enhance the light-matter interaction in optical systems by providing deep-subwavelength light confinement via the excitations of localized surface plasmons (LSPs) [1]. These properties, that are unattainable in nature, lead to various applications ranging from physical to biomedical sciences [2–6]. Especially for biological and chemical sensing, LSPs could offer label-free, ultra-fine and real-time spectroscopies [7–9], which are highly required for security checks, environment monitors, and medical diagnostics. Although plasmomic resonances are featured with small mode volumes, their Q factors are very small due to high intrinsic losses, setting great limitations for their further developments.
Recent achievements of optical BICs in supercavities have attained great attentions [10–14]. In a BIC system, the vanishing coupling between the optical modes and the surrounding radiation channels can be employed to engineer the scattering spectra [15–18]. This coupling degrades when the spatial symmetry of the resonant mode is incompatible with that of the radiating mode. Theoretically, true BICs only exist in lossless and nanophotonic systems of infinite size or in materials with infinite/zero permittivity, giving rise to infinite Q factors [15]. In most cases, BICs transform into quasi-BICs with finite Q factors, which have been demonstrated in various subwavelength dielectric optical systems [19–27].
The route to achieving sharp plasmonic resonances lies in the strong inter-coupling of metallic components. This process is similar to the hybridization between Mie and Fabry-Perot (F-P) photonic resonances in the supercavity [10]. The structural symmetry breaking or dimensional change could be used to manipulate resonances, enabling the excitation of quasi-BICs [28–31]. Compared with optical quasi-BICs, plasmonic ones are characterized as surface lattice resonances with out-of-plane dipoles and few radiations. So far, plasmonic quasi-BICs have been experimentally observed in the terahertz wavelength range [32]. At shorter wavelengths, metal-induced losses increase significantly, posing a huge difficulty in the realization of quasi-BICs. Nevertheless, it is feasible to reduce mode losses by applying hybrid configurations based on the combination of metal and dielectric materials, which is helpful to achieve high-Q plasmonic quasi-BICs [33–37].
Another intriguing feature for plasmonic quasi-BICs is the convenience in chip-scale integration. Through employing photonic-plasmonic hybrid interconnections [38–43], the plasmonic nanostructures can be driven via low-loss dielectric waveguides, paving the way for their applications in photonic integrated circuits (PICs). In particular, the combination of plasmonic components and dielectric waveguides on an silicon-on-insulator (SOI) substrate brings enormous advantages for fiber-chip package and test [44], which is beneficial for many portable usages such as sensing and communications.
In this paper, we propose a novel plasmonic nanocavity that could support quasi-BICs at telecom wavelengths in Si waveguides. The proposed plasmonic nanocavity is composed of an Au nanorod deposited inside an Au symmetric split ring. We demonstrate that the strong interplay between the nanorod and the split ring contributes to enhanced electric fields and Rabi splitting. We show that the radiation losses can be optimized by modifying the rotation angle or the length of the nanorod. By this way, we can control the hybridization of plasmonic modes so as to alter transmission spectral lineshapes of this photonic-plasmonic hybrid circuit and obtain quasi-BICs. Based on fiber-chip end-butt coupling, sharp resonant peaks can be detected in the transmission spectra, exhibiting obvious shifts with the refractive index (RI) change of the surrounding mediums. In experiment, such device provides a high sensitivity (S) of nearly 1090 nm/RIU and a large figure of merit (FOM) of around 60. This work opens up a new avenue for plasmonic nanostructures in nonlinear photonics, quantum optics, photonics integration, and optical communications.
2. Results and discussion
The proposed plasmonic nanocavity consists of an Au symmetric split ring and an Au nanorod with certain rotation angle (θ) and length (L), as shown in Fig. 1(a). It can be characterized by a subwavelength meta-atom sitting on a silica (SiO2) layer. From Fig. 1(b), the widths (w) of both the nanorod and the split ring are 200 nm, which could help to prevent mode leakages at near-IR wavelengths. The outer and inner radii of the split ring are 0.8 um and 0.6 um, respectively. The gap (g) for the split ring is 100 nm. And the thickness of the nanocavity is 200 nm. High-Q plasmonic quasi-BICs could be realized in some systems with customized structural design such as anisotropic nanostructures [45]. In this work, the deposition of the nanorod into the split ring creates several degrees of freedom (DoFs) related to structural asymmetry degrees and geometrical dimensions. As illustrated in Fig. 1(c), this nanocavity can be described by the Jaynes-Cummings (J-C) two-state model. Under the excitation of transverse electric (TE)-polarized light, high symmetry in geometry of either the split ring or the nanorod leads to degenerate electric and magnetic dipoles or high-order multipoles. There is a strong interplay between the nanorod (i.e.,$|R \rangle$) and the split ring (i.e.,$|S \rangle$), leading to hybrid polariton states and Rabi splitting $\hbar {\varOmega _r}$. This condition is also known as the strong-coupling regime [46], where the coupling constant between $|R \rangle$ and $|S \rangle$ is much larger than their damping rates. Additionally, there is a large amount of space inside our nanocavity left for the filling of low-loss dielectric materials such as liquids, which is suitable for RI sensing.
Fig. 1. (a) 3D Schematic of the plasmonic nanocavity. (b) Top view of the nanocavity. (c) Schematic illustration of the strong interplay between the split ring and the nanorod, leading to hybrid polariton states separated by the Rabi splitting.
Figures 2(a) and 2(b) show the simulated eigenfrequencies, radiation losses and Q factors for the proposed nanocavity as a function of θ and L, respectively. We take advantage of the finite difference time domain (FDTD) method and the scattering boundary conditions to do the simulations. In a lossy plasmonic system, the total Q factor can be expressed as 1/Qtot = 1/Qdis + 1/Qrad, where Qdis and Qrad are the dissipative and radiative Q factors, respectively [37]. The dissipative loss induced by the metal is one of the most influential factors limiting the improvements in Qtot, while the rate of Qrad is determined by the mode radiation. The radiative extinction can be estimated by the radiation loss which is calculated by 10 × log(Prad/Ptot), where Prad is the radiated power and Ptot is the total power [47]. The Qtot for the upper (or lower) state resonance rises greatly when θ approaches 33° (or 58°), where the quasi-BIC emerges. Besides, there is also a significant increase in Qtot for the upper (or lower) state resonance in the high structural symmetry point corresponding to 90° (or 0°). They are symmetry-protected quasi-BICs [48]. To study the L-induced strong coupling effects, we set θ to be 50°. As L varies from 0.42 um to 0, Qtot for the lower state resonance decreases to 23, while Qtot for the upper state resonance tends to 140. This indicates that the decrease in L contributes to the weak coupling between the nanorod and the split ring, reducing the dissipation loss and thus increasing the Qdis. Here, the split ring strongly interact with the nanorod near the avoided crossing area in the vicinity of 0.58 um for L. And a significant increase in Qtot for the upper state resonance is verified with L approaching 0.58 um.
Fig. 2. Eigenfrequencies, radiation losses and Q factors for the upper and the lower state resonances vs (a) L and (b) θ, respectively.
The electric field distributions for the upper state resonances are shown in Figs. 3(a) and 3(b), respectively. In an open non-Hermitian system, a small variation in the structural parameter could act as a systematic perturbation δ [49]. For our study, θ and L are responsible for δ. If there is no nanorod, the excited plasmonic modes are confined inside the split ring, forming standing waves. If there is no split ring, the excited plasmonic modes are bounded by the nanorod, which is analogous to Mie resonances. With the combination of them, there is a strong coupling between the split ring and the nanorod, generating hybrid resonances. As we can see, the quasi-BIC modes with high Q factors totally locate within the nanocavity without any couplings to the gaps of the split ring. Their Qtot are mainly decided by dissipation losses, i.e., Qdis. For low-Q eigenmodes, their electric fields are more or less coupled to the gaps of the split ring, manifested themselves as the leaky modes with large radiation losses. Through varying θ and L, we can manipulate Qrad. However, θ and L affect the properties of excited resonances in different ways. L is mainly related with the coupling constant between the split ring and the nanorod. The quasi-BIC mode for L = 0.58 um originates from the hybridization between Mie-like and standing wave-like plasmonic modes. Even a small L could influence the geometrical symmetry in nanocavity, generating a symmetry-protected quasi-BIC at 0.18 um. Due to symmetry protection, quasi-BICs can also be excited in the upper state for θ = 90° and in the lower state for θ = 0°, respectively. In addition, θ plays a dominant role in mode orientations, deciding the field coupling to the gap of the split ring. With θ approaching 33°, the mode leakage is eliminated, resulting in negligible radiations.
Fig. 3. The simulated electric field distributions of the upper state resonant modes for different (a) L and (b) θ of the nanorod in the nanocavity from far field excitations (red fonts indicate quasi-BICs and black fonts indicate non-quasi-BICs).
As shown in Fig. 4(a), the plasmonic nanocavity is integrated with 300 × 200 nm2 (width × height) Si waveguides on an SOI substrate. The Au split ring can be directly excited by the in-plane TE field from the input Si waveguide. Because of the diffraction limit, the Au nanorod can only be indirectly excited through coupling with the Au split ring. In our system, the split ring and the nanorod are defined as the bright and the dark structures, respectively. The transition from $|S \rangle$ to the ground continuum state $|g \rangle$ is always accompanied by both radiative (e.g., photon emission) and nonradiative (e.g., absorption) processes, while $|R \rangle$ decays to $|g \rangle$ is mainly subjected to nonradiative process [50]. Thus, the dark structure (i.e., the nanorod) easily induces higher intrinsic losses. The radiation of the plasmonic nanocavity can be captured by the output Si waveguide via near-field coupling, creating chances to obtain quasi-BIC signals. On the other hand, the constructive (or destructive) interference between two paths, that is $|g \rangle$ to $|S \rangle$ and $|g \rangle$ to $|S \rangle$ to $|R \rangle$ to $|S \rangle$, contributes to nonlinear Fano resonances with high (or low) transmittances. Similar to the spin-flip process in biexciton systems [51], the inter-coupling between $|S \rangle$ and $|R \rangle$ can induce an optical phase shift ranging from 0 to π.
Fig. 4. (a) Schematic diagrams of the plasmonic nanocavity integrated with Si waveguides on an SOI substrate: the 3D view (top), front view (middle), and SEM overview (bottom). (b) Schematic illustrations of the proposed device for RI sensing. The liquids with various RIs are dropped onto the chip as cladding layers for test.
In order to verify the influence of θ and L on this photonic-plasmonic hybrid configuration, Fano characteristics are studied with numerical simulations. The maps of the normalized transmission spectra and the optical phases with different θ are shown in Figs. 5(a) and 5(b), respectively. To model the experimental conditions, the chip is considered to be immersed into the deionized (DI) water, of which RI is nearly 1.3154 in the near-IR region at room temperature [52]. As we know, leaky plasmonic resonant modes offer low Qtot due to their large radiation losses [53], inducing high transmittance in the waveguide in return [54]. In this photonic-plasmonic hybrid circuit, the quasi-BIC appears when the transmitted optical mode becomes almost dark. Here, Qtot is mainly decided by Qdis, and it can be estimated by λr/ΔλFWHM, where λr is the resonant wavelength and ΔλFWHM is the full width at half maximum. Besides, the transmission spectral lineshape is determined by the Fano asymmetry parameter q = -cotΔ, where Δ is the phase of the upper or lower state resonance [55]. In general, the optical phase changes significantly at the resonance for the weakly damped oscillator [46]. This causes an asymmetric Fano resonance spectrum with a sharp variation in amplitude between the peak and the neighboring dip. As depicted in Fig. 5(c), the transmission spectra with various θ show different spectral curves and resonant wavelengths. For further study, the simulated radiation losses, Q factors, and q are shown in Fig. 5(d), respectively. It reveals the strong correlation between the evolutions of q, Qtot, and radiation loss for the upper and the lower state resonances. We can see that q tends to infinity at θ = 28° for the upper state resonance. The corresponding transmission peak shows a narrow Lorentzian lineshape, with a small but nonzero peak amplitude. The modulation depth (|Ton-Toff|/Ton*100%) as large as 100% can be achieved in Lorentz spectral lineshapes with θ setting to be 23°, 28°, 41°, and 78°, respectively. Moreover, the quasi-BIC with a large Q factor of 135 emerges in the upper state at θ = 32°, where the near-field radiation of the nanocavity is also strongly suppressed so that the transmitted optical mode becomes almost dark. Quasi-BIC is always associated with the dark mode [49]. As depicted in Fig. 5(e), the excited upper state resonant mode is mostly bounded by the inner wall of the split ring for θ = 28°, while it partly couples to the nanorod for θ = 36°. Their radiation losses are smaller than −35 dB due to the high near-field coupling efficiency and the strong mode confinement. The quasi-BIC emerges at θ = 32° for the upper state resonance with the smallest radiation loss of −45 dB as well as the highest Q factor of 125. This is within the avoided crossing regime of the resonances, where the excited plasmonic modes strongly interact with each other.
Fig. 5. (a) Electric fields and (b) optical phases revealed in the transmission spectra vs θ. (c) Normalized transmission spectra simulated for θ ranging from 0° to 90° in step of 15°. (d) Evolutions of radiation loss, Q factor, and Fano asymmetry parameter q for the lower and the upper state resonances. (e) The magnetic field distributions of the upper state resonant modes for different θ.
We also simulated the maps of the transmitted electric field and the optical phase as a function of L. As depicted in Fig. 6(a), we can see two avoided resolved resonances with a splitting of nearly 12.5 meV, revealing the existence of strong coupling in our meta-atomic system. Moreover, a significant change of the optical phase is also observed in the wavelength range from 1470 nm to 1620 nm, as shown in Fig. 6(b). Since the coupling constant between the split ring and the nanorod is linked with L, the spectral lineshape could be modulated by modifying L. Figure 6(c) illustrates the transmission spectra simulated by varying L from 0.7 um to 1 um. It is found that two resonant peaks in the transmission spectra are well separated. This anti-crossing behavior contributes to the reversible exchange of energy back and forth between the upper and the lower states. At large detuning, the transmission peak related to the dark mode is significantly narrower and weaker than that originating from the bright mode. q tends to infinity for L = 0.83 um, which is accompanied with a large Q factor of 120. From Fig. 6(d), the quasi-BIC is excited in the upper state for L = 0.775 um, where the radiation loss is the lowest. Compared with the quasi-BIC for θ = 32° and L = 1 um, this one corresponds to a larger peak amplitude. For a supercavity-like resonant system, the peak amplitude of the transmitted mode is determined by the radiation. Once the radiation is totally eliminated, the quasi-BIC becomes the dark mode [49]. With further decreasing L, the radiative extinction degrades slightly but the Q factor grows significantly. As shown in Fig. 6(e), the near-field excitation of the nanocavity is suppressed and the interplay between the nanorod and the split ring becomes weaker for L = 0.75 um, contributing to a significant reduction in dissipative loss. The radiation loss is still greatly limited under this condition, leading to a significant improvement in Qtot of the system.
Fig. 6. (a) Electric fields and (b) optical phases detected by the output Si waveguide vs L. (c) Normalized transmission spectra simulated for L ranging from 0.7 um to 1 um in step of 0.05 um. (d) L-induced evolutions of radiation loss, Q factor, and Fano asymmetry parameter q for the lower and the upper state resonances. (e) The magnetic field distributions of the upper state resonant modes for different L.
The simulated color maps of the electric field and the optical phase for different RIs of the surrounding mediums are revealed in Figs. 7(a) and 7(b). The obvious shifts can be found in the peak positions for both the lower and the upper state resonances, which are ultra-sensitive and linear. This characteristic is crucial for fiber-based on-chip optical sensors. The sensitivities, which are always expressed by the resonant wavelength shift (Δλ) per RI-unit change (S = Δλ/Δn), are about 1000 nm/RIU. There are few differences in S between the upper and the lower state resonant modes. Figures 7(c) and 7(d) show the peak amplitude and the Q factor as a function of RI. It can be seen that the peak amplitude for the upper state resonance varies from 0.0021 to 0.0028 when RI increases from 1.25 to 1.4, while the corresponding Q factor keeps at around 75. For the lower state resonance, the peak amplitude rises with the increase of RI at the cost of a slight degradation in Q factor. Overall, RI-induced variations in Q factors and peak amplitudes for both resonances are very small, imposing few negative impacts on sensing characteristics. The ultra-sensitive properties of these resonant peaks provide an opportunity for the development of a high-performance on-chip RI sensor.
Fig. 7. Sensing characterizations of the plasmonic nanocavity in Si waveguides, with L = 1 um and θ = 50°. The output (a) electric field and (b) optical phase of this device vs RI. (c) The peak amplitudes and (d) the Q factors for the lower and the upper state resonances vs RI.
Most resonant-based RI sensors are characterized and evaluated by ΔλFWHM. Extrapolating to the FOM that is given by the ratio of S to ΔλFWHM, a comprehensive evaluation on the performance characteristics of an optical RI sensor is acquired. As discussed above, enhanced resonances with high FOMs can be achieved by optimizing θ and L in our device. Here, the high FOM is guaranteed by the large variation in transmittance within a small wavelength range, where the spectral curves drop from peak to valley sharply. Experimental verifications on the sensing performance of this device (see Fig. 8(a)) are further conducted. Different concentrations of ethanol and DI water mixtures (0% ∼ 15%) with known RI variations [56] are adopted to confirm S and detection limit (DL). The measured transmission spectra for a series of ethanol/DI water mixtures are presented in Fig. 8(c). It shows a clear redshift of the resonant peak with the increase of ethanol/DI concentration (i.e., the increase of RI). As depicted in Fig. 8(b), the linear fitting demonstrates an experimental S of 1090 nm/RIU (i.e., 0.84 nm/% for the ethanol/DI water mixture), which agrees well with the simulated S. All these data points can be accurately fitted by a straight line, exhibiting good linearity of the RI sensing response. And an averaged FOM is estimated to be 60, which is much better than the most appeared plasmonic sensors. Here, the slight discrepancy in performances (e.g., peak positions, FWHMs, etc) between the measured and the simulated data can be attributed to fabrication errors and measurement instabilities. From Figs. 8(d) and 8(e), it is found that the FOM is highly proportional to the Q factor. Through optimizing θ and L, we could utilize plasmonic quasi-BICs to achieve high FOM optical sensing.
Fig. 8. (a) The SEM schematic of the plasmonic nanocavity (L = 1 um and θ = 50°) integrated with Si waveguides. (b) The simulated (red dashed line) and experimental (black solid circle) spectral shifts of the resonant peak in response to different ethanol/DI water concentrations. (c) Measured (dots) as well as fitted (solid lines) normalized transmission spectra of such device under the conditions of 0%, 5%, 10%, and 15% ethanol and DI water mixtures. The calculated FOMs for the lower and the upper state resonances vs (d) θ and (e) L, respectively.
Asymmetric non-Lorentzian Fano spectral curves are beneficial for obtaining high DL in sensing. The limit of detection for a device can be defined as DL = 3
3. Experiments
An SOI substrate with a 200 nm-thick top Si layer and a 2 um-thick buried oxide (BOX) layer is selected as the integration platform. Si waveguides are patterned with e-beam lithography (EBL), which are dry etched by an inductively coupled plasma (ICP) system. The Si waveguide contains bus and taper parts with the same lengths of 50 um. For the taper part, the width is 100 nm in the tip, which increases linearly to 300 nm in the end. The nanocavity is fabricated by lift-off process.
During the measurement, we take advantage of inverse-taper spot-size convertors (SSCs) for the fiber-chip end-butt coupling. The SSCs have already been demonstrated with a high coupling efficiency between fiber and Si waveguide modes [58]. The secondary waveguide of SSCs is made of SU-8, which can be fabricated by one-time UV photolithography and development. The total fabrication flow is compatible with the nano-electro-mechanical system (NEMS) technologies, meeting the requirements for low-cost and reproducible mass production. There is no upper cladding so that liquids or gases could interact with the nanocavity directly.
The experimental setup for sensing tests has been illustrated in Fig. 4(b). A tunable continuous wave laser from the lightwave measurement system (Agilent 8164A) is firstly launched into a single mode fiber (SMF). Before coupling into the chip, the optical wave is modulated by a polarization controller (PC) so as to ensure only TE mode can be excited in the Si waveguide. Finally, the output signal is monitored by the lightwave measurement system again, reflecting in real-time transmission spectra. This setup is built on a 6-dimensional fiber-chip vibration-proof measurement platform.
4. Conclusion
In summary, we have proposed a novel plasmonic nanocavity integrated with Si waveguides on an SOI substrate. The excited resonant modes can be manipulated through varying the length or the rotation angle of the Au nanorod which is deposited inside an Au split ring. The engineered strong coupling between the nanorod and the split ring contributes to significant reductions in radiation losses, enabling the investigation of plasmonic quasi-BIC signals. With the introduction of Si waveguides, the plasmonic resonances can be excited and detected by the near field coupling. Moreover, this nanocavity allows for enhanced interaction between the plasmonic modes and the surrounding mediums, making this device suitable for ultra-sensitive RI sensing. In this study, we provide an effective method and a practical platform to combine BICs with plasmonics in chip-scale optical interconnections. And it is expected to exploit more properties of quasi-BICs in the area of communications, computing, and beyond.
Funding
National Key Research and Development Program of China (2018YFB1800905, 2018YFB2201903); National Natural Science Foundation of China (12004188, 62075097, 62075038); Beijing University of Posts and Telecommunications.
Acknowledgments
The authors appreciate the professional services offered by the Platforms of Characterization and Test and Nanofabrication Facility at Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences.
Disclosures
The authors declare no conflicts of interests.
Data availability
Data availability. Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef]
2. J. Yamamichi, T. Ojima, K. Yurugi, M. Iida, T. Imamura, E. Ashihara, S. Kimura, and T. Maekawa, ““Single-step, label-free quantification of antibody in human serum for clinical applications based on localized surface plasmon resonance,” Nanomedicine (N. Y., NY, U. S.) 7(6), 889–895 (2011). [CrossRef]
3. E. Petryayeva and U. J. Krull, “Localized surface plasmon resonance: Nanostructures, bioassays and biosensing-A review,” Anal. Chim. Acta 706(1), 8–24 (2011). [CrossRef]
4. N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014). [CrossRef]
5. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008). [CrossRef]
6. F. Yesilkoy, E. R. Arvelo, Y. Jahani, M. Liu, A. Tittl, V. Cevher, Y. S. Kivshar, and H. Altug, “Ultrasensitive hyperspectral imaging and biodetection enabled by dielectric metasurfaces,” Nat. Photonics 13(6), 390–396 (2019). [CrossRef]
7. P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy,” Annu. Rev. Anal. Chem. 1(1), 601–626 (2008). [CrossRef]
8. C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2012). [CrossRef]
9. K. A. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58(1), 267–297 (2007). [CrossRef]
10. 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]
11. C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499(7457), 188–191 (2013). [CrossRef]
12. E. N. Bulgakov and D. N. Maksimov, “Topological Bound States in the Continuum in Arrays of Dielectric Spheres,” Phys. Rev. Lett. 118(26), 267401 (2017). [CrossRef]
13. A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), aag2472 (2016). [CrossRef]
14. M. V. Rybin and Y. S. Kivshar, “Optical physics: Supercavity lasing,” Nature 541(7636), 164–165 (2017). [CrossRef]
15. 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]
16. 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]
17. A. Kodigala, T. Lepetit, Q. Gu, B. Bahari, Y. Fainman, and B. Kanté, “Lasing action from photonic bound states in continuum,” Nature 541(7636), 196–199 (2017). [CrossRef]
18. 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]
19. K. L. Koshelev, G. Favraud, A. A. Bogdanov, Y. S. Kivshar, and A. Fratalocchi, “Nonradiating photonics with resonant dielectric nanostructures,” Nanophotonics 8(5), 725–745 (2019). [CrossRef]
20. J. Jin, X. Yin, L. Ni, M. Soljačić, B. Zhen, and C. Peng, “Topologically enabled ultrahigh-Q guided resonances robust to out-of-plane scattering,” Nature 574(7779), 501–504 (2019). [CrossRef]
21. V. Mylnikov, S. T. Ha, Z. Pan, V. Valuckas, R. Paniagua-Domínguez, H. V. Demir, and A. I. Kuznetsov, “Lasing Action in Single Subwavelength Particles Supporting Supercavity Modes,” ACS Nano 14(6), 7338–7346 (2020). [CrossRef]
22. K. L. Koshelev, S. Lepeshov, M. Liu, A. A. Bogdanov, and Y. S. Kivshar, “Asymmetric Metasurfaces with High- Q Resonances Governed by Bound States in the Continuum,” Phys. Rev. Lett. 121(19), 193903 (2018). [CrossRef]
23. K. L. Koshelev, Y. Tang, K. Li, D. Y. Choi, G. Li, and Y. S. Kivshar, “Nonlinear Metasurfaces Governed by Bound States in the Continuum,” ACS Photonics 6(7), 1639–1644 (2019). [CrossRef]
24. Z. Liu, Y. Xu, Y. Lin, J. Xiang, T. Feng, Q. Cao, J. Li, S. Lan, and J. Liu, “High- Q Quasibound States in the Continuum for Nonlinear Metasurfaces,” Phys. Rev. Lett. 123(25), 253901 (2019). [CrossRef]
25. S. Han, L. Cong, Y. K. Srivastava, B. Qiang, M. V. Rybin, A. Kumar, R. Jain, W. X. Lim, V. G. Achanta, S. S. Prabhu, Q. J. Wang, Y. S. Kivshar, and R. Singh, “All-Dielectric Active Terahertz Photonics Driven by Bound States in the Continuum,” Adv. Mater. 31(37), 1901921 (2019). [CrossRef]
26. L. Cong and R. Singh, “Symmetry-Protected Dual Bound States in the Continuum in Metamaterials,” Adv. Opt. Mater. 7(13), 1900383 (2019). [CrossRef]
27. L. Xu, K. Zangeneh Kamali, L. Huang, M. Rahmani, A. Smirnov, R. Camacho-Morales, Y. Ma, G. Zhang, M. Woolley, D. N. Neshev, and A. E. Miroshnichenko, “Dynamic Nonlinear Image Tuning through Magnetic Dipole Quasi-BIC Ultrathin Resonators,” Adv. Sci. 6(15), 1802119 (2019). [CrossRef]
28. G. Lin, H. Yang, Y. Deng, D. Wu, X. Zhou, Y. Wu, G. Cao, J. Chen, W. Sun, and R. Zhou, “Ultra-compact high-sensitivity plasmonic sensor based on Fano resonance with symmetry breaking ring cavity,” Opt. Express 27(23), 33359–33368 (2019). [CrossRef]
29. F. Hao, Y. Sonnefraud, P. Van Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: Subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett. 8(11), 3983–3988 (2008). [CrossRef]
30. S. Campione, S. Liu, L. I. Basilio, L. K. Warne, W. L. Langston, T. S. Luk, J. R. Wendt, J. L. Reno, G. A. Keeler, I. Brener, and M. B. Sinclair, “Broken Symmetry Dielectric Resonators for High Quality Factor Fano Metasurfaces,” ACS Photonics 3(12), 2362–2367 (2016). [CrossRef]
31. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007). [CrossRef]
32. D. R. Abujetas, N. van Hoof, S. ter Huurne, J. Gómez Rivas, and J. A. Sánchez-Gil, “Spectral and temporal evidence of robust photonic bound states in the continuum on terahertz metasurfaces,” Optica 6(8), 996–1001 (2019). [CrossRef]
33. I. C. Seo, S. Kim, B. H. Woo, I. S. Chung, and Y. C. Jun, “Fourier-plane investigation of plasmonic bound states in the continuum and molecular emission coupling,” Nanophotonics 9(15), 4565–4577 (2020). [CrossRef]
34. M. Meudt, C. Bogiadzi, K. Wrobel, and P. Görrn, “Hybrid Photonic–Plasmonic Bound States in Continuum for Enhanced Light Manipulation,” Adv. Opt. Mater. 8(20), 2000898 (2020). [CrossRef]
35. S. I. Azzam, V. M. Shalaev, A. Boltasseva, and A. V. Kildishev, “Formation of Bound States in the Continuum in Hybrid Plasmonic-Photonic Systems,” Phys. Rev. Lett. 121(25), 253901 (2018). [CrossRef]
36. J. Xiang, Y. Xu, J. D. Chen, and S. Lan, “Tailoring the spatial localization of bound state in the continuum in plasmonic-dielectric hybrid system,” Nanophotonics 9(1), 133–142 (2020). [CrossRef]
37. Y. Liang, K. L. Koshelev, F. Zhang, H. Lin, S. Lin, J. Wu, B. Jia, and Y. S. Kivshar, “Bound States in the Continuum in Anisotropic Plasmonic Metasurfaces,” Nano Lett. 20(9), 6351–6356 (2020). [CrossRef]
38. M. Chamanzar, Z. Xia, S. Yegnanarayanan, and A. Adibi, “Hybrid integrated plasmonic-photonic waveguides for on-chip localized surface plasmon resonance (LSPR) sensing and spectroscopy,” Opt. Express 21(26), 32086–32098 (2013). [CrossRef]
39. C. Chen, D. A. Mohr, H. K. Choi, D. Yoo, M. Li, and S. H. Oh, “Waveguide-Integrated Compact Plasmonic Resonators for On-Chip Mid-Infrared Laser Spectroscopy,” Nano Lett. 18(12), 7601–7608 (2018). [CrossRef]
40. F. Bernal Arango, A. Kwadrin, and A. F. Koenderink, “Plasmonic antennas hybridized with dielectric waveguides,” ACS Nano 6(11), 10156–10167 (2012). [CrossRef]
41. M. Février, P. Gogol, A. Aassime, R. Mégy, C. Delacour, A. Chelnokov, A. Apuzzo, S. Blaize, J. M. Lourtioz, and B. Dagens, “Giant coupling effect between metal nanoparticle chain and optical waveguide,” Nano Lett. 12(2), 1032–1037 (2012). [CrossRef]
42. J. Cuadra, R. Verre, M. Wersäll, C. Krückel, V. Torres-Company, T. J. Antosiewicz, and T. Shegai, “Hybrid dielectric waveguide spectroscopy of individual plasmonic nanoparticles,” AIP Adv. 7(7), 075207 (2017). [CrossRef]
43. A. Espinosa-Soria, A. Griol, and A. Martínez, “Experimental measurement of plasmonic nanostructures embedded in silicon waveguide gaps,” Opt. Express 24(9), 9592–9601 (2016). [CrossRef]
44. L. Carroll, J. S. Lee, C. Scarcella, K. Gradkowski, M. Duperron, H. Lu, Y. Zhao, C. Eason, P. Morrissey, M. Rensing, S. Collins, H. Y. Hwang, and P. O’Brien, “Photonic packaging: Transforming silicon photonic integrated circuits into photonic devices,” Appl. Sci. 6(12), 426 (2016). [CrossRef]
45. K. L. Koshelev, A. A. Bogdanov, and Y. S. Kivshar, “Meta-optics and bound states in the continuum,” Sci. Bull. 64(12), 836–842 (2019). [CrossRef]
46. 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]
47. R. Baets and P. E. Lagasse, “Calculation of radiation loss in integrated-optic tapers and Y-junctions,” Appl. Opt. 21(11), 1972–1978 (1982). [CrossRef]
48. L. Ni, Z. Wang, C. Peng, and Z. Li, “Tunable optical bound states in the continuum beyond in-plane symmetry protection,” Phys. Rev. B 94(24), 245148 (2016). [CrossRef]
49. A. A. Bogdanov, K. L. Koshelev, P. V. Kapitanova, M. V. Rybin, S. A. Gladyshev, Z. F. Sadrieva, K. B. Samusev, Y. S. Kivshar, and M. F. Limonov, “Bound states in the continuum and Fano resonances in the strong mode coupling regime,” Adv. Photon. 1(01), 1 (2018). [CrossRef]
50. B. Luk’Yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef]
51. J. M. Smith, P. A. Dalgarno, R. J. Warburton, A. O. Govorov, K. Karrai, B. D. Gerardot, and P. M. Petroff, “Voltage control of the spin dynamics of an exciton in a semiconductor quantum dot,” Phys. Rev. Lett. 94(19), 197402 (2005). [CrossRef]
52. S. Kedenburg, M. Vieweg, T. Gissibl, and H. Giessen, “Linear refractive index and absorption measurements of nonlinear optical liquids in the visible and near-infrared spectral region,” Opt. Mater. Express 2(11), 1588–1611 (2012). [CrossRef]
53. T. Christopoulos, O. Tsilipakos, G. Sinatkas, and E. E. Kriezis, “On the calculation of the quality factor in contemporary photonic resonant structures,” Opt. Express 27(10), 14505–14522 (2019). [CrossRef]
54. R. J. Mailloux, “Radiation and Near-Field Coupling between Two Collinear Open-Ended Waveguides,” IEEE Trans. Antennas Propag. 17(1), 49–55 (1969). [CrossRef]
55. C. Ott, A. Kaldun, P. Raith, K. Meyer, M. Laux, J. Evers, C. H. Keitel, C. H. Greene, and T. Pfeifer, “Lorentz meets fano in spectral line shapes: A universal phase and its laser control,” Science 340(6133), 716–720 (2013). [CrossRef]
56. R. J. Jiménez Riobóo, M. Philipp, M. A. Ramos, and J. K. Krüger, “Concentration and temperature dependence of the refractive index of ethanol-water mixtures: Influence of intermolecular interactions,” Eur. Phys. J. E 30(1), 19–26 (2009). [CrossRef]
57. J. Wang, M. M. Sanchez, Y. Yin, R. Herzer, L. Ma, and O. G. Schmidt, “Silicon-Based Integrated Label-Free Optofluidic Biosensors: Latest Advances and Roadmap,” Adv. Mater. Technol. 5(6), 1901138 (2020). [CrossRef]
58. Y. Maegami, R. Takei, E. Omoda, T. Amano, M. Okano, M. Mori, T. Kamei, and Y. Sakakibara, “Spot-size converter with a SiO2 spacer layer between tapered Si and SiON waveguides for fiber-to-chip coupling,” Opt. Express 23(16), 21287–21295 (2015). [CrossRef]
