Machine learning method for predicting line-shapes of Fano resonances induced by bound states in the continuum

Machine Learning


  • 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).

    Article 
    ADS 

    Google Scholar 

  • Koshelev, K., Bogdanov, A. & Kivshar, Y. Meta-optics and bound states in the continuum. Sci. Bull. 64, 836–842 (2019).

    Google Scholar 

  • 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).

    Article 

    Google Scholar 

  • 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).

    Google Scholar 

  • 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).

    Article 

    Google Scholar 

  • Zhang, M. & Zhang, X. Ultrasensitive optical absorption in graphene based on bound states in the continuum. Sci. Rep. 5, 1–6 (2015).

    MathSciNet 

    Google Scholar 

  • 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).

    ADS 

    Google Scholar 

  • 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).

    PubMed 
    PubMed Central 

    Google Scholar 

  • 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).

    ADS 

    Google Scholar 

  • 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).

    Google Scholar 

  • 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).

    Article 
    ADS 
    PubMed 
    PubMed Central 

    Google Scholar 

  • 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).

    Article 

    Google Scholar 

  • 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).

    ADS 
    PubMed 

    Google Scholar 

  • 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).

    ADS 
    PubMed 

    Google Scholar 

  • Koshelev, K. et al. Subwavelength dielectric resonators for nonlinear nanophotonics. Science 367, 288–292 (2020).

    ADS 
    PubMed 

    Google Scholar 

  • Kodigala, A. et al. Lasing action from photonic bound states in continuum. Nature 541, 196–199. https://doi.org/10.1038/nature20799 (2017).

    Article 
    ADS 
    PubMed 

    Google Scholar 

  • 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).

    Article 
    ADS 
    PubMed 
    PubMed Central 

    Google Scholar 

  • 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).

    Article 
    ADS 

    Google Scholar 

  • Yang, J.-H. et al. Low-threshold bound state in the continuum lasers in hybrid lattice resonance metasurfaces. Laser Photonics Rev. 15, 2100118 (2021).

    ADS 

    Google Scholar 

  • 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).

    Article 
    ADS 
    PubMed 

    Google Scholar 

  • 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).

    Article 
    ADS 
    PubMed 

    Google Scholar 

  • Shipman, S. P. & Venakides, S. Resonant transmission near nonrobust periodic slab modes. Phys. Rev. E 71, 026611 (2005).

    ADS 

    Google Scholar 

  • 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).

    ADS 

    Google Scholar 

  • 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).

    Article 
    ADS 

    Google Scholar 

  • Bogdanov, A. A. et al. Bound states in the continuum and fano resonances in the strong mode coupling regime. Adv. Photonics 1, 016001 (2019).

    ADS 

    Google Scholar 

  • 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).

    Article 
    PubMed 
    PubMed Central 

    Google Scholar 

  • 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).

    Article 
    ADS 

    Google Scholar 

  • 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).

    Article 
    ADS 
    PubMed 
    PubMed Central 

    Google Scholar 

  • 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).

    Article 
    ADS 

    Google Scholar 

  • 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).

    Article 

    Google Scholar 

  • Zhou, W. et al. Progress in 2d photonic crystal fano resonance photonics. Prog. Quantum Electron. 38, 1–74 (2014).

    ADS 

    Google Scholar 

  • 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).

    Article 

    Google Scholar 

  • Krasnok, A. et al. Anomalies in light scattering. Adv. Opt. Photonics 11, 892. https://doi.org/10.1364/aop.11.000892 (2019).

    Article 
    ADS 

    Google Scholar 

  • 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).

    Article 
    ADS 

    Google Scholar 

  • 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).

    Article 

    Google Scholar 

  • 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).

    Article 
    ADS 
    PubMed 

    Google Scholar 

  • Zhou, H. et al. Perfect single-sided radiation and absorption without mirrors. Optica 3, 1079. https://doi.org/10.1364/optica.3.001079 (2016).

    Article 
    ADS 

    Google Scholar 

  • 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).

    ADS 

    Google Scholar 

  • 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).

    Article 
    ADS 
    PubMed 

    Google Scholar 

  • 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).

    Article 
    ADS 

    Google Scholar 

  • 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).

    Article 
    ADS 
    MathSciNet 

    Google Scholar 

  • 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).

    Article 

    Google Scholar 

  • 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).

    Article 
    ADS 

    Google Scholar 

  • 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).

    Article 
    MathSciNet 

    Google Scholar 

  • 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).

    Article 
    ADS 
    PubMed 

    Google Scholar 

  • 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).

    Article 
    ADS 

    Google Scholar 

  • 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).

    Article 
    ADS 
    MathSciNet 

    Google Scholar 

  • Ma, W. et al. Deep learning for the design of photonic structures. Nat. Photonics 15, 77–90 (2021).

    ADS 

    Google Scholar 

  • 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).

    ADS 

    Google Scholar 

  • So, S., Badloe, T., Noh, J., Bravo-Abad, J. & Rho, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020).

    Google Scholar 

  • Pilozzi, L., Farrelly, F. A., Marcucci, G. & Conti, C. Machine learning inverse problem for topological photonics. Commun. Phys. 1, 57 (2018).

    Google Scholar 

  • Kudyshev, Z. A., Shalaev, V. M. & Boltasseva, A. Machine learning for integrated quantum photonics. ACS Photonics 8, 34–46 (2020).

    Google Scholar 

  • 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).

    Google Scholar 

  • Ma, X. et al. Strategical deep learning for photonic bound states in the continuum. Laser Photonics Rev. 16, 2100658 (2022).

    ADS 

    Google Scholar 

  • Wang, F. et al. Automatic optimization of miniaturized bound states in the continuum cavity. Opt. Express 31, 12384–12396 (2023).

    ADS 
    PubMed 

    Google Scholar 

  • 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).

    Article 

    Google Scholar 

  • 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).

    Article 
    PubMed 
    PubMed Central 

    Google Scholar 

  • 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).

    Article 
    ADS 

    Google Scholar 

  • 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).

    Article 
    ADS 
    PubMed 

    Google Scholar 

  • 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).

    Article 
    ADS 

    Google Scholar 

  • Zhong, H., He, T., Meng, Y. & Xiao, Q. Photonic bound states in the continuum in nanostructures. Materials 16, 7112 (2023).

    ADS 
    PubMed 
    PubMed Central 

    Google Scholar 

  • 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).

    Google Scholar 

  • 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).

    ADS 
    MathSciNet 

    Google Scholar 

  • 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).

    Google Scholar 

  • 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).

    ADS 
    PubMed 

    Google Scholar 

  • 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).

    PubMed 

    Google Scholar 

  • 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).

    Google Scholar 

  • 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).

    Article 
    ADS 

    Google Scholar 

  • 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).

    Article 

    Google Scholar 

  • 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).

    Article 
    PubMed 

    Google Scholar 

  • 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).

    Article 
    ADS 

    Google Scholar 



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