Hsu, C. W., Zhen, B., Stone, A. D., Joannopoulos, J. D. & Soljačić, M. Bound states in the continuum. Nat. Rev. Mater. 1, 16048. https://doi.org/10.1038/natrevmats.2016.48 (2016).
Koshelev, K., Bogdanov, A. & Kivshar, Y. Meta-optics and bound states in the continuum. Sci. Bull. 64, 836–842 (2019).
Koshelev, K., Favraud, G., Bogdanov, A., Kivshar, Y. & Fratalocchi, A. Nonradiating photonics with resonant dielectric nanostructures. Nanophotonics 8, 725–745. https://doi.org/10.1515/nanoph-2019-0024 (2019).
Joseph, S., Pandey, S., Sarkar, S. & Joseph, J. Bound states in the continuum in resonant nanostructures: An overview of engineered materials for tailored applications. Nanophotonics 10, 4175–4207 (2021).
Kang, M., Liu, T., Chan, C. T. & Xiao, M. Applications of bound states in the continuum in photonics. Nat. Rev. Phys. 5, 659–678. https://doi.org/10.1038/s42254-023-00642-8 (2023).
Zhang, M. & Zhang, X. Ultrasensitive optical absorption in graphene based on bound states in the continuum. Sci. Rep. 5, 1–6 (2015).
Wang, X. et al. Controlling light absorption of graphene at critical coupling through magnetic dipole quasi-bound states in the continuum resonance. Phys. Rev. B 102, 155432 (2020).
Sang, T., Dereshgi, S. A., Hadibrata, W., Tanriover, I. & Aydin, K. Highly efficient light absorption of monolayer graphene by quasi-bound state in the continuum. Nanomaterials 11, 484 (2021).
Xiao, S., Wang, X., Duan, J., Liu, T. & Yu, T. Engineering light absorption at critical coupling via bound states in the continuum. JOSA B 38, 1325–1330 (2021).
Cai, Y., Liu, X., Zhu, K., Wu, H. & Huang, Y. Enhancing light absorption of graphene with dual quasi bound states in the continuum resonances. J. Quant. Spectrosc. Radiat. Transf. 283, 108150 (2022).
Liu, Y., Zhou, W. & Sun, Y. Optical refractive index sensing based on high-Q bound states in the continuum in free-space coupled photonic crystal slabs. Sensors 17, 1861. https://doi.org/10.3390/s17081861 (2017).
Romano, S. et al. Label-free sensing of ultralow-weight molecules with all-dielectric metasurfaces supporting bound states in the continuum. Photonics Res. 6, 726. https://doi.org/10.1364/prj.6.000726 (2018).
Ndangali, F. R. & Shabanov, S. V. The resonant nonlinear scattering theory with bound states in the radiation continuum and the second harmonic generation. In Active Photonic Materials V, vol. 8808, 88081F (International Society for Optics and Photonics, 2013).
Wang, T. & Zhang, S. Large enhancement of second harmonic generation from transition-metal dichalcogenide monolayer on grating near bound states in the continuum. Opt. Express 26, 322–337 (2018).
Carletti, L., Koshelev, K., De Angelis, C. & Kivshar, Y. Giant nonlinear response at the nanoscale driven by bound states in the continuum. Phys. Rev. Lett. 121, 033903 (2018).
Koshelev, K. et al. Subwavelength dielectric resonators for nonlinear nanophotonics. Science 367, 288–292 (2020).
Kodigala, A. et al. Lasing action from photonic bound states in continuum. Nature 541, 196–199. https://doi.org/10.1038/nature20799 (2017).
Hwang, M.-S. et al. Ultralow-threshold laser using super-bound states in the continuum. Nat. Commun. 12, 4135. https://doi.org/10.1038/s41467-021-24502-0 (2021).
Yu, Y. et al. Ultra-coherent fano laser based on a bound state in the continuum. Nat. Photonics 15, 758–764. https://doi.org/10.1038/s41566-021-00860-5 (2021).
Yang, J.-H. et al. Low-threshold bound state in the continuum lasers in hybrid lattice resonance metasurfaces. Laser Photonics Rev. 15, 2100118 (2021).
Koshelev, K., Lepeshov, S., Liu, M., Bogdanov, A. & Kivshar, Y. Asymmetric metasurfaces with high-Q resonances governed by bound states in the continuum. Phys. Rev. Lett. 121, 193903. https://doi.org/10.1103/physrevlett.121.193903 (2018).
Maksimov, D. N., Gerasimov, V. S., Romano, S. & Polyutov, S. P. Refractive index sensing with optical bound states in the continuum. Opt. Express 28, 38907. https://doi.org/10.1364/oe.411749 (2020).
Shipman, S. P. & Venakides, S. Resonant transmission near nonrobust periodic slab modes. Phys. Rev. E 71, 026611 (2005).
Sadreev, A. F., Bulgakov, E. N. & Rotter, I. Bound states in the continuum in open quantum billiards with a variable shape. Phys. Rev. B 73, 235342 (2006).
Blanchard, C., Hugonin, J.-P. & Sauvan, C. Fano resonances in photonic crystal slabs near optical bound states in the continuum. Phys. Rev. B 94, 155303. https://doi.org/10.1103/physrevb.94.155303 (2016).
Bogdanov, A. A. et al. Bound states in the continuum and fano resonances in the strong mode coupling regime. Adv. Photonics 1, 016001 (2019).
Pankin, P. S., Maksimov, D. N., Chen, K.-P. & Timofeev, I. V. Fano feature induced by a bound state in the continuum via resonant state expansion. Sci. Rep. 10, 13691. https://doi.org/10.1038/s41598-020-70654-2 (2020).
Bulgakov, E. N. & Maksimov, D. N. Optical response induced by bound states in the continuum in arrays of dielectric spheres. J. Opt. Soc. Am. B 35, 2443. https://doi.org/10.1364/josab.35.002443 (2018).
Yoon, J. W., Song, S. H. & Magnusson, R. Critical field enhancement of asymptotic optical bound states in the continuum. Sci. Rep. 5, 18301. https://doi.org/10.1038/srep18301 (2015).
Mocella, V. & Romano, S. Giant field enhancement in photonic resonant lattices. Phys. Rev. B 92, 155117. https://doi.org/10.1103/physrevb.92.155117 (2015).
Campione, S. et al. Broken symmetry dielectric resonators for high quality factor fano metasurfaces. ACS Photonics 3, 2362–2367. https://doi.org/10.1021/acsphotonics.6b00556 (2016).
Zhou, W. et al. Progress in 2d photonic crystal fano resonance photonics. Prog. Quantum Electron. 38, 1–74 (2014).
Limonov, M. F., Rybin, M. V., Poddubny, A. N. & Kivshar, Y. S. Fano resonances in photonics. Nat. Photonics 11, 543–554. https://doi.org/10.1038/nphoton.2017.142 (2017).
Krasnok, A. et al. Anomalies in light scattering. Adv. Opt. Photonics 11, 892. https://doi.org/10.1364/aop.11.000892 (2019).
Fan, S., Suh, W. & Joannopoulos, J. D. Temporal coupled-mode theory for the fano resonance in optical resonators. J. Opt. Soc. Am. A 20, 569. https://doi.org/10.1364/josaa.20.000569 (2003).
Alpeggiani, F., Parappurath, N., Verhagen, E. & Kuipers, L. Quasinormal-mode expansion of the scattering matrix. Phys. Rev. X 7, 021035. https://doi.org/10.1103/PhysRevX.7.021035 (2017).
Ming, X., Liu, X., Sun, L. & Padilla, W. J. Degenerate critical coupling in all-dielectric metasurface absorbers. Opt. Express 25, 24658. https://doi.org/10.1364/oe.25.024658 (2017).
Zhou, H. et al. Perfect single-sided radiation and absorption without mirrors. Optica 3, 1079. https://doi.org/10.1364/optica.3.001079 (2016).
Maksimov, D. N., Bogdanov, A. A. & Bulgakov, E. N. Optical bistability with bound states in the continuum in dielectric gratings. Phys. Rev. A 102, 033511 (2020).
Bikbaev, R. G., Maksimov, D. N., Pankin, P. S., Chen, K.-P. & Timofeev, I. V. Critical coupling vortex with grating-induced high q-factor optical tamm states. Opt. Express 29, 4672. https://doi.org/10.1364/oe.416132 (2021).
Zhang, J. et al. Physics-driven machine-learning approach incorporating temporal coupled mode theory for intelligent design of metasurfaces. IEEE Trans. Microw. Theory Tech. 71, 2875–2887. https://doi.org/10.1109/tmtt.2023.3238076 (2023).
Wu, H., Yuan, L. & Lu, Y. Y. Approximating transmission and reflection spectra near isolated nondegenerate resonances. Phys. Rev. A 105, 063510. https://doi.org/10.1103/physreva.105.063510 (2022).
Huang, Z., Wang, J., Jia, W., Zhang, S. & Zhou, C. All-dielectric metasurfaces enabled by quasi-bic for high-q near-perfect light absorption. Opt. Lett. 50, 105. https://doi.org/10.1364/ol.541553 (2024).
Popov, E., Mashev, L. & Maystre, D. Theoretical study of the anomalies of coated dielectric gratings. Opt. Acta Int. J. Opt. 33, 607–619. https://doi.org/10.1080/713821994 (1986).
Shipman, S. P. & Tu, H. Total resonant transmission and reflection by periodic structures. SIAM J. Appl. Math. 72, 216–239. https://doi.org/10.1137/110834196 (2012).
Wang, K. X., Yu, Z., Sandhu, S. & Fan, S. Fundamental bounds on decay rates in asymmetric single-mode optical resonators. Opt. Lett. 38, 100. https://doi.org/10.1364/ol.38.000100 (2013).
Bykov, D. A. & Doskolovich, L. L. \(\omega -k_x\) Fano line shape in photonic crystal slabs. Phys. Rev. A 92, 013845. https://doi.org/10.1103/physreva.92.013845 (2015).
Yuan, L., Zhang, M. & Lu, Y. Y. Real transmission and reflection zeros of periodic structures with a bound state in the continuum. Phys. Rev. A 106, 013505. https://doi.org/10.1103/physreva.106.013505 (2022).
Ma, W. et al. Deep learning for the design of photonic structures. Nat. Photonics 15, 77–90 (2021).
Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nat. Rev. Mater. 6, 679–700 (2021).
So, S., Badloe, T., Noh, J., Bravo-Abad, J. & Rho, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020).
Pilozzi, L., Farrelly, F. A., Marcucci, G. & Conti, C. Machine learning inverse problem for topological photonics. Commun. Phys. 1, 57 (2018).
Kudyshev, Z. A., Shalaev, V. M. & Boltasseva, A. Machine learning for integrated quantum photonics. ACS Photonics 8, 34–46 (2020).
Zhao, Z. et al. Advancements in microwave absorption motivated by interdisciplinary research. Adv. Mater. 36. https://doi.org/10.1002/adma.202304182 (2023).
Deng, Y., Fan, K., Jin, B., Malof, J. & Padilla, W. J. Physics-informed learning in artificial electromagnetic materials. Appl. Phys. Rev. 12. https://doi.org/10.1063/5.0232675 (2025).
Lin, R., Alnakhli, Z. & Li, X. Engineering of multiple bound states in the continuum by latent representation of freeform structures. Photonics Res. 9, B96–B103 (2021).
Ma, X. et al. Strategical deep learning for photonic bound states in the continuum. Laser Photonics Rev. 16, 2100658 (2022).
Wang, F. et al. Automatic optimization of miniaturized bound states in the continuum cavity. Opt. Express 31, 12384–12396 (2023).
Wang, Z. et al. Customizing 2.5d out-of-plane architectures for robust plasmonic bound-states-in-the-continuum metasurfaces. Adv. Sci. 10, 2206236. https://doi.org/10.1002/advs.202206236 (2023).
Zhang, Y. et al. Dynamics of polarization-tuned mirror symmetry breaking in a rotationally symmetric system. Nat. Commun. 15, 5586. https://doi.org/10.1038/s41467-024-49696-x (2024).
Su, J. L. et al. Metaphynet: intelligent design of large-scale metasurfaces based on physics-driven neural network. J. Phys. Photonics 6, 035010. https://doi.org/10.1088/2515-7647/ad4cc8 (2024).
Molokeev, M. S. et al. Infrared bound states in the continuum: random forest method. Opt. Lett. 48, 4460. https://doi.org/10.1364/ol.494629 (2023).
Bulgakov, E. N., Maksimov, D. N., Semina, P. N. & Skorobogatov, S. A. Propagating bound states in the continuum in dielectric gratings. J. Opt. Soc. Am. B 35, 1218–1222. https://doi.org/10.1364/josab.35.001218 (2018).
Zhong, H., He, T., Meng, Y. & Xiao, Q. Photonic bound states in the continuum in nanostructures. Materials 16, 7112 (2023).
Son, H. et al. Strong coupling induced bound states in the continuum in a hybrid metal-dielectric bilayer nanograting resonator. ACS Photonics 11, 3221–3231 (2024).
Maksimov, D. N., Gerasimov, V. S., Bogdanov, A. A. & Polyutov, S. P. Enhanced sensitivity of an all-dielectric refractive index sensor with an optical bound state in the continuum. Phys. Rev. A 105, 033518 (2022).
Wu, W., Wang, K. & Qian, L. All-dielectric grating-based refractive index sensor with a high figure of merit driven by bound states in the continuum. Opt. Eng. 63, 127104–127104 (2024).
Li, Z., Nie, G., Chen, Z., Zhan, S. & Lan, L. High-quality quasi-bound state in the continuum enabled single-nanoparticle virus detection. Opt. Lett. 49, 3380–3383 (2024).
Yao, H.-Y., Kang, Y.-T. & Her, T.-H. Ultra-sensitive refractive index sensing enabled by accidental bound states in the continuum on ultrathin dielectric grating metasurfaces. Opt. Express 33, 13298–13315 (2025).
Yadav, G., Sahu, S., Kumar, R. & Jha, R. Bound states in the continuum empower subwavelength gratings for refractometers in visible. In Photonics, vol. 9, 292 (MDPI, 2022).
Liu, J. & Liu, Y. Perfect narrow-band absorber of monolayer borophene in all-dielectric grating based on quasi-bound state in the continuum. Ann. Phys. 535, 2200500 (2023).
Zhao, Z., Guo, C. & Fan, S. Connection of temporal coupled-mode-theory formalisms for a resonant optical system and its time-reversal conjugate. Phys. Rev. A 99, 033839. https://doi.org/10.1103/physreva.99.033839 (2019).
Maksimov, D. et al. Dataset: Regression. https://opticapublishing.figshare.com/s/99bdf72248fca9e967a3.
Breiman, L. Random forests. Mach. Learn. 45, 5–32. https://doi.org/10.1023/A:1010933404324 (2001).
Ho, T. K. Random decision forests. In Proceedings of 3rd International Conference on Document Analysis and Recognition, vol. 1, 278–282. https://doi.org/10.1109/ICDAR.1995.598994 (1995).
Liu, Y., Wang, Y. & Zhang, J. New Machine Learning Algorithm: Random Forest, 246–252. (Springer, 2012).
Segal, M. R. Machine learning benchmarks and random forest regression. https://escholarship.org/uc/item/35x3v9t4.
Van Rossum, G. & Python Dev Team. Python 3.6 Language Reference (Samurai Media, 2016).
Altmann, A., Toloşi, L., Sander, O. & Lengauer, T. Permutation importance: A corrected feature importance measure. Bioinformatics 26, 1340–1347. https://doi.org/10.1093/bioinformatics/btq134 (2010).
Wehenkel, M., Sutera, A., Bastin, C., Geurts, P. & Phillips, C. Random forests based group importance scores and their statistical interpretation: Application for alzheimer’s disease. Front. Neurosci. 12. https://doi.org/10.3389/fnins.2018.00411 (2018).
Gippius, N. A., Tikhodeev, S. G. & Ishihara, T. Optical properties of photonic crystal slabs with an asymmetrical unit cell. Phys. Rev. B 72, 045138. https://doi.org/10.1103/physrevb.72.045138 (2005).