Abstract

Fano resonance is a universal phenomenon observed in many areas where wave propagation and interference are possible. Fano resonance arises from the interference of broad and narrow spectra of radiation and becomes an important tool for many applications in the physical, chemical, and biological sciences. At the beginning of this paper, we consider Fano resonances in individual particles, primarily of spherical and cylindrical shapes, and discuss their connection with the physics of bound states in the continuum that determine the high quality factors of resonators. Further, we discuss two areas in which structures with Fano resonances have already found or will find real application in the nearest future—sensors and lasers. The penultimate section concerns our future, which will be associated with the complete replacement of electronic processing, transmission, and storage of information with optical devices as many hope. It is believed that this sophisticated goal can be achieved with devices that implement the slow-light regime associated with the phenomenon of electromagnetically induced transparency, which can be considered as a special case of Fano resonance. The review completes with one more promising topic related to quantum electrodynamics in structures with Fano cavities.

© 2021 Optical Society of America

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H.-J. Chen, “Fano resonance induced fast to slow light in a hybrid semiconductor quantum dot and metal nanoparticle system,” Laser Phys. Lett. 17, 025201 (2020).
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Z. H. Han, W. N. Han, F. R. Liu, Z. Han, Y. P. Yuan, and Z. C. Cheng, “Ultrafast temporal-spatial dynamics of amorphous-to-crystalline phase transition in Ge2Sb2Te5 thin film triggered by multiple femtosecond laser pulses irradiation,” Nanotechnology 31, 115706 (2020).
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W. Zhu, Y. Fan, C. Li, R. Yang, S. Yan, Q. Fu, F. Zhang, C. Gu, and J. Li, “Realization of a near-infrared active Fano-resonant asymmetric metasurface by precisely controlling the phase transition of Ge2Sb2Te5,” Nanoscale 12, 8758–8767 (2020).
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M. Chen, Z. Xiao, X. Lu, F. Lv, and Y. Zhou, “Simulation of dynamically tunable and switchable electromagnetically induced transparency analogue based on metal-graphene hybrid metamaterial,” Carbon 159, 273–282 (2020).
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Y. Hu, T. Jiang, J. Zhou, H. Hao, H. Sun, H. Ouyang, M. Tong, Y. Tang, H. Li, J. You, X. Zheng, Z. Xu, and X. Cheng, “Ultrafast terahertz transmission/group delay switching in photoactive WSe2-functionalized metaphotonic devices,” Nano Energy 68, 104280 (2020).
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E. Janitz, M. K. Bhaskar, and L. Childress, “Cavity quantum electrodynamics with color centers in diamond,” Optica 7, 1232–1252 (2020).
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K. S. Modi, J. Kaur, S. P. Singh, U. Tiwari, and R. K. Sinha, “Extremely high figure of merit in all-dielectric split asymmetric arc metasurface for refractive index sensing,” Opt. Commun. 462, 125327 (2020).
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N. L. Kazanskiy, S. N. Khonina, and M. A. Butt, “Plasmonic sensors based on metal-insulator-metal waveguides for refractive index sensing applications: a brief review,” Phys. E 117, 113798 (2020).
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S. I. Azzam, A. V. Kildishev, R.-M. Ma, C.-Z. Ning, R. Oulton, V. M. Shalaev, M. I. Stockman, J.-L. Xu, and X. Zhang, “Ten years of spasers and plasmonic nanolasers,” Light Sci. Appl. 9, 90 (2020).
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C. Bauer and H. Giessen, “Tailoring the plasmonic Fano resonance in metallic photonic crystals,” Nanophotonics 9, 523–531 (2020).
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K. Y. Yang, J. Skarda, M. Cotrufo, A. Dutt, G. H. Ahn, M. Sawaby, D. Vercruysse, A. Arbabian, S. Fan, A. Alù, and J. Vuckovic, “Inverse-designed non-reciprocal pulse router for chip-based lidar,” Nat. Photonics 14, 369–374 (2020).
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Z. Liu, Y. Xu, C.-Y. Ji, S. Chen, X. Li, X. Zhang, Y. Yao, and J. Li, “Fano-enhanced circular dichroism in deformable stereo metasurfaces,” Adv. Mater. 32, 1907077 (2020).
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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, 2000489 (2020).
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T. Lee, T. Nomura, X. Su, and H. Iizuka, “Fano-like acoustic resonance for subwavelength directional sensing: 0–360 degree measurement,” Adv. Sci. 7, 1903101 (2020).
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K. Koshelev, S. Kruk, E. Melik-Gaykazyan, J.-H. Choi, A. Bogdanov, H.-G. Park, and Y. Kivshar, “Subwavelength dielectric resonators for nonlinear nanophotonics,” Science 367, 288–292 (2020).
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X. Long, M. Zhang, Z. Xie, M. Tang, and L. Li, “Sharp Fano resonance induced by all-dielectric asymmetric metasurface,” Opt. Commun. 459, 124942 (2020).
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C. De-Eknamkul, X. Zhang, M.-Q. Zhao, W. Huang, R. Liu, A. T. C. Johnson, and E. Cubukcu, “MoS2-enabled dual-mode optoelectronic biosensor using a water soluble variant of mu-opioid receptor for opioid peptide detection,” 2D Mater. 7, 014004 (2020).
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2019 (17)

X. Luo, D. Tsai, M. Gu, and M. Hong, “Extraordinary optical fields in nanostructures: from sub-diffraction-limited optics to sensing and energy conversion,” Chem. Soc. Rev. 48, 2458–2494 (2019).
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F. Zangeneh-Nejad and R. Fleury, “Topological Fano resonances,” Phys. Rev. Lett. 122, 014301 (2019).
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A. A. Bogdanov, K. L. Koshelv, 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, 016001 (2019).
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K. V. Baryshnikova, D. A. Smirnova, B. S. Luk’yanchuk, and Y. S. Kivshar, “Optical anapoles: concepts and applications,” Adv. Opt. Mater. 7, 1801350 (2019).
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A. Krasnok, D. Baranov, H. Li, M.-A. Miri, F. Monticone, and A. Alù, “Anomalies in light scattering,” Adv. Opt. Photon. 11, 892–951 (2019).
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R.-M. Ma and R. F. Oulton, “Applications of nanolasers,” Nat. Nanotechnol. 14, 12–22 (2019).
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M.-H. Zhuge, C. Pan, Y. Zheng, J. Tang, S. Ullah, Y. Ma, and Q. Yang, “Wavelength-tunable micro/nanolasers,” Adv. Opt. Mater. 7, 1900275 (2019).
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J. Zhu, G. Wang, F. Jiang, Y. Qin, and H. Cong, “Temperature sensor of MoS2 based on hybrid plasmonic waveguides,” Plasmonics 14, 1863–1870 (2019).
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S. Zhang, S.-J. Tang, S. Feng, Y.-F. Xiao, W. Cui, X. Wang, W. Sun, J. Ye, P. Han, X. Zhang, and Y. Zhang, “High-Q polymer microcavities integrated on a multicore fiber facet for vapor sensing,” Adv. Opt. Mater. 7, 1900602 (2019).
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G. Q. 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, 33358–33367 (2019).
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D.-S. Su, D. P. Tsai, T.-J. Yen, and T. Tanaka, “Ultrasensitive and selective gas sensor based on a channel plasmonic structure with an enormous hot spot region,” ACS Sens. 4, 2900–2907 (2019).
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Y. Wen, Y. Sun, C. Deng, L. Huang, G. Hu, B. Yun, R. Zhang, and Y. Cui, “High sensitivity and FOM refractive index sensing based on Fano resonance in all-grating racetrack resonators,” Opt. Commun. 446, 141–146 (2019).
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J. Diao, B. Han, J. Yin, X. Li, T. Lang, and Z. Hong, “Analogue of electromagnetically induced transparency in an S-shaped all-dielectric metasurface,” IEEE Photon. J. 11, 4601110 (2019).
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O. S. Latcham, Y. I. Gusieva, A. V. Shytov, O. Y. Gorobets, and V. V. Kruglyak, “Controlling acoustic waves using magnetoelastic Fano resonances,” Appl. Phys. Lett. 115, 082403 (2019).
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O. Černotík, A. Dantan, and C. Genes, “Cavity quantum electrodynamics with frequency-dependent reflectors,” Phys. Rev. Lett. 122, 243601 (2019).
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D. Bekele, Y. Yu, K. Yvind, and J. Mørk, “In-plane photonic crystal devices using Fano resonances,” Laser Photon. Rev. 13, 1900054 (2019).
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E. V. Denning, J. Iles-Smith, and J. Mørk, “Quantum light-matter interaction and controlled phonon scattering in a photonic Fano cavity,” Phys. Rev. B 100, 214306 (2019).
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2018 (17)

Z. Liu, H. Du, J. Li, L. Lu, Z.-Y. Li, and N. X. Fang, “Nano-Kirigami with giant optical chirality,” Sci. Adv. 4, eaat4436 (2018).
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B. Gurlek, V. Sandoghdar, and D. Martín-Cano, “Manipulation of quenching in nanoantenna-emitter systems enabled by external detuned cavities: a path to enhance strong-coupling,” ACS Photon. 5, 456–461 (2018).
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B. Yang, W. Liu, Z. Li, H. Cheng, S. Chen, and J. Tian, “Polarization-sensitive structural colors with Hue-and-saturation tuning based on all-dielectric nanopixels,” Adv. Opt. Mater. 6, 1701009 (2018).
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A. Ahmadivand, B. Gerislioglu, and N. Pala, “Optothermally controllable multiple high-order harmonics generation by Ge2Sb2Te5-mediated Fano clusters,” Opt. Mater. 84, 301–306 (2018).
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S. Wehner, D. Elkouss, and R. Hanson, “Quantum internet: a vision for the road ahead,” Science 362, eaam9288 (2018).
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Z.-X. Liu, B. Wang, C. Kong, H. Xiong, and Y. Wu, “Magnetic-field-dependent slow light in strontium atom-cavity system,” Appl. Phys. Lett. 112, 111109 (2018).
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B. Wei and S. Jian, “A nanoscale Fano resonator by graphene-gold dipolar interference,” Plasmonics 13, 1889–1895 (2018).
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H. Xu, M. Zhao, C. Xiong, B. Zhang, M. Zheng, J. Zeng, H. Xia, and H. Li, “Dual plasmonically tunable slow light based on plasmon-induced transparency in planar graphene ribbon metamaterials,” Phys. Chem. Chem. Phys. 20, 25959–25966 (2018).
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B. Wei and S. Jian, “Fano resonance in a U-shaped tunnel assisted graphene-based nanoring resonator waveguide system,” Opt. Commun. 425, 24–28 (2018).
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Z. Yan, L. Qian, P. Zhan, and Z. Wang, “Generation of tunable double Fano resonances by plasmon hybridization in graphene-metal metamaterial,” Appl. Phys. Express 11, 072001 (2018).
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Z. Gao, L. Wu, F. Gao, Y. Luo, and B. Zhang, “Spoof plasmonics: from metamaterial concept to topological description,” Adv. Mater. 30, 1706683 (2018).
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J. Wang, X. Zhang, M. Yan, L. Yang, F. Hou, W. Sun, X. Zhang, L. Yuan, H. Xiao, and T. Wang, “Embedded whispering-gallery mode microsphere resonator in a tapered hollow annular core fiber,” Photon. Res. 6, 1124–1129 (2018).
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J. Chen, J. Yuan, Q. Zhang, H. Ge, C. Tang, Y. Liu, and B. Guo, “Dielectric waveguide-enhanced localized surface plasmon resonance refractive index sensing,” Opt. Mater. Express 8, 342–347 (2018).
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Z.-M. Meng and Z.-Y. Li, “Control of Fano resonances in photonic crystal nanobeams side-coupled with nanobeam cavities and their applications to refractive index sensing,” J. Phys. D 51, 095106 (2018).
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B. Ai, C. Song, L. Bradley, and Y. Zhao, “Strong Fano resonance excited in an array of nanoparticle-in-ring nanostructures for dual plasmonic sensor applications,” J. Phys. Chem. C 122, 20935–20944 (2018).
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T. S. Rasmussen, Y. Yu, and J. Mork, “Modes, stability, and small-signal response of photonic crystal Fano lasers,” Opt. Express 26, 16365–16376 (2018).
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Y. Kivshar, “All-dielectric meta-optics and non-linear nanophotonics,” Natl. Sci. Rev. 5, 144–158 (2018).
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2017 (26)

S. S. Kruk, R. Camacho-Morales, L. Xu, M. Rahmani, D. A. Smirnova, L. Wang, H. H. Tan, C. Jagadish, D. N. Neshev, and Y. S. Kivshar, “Nonlinear optical magnetism revealed by second-harmonic generation in nanoantennas,” Nano Lett. 17, 3914–3918 (2017).
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J. Cambiasso, G. Grinblat, Y. Li, A. Rakovich, E. Cortés, and S. A. Maier, “Bridging the gap between dielectric nanophotonics and the visible regime with effectively lossless gallium phosphide antennas,” Nano Lett. 17, 1219–1225 (2017).
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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, 243901 (2017).
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W. Lin, H. Zhang, S.-C. Chen, B. Liu, and Y.-G. Liu, “Microstructured optical fiber for multichannel sensing based on Fano resonance of the whispering gallery modes,” Opt. Express 25, 994–1004 (2017).
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V. V. Klimov, A. A. Pavlov, I. V. Treshin, and I. V. Zabkov, “Fano resonances in a photonic crystal covered with a perforated gold film and its application to bio-sensing,” J. Phys. D 50, 285101 (2017).
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F. B. Zarrabi, M. Bazgir, S. Ebrahimi, and A. S. Arezoomand, “Fano resonance for U-I nano-array independent to the polarization providing bio-sensing applications,” J. Electromagn. Waves. Appl. 31, 1444–1452 (2017).
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Y.-L. Shang, M.-Y. Ye, and X.-M. Lin, “Experimental observation of Fano-like resonance in a whispering-gallery-mode microresonator in aqueous environment,” Photon. Res. 5, 119–123 (2017).
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G. Zheng, X. Zou, Y. Chen, L. Xu, and W. Rao, “Fano resonance in graphene-MoS2 heterostructure-based surface plasmon resonance biosensor and its potential applications,” Opt. Mater. 66, 171–178 (2017).
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M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11, 543–554 (2017).
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Editorial, “Fano still resonating,” Nat. Photonics 11, 529 (2017).
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C. Forestiere and G. Miano, “On the nanoparticle resonances in the full-retarded regime,” J. Opt. 19, 075601 (2017).
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M. Rybin and Yu. Kivshar, “Supercavity lasing,” Nature 541, 164–165 (2017).
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T. S. Rasmussen, Y. Yu, and J. Mork, “Theory of self-pulsing in photonic crystal Fano lasers,” Laser Photon. Rev. 11, 1700089 (2017).
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Y. Yu, W. Xue, E. Semenova, K. Yvind, and J. Mork, “Demonstration of a self-pulsing photonic crystal Fano laser,” Nat. Photonics 11, 81–84 (2017).
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I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11, 149–158 (2017).
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Y.-C. Liu, B.-B. Li, and Y.-F. Xiao, “Electromagnetically induced transparency in optical microcavities,” Nanophotonics 6, 789–811 (2017).
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K. L. Tsakmakidis, O. Hess, R. W. Boyd, and X. Zhang, “Ultraslow waves on the nanoscale,” Science 358, eaan5196 (2017).
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L.-H. Du, J. Li, Q. Liu, J.-H. Zhao, and L.-G. Zhu, “High-Q Fano-like resonance based on a symmetric dimer structure and its terahertz sensing application,” Opt. Mater. Express 7, 1335–1342 (2017).
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S. Zhang, J. Li, R. Yu, W. Wang, and Y. Wu, “Optical multistability and Fano line-shape control via mode coupling in whispering-gallery-mode microresonator optomechanics,” Sci. Rep. 7, 39781 (2017).
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M. J. Akram, F. Ghafoor, M. M. Khan, and F. Saif, “Control of Fano resonances and slow light using Bose-Einstein condensates in a nanocavity,” Phys. Rev. A 95, 023810 (2017).
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G. Zhao, S. 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).
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S. Hu, D. Liu, H. Lin, J. Chen, Y. Yi, and H. Yang, “Analogue of ultra-broadband and polarization-independent electromagnetically induced transparency using planar metamaterial,” J. Appl. Phys. 121, 123103 (2017).
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C. Jiang, L. Jiang, H. Yu, Y. Cui, X. Li, and G. Chen, “Fano resonance and slow light in hybrid optomechanics mediated by a two-level system,” Phys. Rev. A 96, 053821 (2017).
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V. Nadtochenko, N. Denisov, A. Aybush, F. Gostev, I. Shelaev, A. Titov, S. Umanskiy, and D. Cherepanov, “Ultrafast spectroscopy of Fano-like resonance between optical phonon and excitons in CdSe quantum dots: dependence of coherent vibrational wave-packet dynamics on pump fluence,” Nanomaterials 7, 371 (2017).
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A. Kristensen, J. W. K. Yang, S. I. Bozhevolnyi, P. Nordlander, N. J. Halas, and N. A. Mortensen, “Plasmonic colour generation,” Nat. Rev. Mater. 2, 16088 (2017).
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Z. Liu, J. Li, Z. Liu, W. Li, J. Li, C. Gu, and Z.-Y. Li, “Fano resonance Rabi splitting of surface plasmons,” Sci. Rep. 7, 8010 (2017).
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2016 (17)

Z. Liu, Z. Liu, J. Li, W. Li, J. Li, C. Gu, and Z.-Y. Li, “3D conductive coupling for efficient generation of prominent Fano resonances in metamaterials,” Sci. Rep. 6, 27817 (2016).
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H. Zhu, F. Yi, and E. Cubukcu, “Plasmonic metamaterial absorber for broadband manipulation of mechanical resonances,” Nat. Photonics 10, 709–714 (2016).
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Q. Wang, E. T. F. Rogers, B. Gholipour, C.-M. Wang, G. Yuan, J. Teng, and N. I. Zheludev, “Optically reconfigurable metasurfaces and photonic devices based on phase change materials,” Nat. Photonics 10, 60–65 (2016).
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J. Li, R. Yu, J. Liu, C. Ding, and Y. Wu, “Fano line-shape control and superluminal light using cavity quantum electrodynamics with a partially transmitting element,” Phys. Rev. A 93, 053814 (2016).
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S. Zhan, Y. Peng, Z. He, B. Li, Z. Chen, H. Xu, and H. Li, “Tunable nanoplasmonic sensor based on the asymmetric degree of Fano resonance in MDM waveguide,” Sci. Rep. 6, 22428 (2016).
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B. Yun, R. Zhang, G. Hu, and Y. Cui, “Ultra sharp Fano resonances induced by coupling between plasmonic stub and circular cavity resonators,” Plasmonics 11, 1157–1162 (2016).
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S. Pang, Y. Huo, Y. Xie, and L. Hao, “Fano resonance in MIM waveguide structure with oblique rectangular cavity and its application in sensor,” Opt. Commun. 381, 409–413 (2016).
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N. Dabidian, S. Dutta-Gupta, I. Kholmanov, K. Lai, F. Lu, J. Lee, M. Jin, S. Trendafilov, A. Khanikaev, B. Fallahazad, E. Tutuc, M. A. Belkin, and G. Shvets, “Experimental demonstration of phase modulation and motion sensing using graphene-integrated metasurfaces,” Nano Lett. 16, 3607–3615 (2016).
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B. Yun, G. Hu, R. Zhang, and C. Yiping, “Fano resonances in a plasmonic waveguide system composed of stub coupled with a square cavity resonator,” J. Opt. 18, 055002 (2016).
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C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
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M. I. Tribelsky and A. E. Miroshnichenko, “Giant in-particle field concentration and Fano resonances at light scattering by high-refractive-index particles,” Phys. Rev. A 93, 053837 (2016).
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X. Kong and G. Xiao, “Fano resonance in high-permittivity dielectric spheres,” J. Opt. Soc. Am. A 33, 707–711 (2016).
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Y. Zhang, S. Li, X. Zhang, Y. Chen, L. Wang, Y. Zhang, and L. Yu, “Evolution of Fano resonance based on symmetric/asymmetric plasmonic waveguide system and its application in nanosensor,” Opt. Commun. 370, 203–208 (2016).
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V. F. Gili, L. Carletti, A. Locatelli, D. Rocco, M. Finazzi, L. Ghirardini, I. Favero, C. Gomez, A. Lemaître, M. Celebrano, C. De Angelis, and G. Leo, “Monolithic AlGaAs second-harmonic nanoantennas,” Opt. Express 24, 15965–15971 (2016).
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J. Lee, N. Nookala, J. S. Gomez-Diaz, M. Tymchenko, F. Demmerle, G. Boehm, M.-C. Amann, A. Alù, and M. A. Belkin, “Ultrathin second-harmonic metasurfaces with record-high nonlinear optical response,” Adv. Opt. Mater. 4, 664–670 (2016).
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S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11, 23–36 (2016).
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A. S. Shorokhov, E. V. Melik-Gaykazyan, D. A. Smirnova, B. Hopkins, K. E. Chong, D.-Y. Choi, M. R. Shcherbakov, A. E. Miroshnichenko, D. N. Neshev, A. A. Fedyanin, and Y. S. Kivshar, “Multifold enhancement of third-harmonic generation in dielectric nanoparticles driven by magnetic Fano resonances,” Nano Lett. 16, 4857–4861 (2016).
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2015 (13)

M. Celebrano, X. Wu, M. Baselli, S. Großmann, P. Biagioni, A. Locatelli, C. De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duò, F. Ciccacci, and M. Finazzi, “Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation,” Nat. Nanotechnol. 10, 412–417 (2015).
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P. Markoš, “Fano resonances and band structure of two-dimensional photonic structures,” Phys. Rev. A 92, 043814 (2015).
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L. H. Guessi, R. S. Machado, Y. Marques, L. S. Ricco, K. Kristinsson, M. Yoshida, I. A. Shelykh, M. De Souza, and A. C. Seridonio, “Catching the bound states in the continuum of a phantom atom in graphene,” Phys. Rev. B 92, 045409 (2015).
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L. H. Guessi, Y. Marques, R. S. Machado, K. Kristinsson, L. S. Ricco, I. A. Shelykh, M. S. Figueira, M. De Souza, and A. C. Seridonio, “Quantum phase transition triggering magnetic bound states in the continuum in graphene,” Phys. Rev. B 92, 245107 (2015).
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M. V. Rybin, D. S. Filonov, P. A. Belov, Y. S. Kivshar, and M. F. Limonov, “Switching from visibility to invisibility via Fano resonances: theory and experiment,” Sci. Rep. 5, 8774 (2015).
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D.-J. Cai, Y.-H. Huang, W.-J. Wang, W.-B. Ji, J.-D. Chen, Z.-H. Chen, and S.-D. Liu, “Fano resonances generated in a single dielectric homogeneous nanoparticle with high structural symmetry,” J. Phys. Chem. C 119, 4252–4260 (2015).
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C. Zheng, T. Jia, H. Zhao, S. Zhang, D. Feng, and Z. Sun, “Low threshold tunable spaser based on multipolar Fano resonances in disk–ring plasmonic nanostructures,” J. Phys. D 49, 015101 (2015).
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A. Cui, Z. Liu, J. Li, T. H. Shen, X. Xia, Z. Li, Z. Gong, H. Li, B. Wang, J. Li, H. Yang, W. Li, and C. Gu, “Directly patterned substrate-free plasmonic ‘nanograter’ structures with unusual Fano resonances,” Light Sci. Appl. 4, e308 (2015).
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K.-H. Gu, X.-B. Yan, Y. Zhang, C.-B. Fu, Y.-M. Liu, X. Wang, and J.-H. Wu, “Tunable slow and fast light in an atom-assisted optomechanical system,” Opt. Commun. 338, 569–573 (2015).
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M. Manjappa, S.-Y. Chiam, L. Cong, A. A. Bettiol, W. Zhang, and R. Singh, “Tailoring the slow light behavior in terahertz metasurfaces,” Appl. Phys. Lett. 106, 181101 (2015).
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A. Reiserer and G. Rempe, “Cavity-based quantum networks with single atoms and optical photons,” Rev. Mod. Phys. 87, 1379 (2015).
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Y. Shen, V. Rinnerbauer, I. Wang, V. Stelmakh, J. D. Joannopoulos, and M. Soljačić, “Structural colors from Fano resonances,” ACS Photon. 2, 27–32 (2015).
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Y. Yu, Y. Chen, H. Hu, W. Xue, K. Yvind, and J. Mørk, “Nonreciprocal transmission in a nonlinear photonic-crystal Fano structure with broken symmetry,” Laser Photon. Rev. 9, 241–247 (2015).
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2014 (15)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
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H.-K. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photonics 8, 595–604 (2014).
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W. Zhou, D. Zhao, Y.-C. Shuai, H. Yang, S. Chuwongin, A. Chadha, J.-H. Seo, K. X. Wang, V. Liu, Z. Ma, and S. Fan, “Progress in 2D photonic crystal Fano resonance photonics,” Prog. Quantum Electron. 38, 1–74 (2014).
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J. Qi, Z. Chen, J. Chen, Y. Li, W. Qiang, J. Xu, and Q. Sun, “Independently tunable double Fano resonances in asymmetric MIM waveguide structure,” Opt. Express 22, 14688–14695 (2014).
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F. Krausz and M. I. Stockman, “Attosecond metrology: from electron capture to future signal processing,” Nat. Photonics 8, 205–213 (2014).
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Y. Y. Huo, T. Q. Jia, Y. Zhang, H. Zhao, S. A. Zhang, D. H. Feng, and Z. R. Sun, “Spaser based on Fano resonance in a rod and concentric square ring-disk nanostructure,” Appl. Phys. Lett. 104, 113104 (2014).
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Figures (42)

Figure 1.
Figure 1. Ugo Fano (1912–2001), Italian–US theoretical physicist. Reprinted with permission from the Emilio Segrè Visual Archives.
Figure 2.
Figure 2. (a) Asymmetric profile of $|D{|^2}$ for some values of $|{D_0}|$, $|{D_c}|$, and $\bar q$, given in the text. Adapted with permission from Springer Nature: Fano, Nuovo Cimento 12, 154–161 (1935) [1]. (b) Fano lineshapes for different values of $q$. (Reverse the scale of abscissas for negative $q$.) This function is plotted in (b) from [5] for a number of values of $q$, which is regarded as constant in the range of interest. Figure 1 reprinted with permission from Fano, Phys. Rev. 124, 1866–1878 (1961) [5]. Copyright 1961 by the American Physical Society.
Figure 3.
Figure 3. Diagram showing the shape of the characteristic Fano profiles (red curve, compilation of five lines), the corresponding formulas (in square frames), and the main areas of application of the Fano resonance depending on the Fano parameter $q = \cot \delta$ (magenta curve) where $\delta$ is the phase shift. The blue curve is the symmetrical Lorentzian profile.
Figure 4.
Figure 4. Example of FDTD-simulated transmission spectrum for a single blockade-hole centered at the midplane. ${\lambda _0}$ is the resonant wavelength. The insets show snapshots of the mode distributions for continuous-wave excitation at the “on” and “off” states of the Fano profile, respectively. Reprinted with permission from Yu et al., Appl. Phys. Lett. 105, 061117 (2014) [19]. Copyright 2014 AIP Publishing LLC.
Figure 5.
Figure 5. (a) Total scattering efficiency spectra of a 220-nm-wide and 50-nm-thick Si nanostripe under different illumination angles with the electric field polarized along the stripe length. The vertical dashed gray line represents the absorption resonance peak position located at 580 nm. The arrows on the scattering spectra highlight the variation of the position of the dip in scattering spectra at different incident angles. Reprinted by permission from Macmillan Publishers Ltd.: Fan et al., Nat. Mater. 13, 471–475 (2014) [20]. Copyright 2014. (b) Scattering (black solid line) and absorption (red dashed line) spectra of single Si nanodisks, where the disk radius $r = {160}\;{\rm nm}$, the incident plane wave propagates along the z-axis, and the polarization is along the x-axis. The disk thickness $h = {30}\;{\rm nm}$. Schematic representations of structures in which the Fano resonance can be observed are presented. Reprinted with permission from Cai et al., J. Phys. Chem. C 119, 4252–4260 (2015) [21]. Copyright 2015 American Chemical Society.
Figure 6.
Figure 6. (a) Spectra of the Mie scattering efficiency ${Q_{{\rm sca},0}}$ for the dipole mode ${{\rm TE}_{0k}}$ for a single dielectric cylinder and different values of real dielectric permittivity ${\varepsilon _1}$1. The cylinder is embedded in air, ${\varepsilon _2} = {1}$. The corresponding values of the Fano parameter $q$ are shown above the plot. Curves are shifted vertically by the values shown. Adapted with permission from [24]. Inset: part of schematic from Fig. 3. (b) Dependence of the Fano parameter $q$ on the size parameter $x = {2}\pi {r/}\lambda$ for the dipole mode ${{\rm TE}_{0k}}$ and multipole modes ${{\rm TE}_{1k}}$ and ${{\rm TE}_{2k}}$ for a cylinder (${\varepsilon _1} = {50}$) embedded in air (${\varepsilon _2} = {1}$).
Figure 7.
Figure 7. Fano resonances in Mie scattering on a dielectric cylinder. (a) Spectra of squared modules of the Lorenz–Mie coefficient $|{a_0}{|^2}$ describing magnetic field outside a cylinder with ${\varepsilon _1} = 60$ and examples of the Fano fitting of ${{\rm TE}_{02}}$ mode (blue curve, ${q_{02}} = {2.82}$), ${{\rm TE}_{05}}$ mode (black curve, ${q_{05}} = {0/08}$), and ${{\rm TE}_{07}}$ mode (green curve, ${q_{07}} = - {0.95}$). (b) The background spectrum. (c) Spectra of squared modules of the Lorenz–Mie coefficient ${| {{d_0}} |^2}$ describing magnetic field inside a cylinder with ${\varepsilon _1} = 60$. Top: the equation expressed the Fano resonance condition and the Maxwell boundary condition. ${J_n}(\zeta)$ and $H_n^{(1)}(\zeta)$ are the Bessel and Hankel functions. Adapted from [25] with permission from Springer Nature under a Creative Commons CC BY license.
Figure 8.
Figure 8. (a) Dependence of the asymmetry parameter $q$ on the size parameter $x: q_1^{(a)}(x)$ (solid blue line) and $q_1^{(b)}(x)$ (dashed red line). Figure 5 reprinted with permission from Tribelsky and Miroshnichenko, Phys. Rev. A 93, 053837 (2016) [26]. Copyright 2016 by the American Physical Society. (b) Squared norm of Mie coefficient $|{a_1}{|^2}$ (blue curve), slowly varying background (green curve), and narrow resonance (red dashed–dotted line) for a sphere with ${\varepsilon _1} = 1000$. Reprinted with permission from [27]. Copyright 2016 Optical Society of America.
Figure 9.
Figure 9. Scattering efficiency ${\sigma _{\rm{sca}}}$ of (a) Si  and (c) Ag  spheres as a function of size parameter $x$. Absolute value of the coefficients ${a_{n1}}$ and ${b_{n1}}$ as a function of $x$ for (b) Si  and (d) Ag  spheres. The vertical dashed lines represent the positions of the resonance modes. Reprinted from [28] under the terms of the Creative Commons Attribution 3.0 licence.
Figure 10.
Figure 10. (a) Illustration of different possible photonic states including BIC. Reprinted by permission from Macmillan Publishers Ltd.: Hsu et al., Nat. Rev. Mater. 1, 16048 (2016) [34]. Copyright 2016. (b) $Q$-factor of BIC in a theoretical structure in which at least one of the dimensions extends to infinity (gray). The $Q$-factor of a real structure in the quasi-BIC mode can take finite, but extremely large, values (red). In conventional lasers, an optical resonator is used, the $Q$-factor of which weakly depends on the geometric dimensions (blue). Adapted by permission from Macmillan Publishers Ltd.: Rybin and Kivshar, Nature 541, 164–165 (2017) [36]. Copyright 2017.
Figure 11.
Figure 11. Strong coupling of modes in a dielectric cylinder. (a) Simulated far-field patterns of the high-$Q$ mode for cylinder of different aspect ratios $r/l$ shown schematically. For calculations, ${| \textbf{E} |^2}$ is normalized to the full mode energy. Reprinted with permission from an AAAS license from Koshelev et al., Science 367, 288–292 (2020) [51]. (b) Fabry–Perot and Mie modes of a cylindrical resonator are shown schematically. (c) Distribution of the electric field amplitude ${| {E} |}$ for the Mie-like mode ${{\rm TE}_{1,1,0}}$ (point A) and Fabry–Perot-like mode ${{\rm TM}_{1, 1,1}}$ (point B). (b) and (c) Reprinted from [52] under a Creative Commons Attribution 4.0 Unported License.
Figure 12.
Figure 12. Avoided resonance crossing, $Q$-factor, and Fano resonance. (a) Spectra of the normalized total scattering cross section of the cylinder resonator as a function of its aspect ratio $r/l$ in the region of the avoided resonance crossing between the modes ${{\rm TE}_{1,1,0}}$ and ${{\rm TM}_{1,1,1}}$. (b) Peak positions for the low- and high-frequency modes in the spectra. (c)–(e) Evolution of the quality factor $Q$, the peak amplitude A, and the Fano asymmetry parameter $q$ for the high-frequency mode. Reprinted from [52] under a Creative Commons Attribution 4.0 Unported License.
Figure 13.
Figure 13. Calculated $Q$-factors of the quasi-BIC modes realized in subwavelength dielectric resonators. (a) Dependence of the $Q$-factor of the modes with the azimuthal numbers ${m} = {0}$ and ${m} = {1}$ on the dielectric permittivity. For high values of permittivity, the $Q$-factor demonstrates power growth. The case of silicon is marked by a vertical line. (b) Relative dimensions of a dielectric cylindrical resonator supporting a quasi-BIC mode. A resonator becomes subwavelength below a boundary marked by a horizontal line. Figure 4 reprinted with permission from Rybin et al., Phys. Rev. Lett. 119, 243901 (2017) [53]. Copyright 2017 by the American Physical Society. (c) Complex spectrum of eigenmodes. The spectrum is shown for the modes with the azimuthal index $n = {0}$ (red dotted lines) and $n = \pm {1}$ (blue dotted lines), which are even with respect to $(z \to - z)$ symmetry. Dot sizes are proportional to the $Q$-factor. The region of the avoided crossing between modes ${{\rm TE}_{1,1,0}}$ and ${{\rm TM}_{1,1,1}}$ is marked by the green ellipse. (d) Dependence of the total quality factor $Q$ on the aspect ratio for various levels of material losses. Reprinted from [52] under a Creative Commons Attribution 4.0 Unported License.
Figure 14.
Figure 14. Normalized scattering cross section of the layered particle in the right inset, as a function of the aspect ratio ${\eta _2} = {a}/{{a}_{c2}}$ and wavelength (${\lambda _c} = {378}\;{\rm nm}$). Numbers within the contour plot indicate the regions where Fano features disappear, as their lifetime diverges (detail of region 4 is shown in the left inset). Figure 1 reprinted with permission from Monticone and Alù, Phys. Rev. Lett. 112, 213903 (2014) [56]. Copyright 2014 by the American Physical Society.
Figure 15.
Figure 15. Second-harmonic generation with a dielectric Fano nanoantenna. (a) Diagram of the SHG in a Fano nanoresonator under azimuthally polarized vector beam excitation. (b) Schematic of the SHG process in a nonlinear dielectric nanoantenna. Each term of the formula describes one step of the process. (c) Percentage of pump power coupled to the quasi-BIC for different polarizations of pump depending on the ratio between the beam waist radius ${{\rm w}_0}$ and the pump wavelength. The calculation is done for a free-standing nanoresonator in air. The diffraction limit is 0.61. (d) Spectral overlap ${L_2}({2}{\omega _1})$ between the high-$Q$ mode at the pump frequency and the high-order Mie mode at the SH frequency versus the disk diameter. The inset shows the near-field profiles of both modes. (e) Experimental ellipsometry data for the permittivity of the ITO layer. Wavelength ranges of the excitation and collection are marked with red and blue shading, respectively. Reprinted with permission from AAAS license: Koshelev et al., Science 367, 288–292 (2020) [51].
Figure 16.
Figure 16. (a) Measured and (b) simulated reflectance spectra and retrieved $Q$-factor of the observed resonance for a 930 nm disk on a three-layer substrate excited with an azimuthal pump. The measured $Q$-factor is extracted from the experimental scattering spectrum using the single-peak fitting to the Fano lineshape. The inset in (b) shows the near-field pattern of the excited quasi-BIC resonance at the dip wavelength. (c) 3D map of SH intensity measured as a function of the pump wavelength and particle diameter for an azimuthally polarized beam. The SH intensity is normalized on the square of the pump power. Reprinted with AAAS license from Koshelev et al., Science 367, 288–292 (2020) [51].
Figure 17.
Figure 17. Experimental nonlinear conversion efficiency. (a) and (b) Measured SH intensity as a function of the pump wavelength (a) for a nanoresonator with diameter of ${\sim}\;{930}\;{\rm nm}$ and (b) as a function of the nanoresonator diameter at a 1570 nm pump wavelength for different pump polarizations. The SH intensity is normalized on the square of the pump power. (c) Measured peak SH power versus the peak pump power for a nanoresonator with a diameter of ${\sim}\;{930}\;{\rm nm}$ (${{\rm log}_{10}} - {{\rm log}_{10}}$ scale). Line shows the fit with a quadratic dependence with the nonlinear conversion coefficient ${1.3}\; \times \;{{\rm 10}^{ - 6}}\;{{\rm W}^{ - 1}}$. Reprinted with AAAS license from Koshelev et al., Science 367, 288–292 (2020) [51].
Figure 18.
Figure 18. Topological Fano resonance. (a) Interaction between a bright resonance and a dark narrower resonance can lead to an ultrasharp and asymmetric lineshape, characteristic of Fano resonance. Even small levels of disorder, however, can severely destroy the lineshape of the resonance, by introducing new dips and peaks. (b) To make Fano resonances immune to disorder, one can instead start from bright and dark modes whose existence is topologically guaranteed. The resulting topological Fano lineshape is robust against a large class of geometrical imperfections: the occurrence of new disorder-induced dips and peaks is prevented by topology. Figure 1 reprinted with permission from Zangeneh-Nejad and Fleury, Phys. Rev. Lett. 122, 014301 (2019) [65]. Copyright 2019 by the American Physical Society.
Figure 19.
Figure 19. Full-wave numerical demonstration of topologically protected Fano resonances. (a) Four unit cells from the trivial lattice are connected to four cells from the nontrivial system. Even and odd topological edge modes accordingly form at the interface between the two insulators. (b) Transmission spectrum of the waveguide when the obstacles are randomly moved from their original places. The Fano lineshape is preserved due to topology. (c) Evolution of the transmission spectrum versus disorder strength (d),(e),(f), Same as (a),(b),(c) for a similar acoustic system with a topologically trivial Fano resonance. Figure 3 reprinted with permission from Zangeneh-Nejad and Fleury, Phys. Rev. Lett. 122, 014301 (2019) [65]. Copyright 2019 by the American Physical Society.
Figure 20.
Figure 20. Experimental validation of topological Fano resonances and their robustness. Figure 4 reprinted with permission from Zangeneh-Nejad and Fleury, Phys. Rev. Lett. 122, 014301 (2019) [65]. Copyright 2019 by the American Physical Society.
Figure 21.
Figure 21. Output spectrum of the TE mode with different media in the channels: (a) both channels filled with water. (b) Channel 1, bio-samples with different refractive indices channel 2, water. (c) Channel 1, water, and channel 2, bio-samples with different refractive indices. The color of an individual spectrum changes from red to blue indicating Fano resonance shifts towards longer wavelengths with increasing refractive index. Reprinted with permission from [66]. Copyright 2017 Optical Society of America.
Figure 22.
Figure 22. Spectral position of Fano resonances for the TE mode as a function of the refractive index. (a) Channel 1 is filled with bio-samples and channel 2 is filled with water. (b) Channel 1 is filled with water and channel 2 is filled with bio-samples. Reprinted with permission from [66]. Copyright 2017 Optical Society of America.
Figure 23.
Figure 23. Schematics of 10 Fano-sensors; description of the two modes that determine the Fano resonance, sensitivity (S), figure of merit (FOM), and the numbers of the corresponding references. (a) Reprinted with permission from [66]. Copyright 2017 Optical Society of America. (b) Reprinted from Zhang et al., Opt. Commun. 370, 203–208 (2016) [71]. Copyright 2016, with permission from Elsevier. (c) Reprinted from Pang et al., Opt. Commun. 381, 409–413 (2016) [92]. Copyright 2016, with permission from Elsevier. (d) Reprinted from Chen et al., Opt. Commun. 482, 126563 (2021) [93]. Copyright 2021, with permission from Elsevier. (e) Reprinted from Wen et al., Opt. Commun. 446, 141–146 (2019) [94]. Copyright 2019, with permission from Elsevier. (f) Reprinted from [73] under the terms of the Creative Commons Attribution 3.0 licence. (g) Reprinted from Modi et al., Opt. Commun. 462, 125327 (2020) [98]. Copyright 2020, with permission from Elsevier. (h) Reprinted from [96] under the terms of the Creative Commons Attribution 3.0 licence. (i) Reprinted with permission from Ai et al., J. Phys. Chem. C 122, 20935–20944 (2018) [97]. Copyright 2018 American Chemical Society. (j) Reprinted with permission from [89]. Copyright 2018 Optical Society of America.
Figure 24.
Figure 24. Schematics of Fano sensors (left column), corresponding spectra showing Fano resonances (middle column), and spectral dependences (right column). (a)–(c) Refractive index sensor. Reprinted with permission from Cui et al., Light Sci. Appl. 4, e308 (2015) [95]. Copyright 2015 American Chemical Society. (d)–(f) Temperature sensor. Reprinted with permission from [85]. Copyright 2013 Optical Society of America. (g)–(i) Terahertz sensing. Reprinted with permission from [108]. Copyright 2017 Optical Society of America. (j)–(l) Refractive index sensor. Reprinted with permission from Ai et al., J. Phys. Chem. C 122, 20935–20944 (2018) [97]. Copyright 2018 American Chemical Society.
Figure 25.
Figure 25. (a) Modeling of the waveguide Bragg reflector using the 1D transfer matrix method. The region from the facet to the periodic structure is modeled to be a phase plate with thickness $d$ and effective index ${n_{\rm{eff}}}$; the rest of the region is modeled to be a DBR mirror with period $\Lambda$ and an array of refractive indices that gradually change between ${n_{{\rm eff}1}}$ and ${n_{{\rm eff}2}}$. (b) Transfer matrix simulation of the reflected power for different phase plate thicknesses ranging from 650 nm to 800 nm. Different asymmetric lineshapes can be achieved by changing the phase plate thickness with a periodicity of about 200 nm. Reprinted with permission from [85]. Copyright 2013 Optical Society of America.
Figure 26.
Figure 26. (a) Schematic drawing of the two lowest singlet energy levels of a dye molecule and the transitions it undergoes during fluorescence emission. (b) Schematic drawing of the experimental setup of the angle-resolved fluorescence measurements of R6G dissolved in methanol at the concentration of 1 mM placed on top of the PhC. The gray substrate is the macroscopic PhC slab. The orange spheres are schematic drawings of the R6G molecules in solution. The blue surface represents the equal energy density surface of the Fano resonance. Reprinted by permission from United States National Academy of Sciences: Zhen et al., Proc. Natl. Acad. Sci. USA 110, 13711–13716 (2013) [112].
Figure 27.
Figure 27. (a) Fluorescence  and (b) lasing  measurements. (a) Significantly enhanced fluorescence emission from R6G molecules. Comparison of fluorescence spectra of R6G molecules measured in the normal direction on the PhC (solid lines) pumped on-resonance (blue) and off-resonance (red), as well as on a uniform unpatterned slab (dashed green line). Blue line has been multiplied by a factor of 0.1 for the simplicity of comparison with others. (Inset) FDTD calculation results of the band structure. (b) Low-threshold lasing of a 100 nm thin layer of R6G molecules in solution. Input–output energy characteristics of lasing through mode 4 (580 nm) under pulsed excitation. The solid lines are analytical predictions, and the green circles are measured energies (Meas.). Red circles are measurement results using the spectrometer. The jump in output power clearly indicates the onset of lasing. (Lower inset) Same results in linear scale, where the output grows linearly with the pump energy beyond threshold. (Upper inset) Measured spectrum of emission from the PhC slab at normal direction when pumped below (blue) and above (red) the lasing threshold. Reprinted by permission from United States National Academy of Sciences: Zhen et al., Proc. Natl. Acad. Sci. USA 110, 13711–13716 (2013) [112].
Figure 28.
Figure 28. (a) Schematic of a Fano laser based on an InP photonic-crystal membrane, which contains an active region with three layers of InAs quantum dots. The laser cavity is composed of a photonic-crystal line-defect waveguide, terminated by a broadband left mirror and a narrowband right Fano mirror realized by Fano interference between a waveguide continuum mode and a discrete mode in a side-coupled H0 nanocavity. Adapted by permission from Macmillan Publishers Ltd.: Yu et al., Nat. Photonics 11, 81–84 (2017) [120]. Copyright 2017. (b) The red dots indicate quantum dot active material, and the arrows show possible decay channels. (c) Fano mirror reflection and phase as function of frequency detuning for ${\gamma _c}/{\gamma _{{\mathop{\rm int}}}} = 16$, where the nanocavity is in close proximity to the waveguide (see schematic inset), leading to a large peak reflectivity. (d) Fano mirror reflection and phase for the case where the nanocavity is far from the waveguide, as illustrated by the schematic inset, leading to weak coupling ${\gamma _c}/{\gamma _{{\mathop{\rm int}} }} = 1$, and low reflectivity. Reprinted with permission from [121]. Copyright 2018 Optical Society of America.
Figure 29.
Figure 29. Static characteristics of the Fano laser. (a) Measured output peak power versus pump power. Blue line, experimental data; black line, theoretical fit using the conventional rate equation model, giving a spontaneous emission factor of ${\sim}1\%$. (b) Optical spectra for pump powers of 7.5 dBm (red) and 3 dBm (black). For clarity, the black curve is shifted vertically and the spectrometer integration time is ${\sim}{12}$ times larger than for the red curve. Adapted by permission from Macmillan Publishers Ltd.: Yu et al., Nat. Photonics 11, 81–84 (2017) [120]. Copyright 2017.
Figure 30.
Figure 30. Phase diagram of Fano laser output as function of pumping current and cavity frequency, with the laser threshold curve also shown in green. Current is normalized to minimum threshold current, and detuning is normalized to the line-width ${\gamma _T}$. Gray is below threshold-solution, light blue is continuous-wave, and yellow is self-pulsing. Insets show temporal output profiles in the different domains. Rasmussen et al., Laser Photon. Rev. 11, 1700089 (2017) [119]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.
Figure 31.
Figure 31. Dynamic characteristics of the Fano laser. (a) Measured optical spectra of the Fano laser for pump powers of 24, 60, 78, and 96 mW. For clarity, the spectra are shifted vertically. (b) Measured radiofrequency spectra of the laser power for pump powers of 24, 60, 78, and 96 mW. Adapted by permission from Macmillan Publishers Ltd.: Yu et al., Nat. Photonics 11, 81–84 (2017) [120]. Copyright 2017.
Figure 32.
Figure 32. (a) Scattering and absorption spectra of a single nanoring with an elliptic degree of 0.9/1.11. (b) Sketch of the disk-ring nanostructure coated with gain medium. (c) Electric field amplitudes at the quadrupolar, (d) hexapolar, and (e) octupolar resonance modes. (f) Spaser spectra for the nanoring in disk-ring nanostructures with different elliptic partial degrees. (g) Electric field amplitude at the quadrupolar and (h) at the octupolar resonance wavelength for the elliptic partial degree of 0.9/1.11. (i)–(j) The two modes for the partial degree of 1/0.9; and (k)–(l), the partial degree of 1/0.65. Reprinted from [130] under the terms of the Creative Commons Attribution 3.0 licence.
Figure 33.
Figure 33. (a) Sketch of the spaser structure coated with gain media and the incident light. (b) Scattering and absorption spectra of the structure with no gain media. (c) Induced surface charges on the top surface. (d) Electric field amplitude in the middle section at the Fano resonance wavelength. (e)–(g) Scattering and absorption spectra with different gain coefficient $k$. (h) Scattering intensity at the Fano resonance wavelength as a function of $k$. Reprinted with permission from Huo et al., Appl. Phys. Lett. 104, 113104 (2014) [131]. Copyright 2014 AIP Publishing LLC.
Figure 34.
Figure 34. (a) From top to bottom: SEM image of top-view of single optomechanical crystal nanocavitie; SEM micrograph of a zoomed-in region showing the optomechanical crystal defect region; simulation results for the optical field showing the electrical field intensity $|E(r)|$; simulated mechanical mode. (b) Left panel: optical reflection response at temperature $T = {8.7}\;{\rm K}$. Measured normalized reflection of the signal beam as a function of the two-photon detuning. Middle panel: reflected signal about the transparency window. Right panel: intensity plots for the signal beam reflection as a function of both control laser detuning and two-photon detuning for different control beam powers. The top plot is the theoretically predicted reflection spectrum for the highest control beampower. (c) Top panel: schematic diagram of the hybrid optomechanical system. Bottom panel: equivalent circuit diagram. (d) Absorption as a function of the probe-cavity detuning for different values of cavity control–field detuning. (a) and (b) Reprinted by permission from Macmillan Publishers Ltd.: Safavi-Naeini et al., Nature 472, 69–73 (2011) [178]. Copyright 2011. (c) and (d) Figures 1, 2, and 6 reprinted with permission from Jiang et al., Phys. Rev. A 96, 053821 (2017) [179]. Copyright 2017 by the American Physical Society.
Figure 35.
Figure 35. (a) Transmission $|{t_p}{|^2}$ and (b) phase ${\varphi _t}$ of the probe field as a function of the probe-cavity detuning ${\Delta _p}$ with ${\Delta _a} = {\omega _m}$ and ${\Delta _a} = {0.9}{\omega _m}$, respectively. The insets of (b) are the enlarged images around ${\Delta _p}/2\pi = 10\;{\rm MHz}$ and ${\Delta _p}/2\pi = 20\;{\rm MHz}$. Figures 1, 2, and 6 reprinted with permission from Jiang et al., Phys. Rev. A 96, 053821 (2017) [179]. Copyright 2017 by the American Physical Society.
Figure 36.
Figure 36. (a) Experimental schematic of the optical pump-terahertz probe measurements of the EIT metamaterial. (b) Measured amplitude transmission spectra of the sole-cut wire (pink), pair of split-ring resonators (orange), and EIT metamaterial sample (olive). The insets in (b) are the structural geometries of the sole-cut wire, pair of split-ring resonators, and EIT metamaterial samples with Si islands positioned in ring gaps (red points). (c) Microscopic photo of the fabricated metasurface on the quartz substrate (left) and corresponding image of the hybrid metasurface covered by a ${{\rm WSe}_2}$ multilayer with 40 nm thickness. Scale bar, 20 µm. (d) Measured group-delay spectra map of the metasurface against pump-probe time delay. The pump fluence is fixed at ${800}\;\unicode{x00B5}{{\rm J/cm}^2}$. (e) Metasurface with split-ring resonator–gap asymmetry. (f) Experimentally measured and simulated transmission spectra in the terahertz region. (a) and (b) Reprinted by permission from Macmillan Publishers Ltd.: Gu et al., Nat. Commun. 3, 1151 (2012) [170]. Copyright 2012. (c) and (d) Reprinted from Hu et al., Nano Energy 68, 104280 (2020) [171]. Copyright 2020, with permission from Elsevier. (e) and (f) Reprinted with permission from Manjappa et al., Appl. Phys. Lett. 106, 181101 (2015) [176]. Copyright 2015 AIP Publishing LLC.
Figure 37.
Figure 37. (a) Top-view microscopic picture of the fabricated device. (b)–(d) Transmission spectra for the three stages of operations: (b) open cavity, (c) closed cavity after the first control pulse, and (d) reopened cavity after the second control pulse. Adapted by permission from Macmillan Publishers Ltd.: Xu et al., Nat. Phys. 3, 406–410 (2007) [154]. Copyright 2007.
Figure 38.
Figure 38. (a) Broadband slow light: the medium is composed of multiple layers of double continuum Fano metamaterials with spatially varying resonance frequency ${\Omega _{Q}}$ in the ${\omega _0} - \Delta \omega \lt {\Omega _{Q}} \lt {\omega _0} + \Delta \omega$ range. The incoming light undergoes polarization transformation and is slowed down. (b) Photonic band structure for slow-light metamaterials based on the double continuum Fano resonance. The insets show the geometry and dimensions of the unit cell and the three supported resonances: (i) horizontal dipole, (ii) vertical dipole, and (iii) quadrupole. (c) Transmission (solid green lines), absorption (dashed red lines), and group velocity (solid blue lines) of adiabatic double continuum Fano-based metamaterial. Figures 1, 2, and 4 reprinted with permission from Wu et al., Phys. Rev. Lett. 106, 107403 (2011) [175]. Copyright 2011 by the American Physical Society.
Figure 39.
Figure 39. (a) Diagram for one instance of CQED energy levels, comparing coherent coupling rates (green) to decoherence rates (gray, red). Quantum information (blue oval) is stored in the color center spin states. (b) Schematic of diamond CQED system. Reprinted with permission from [187]. Copyright 2020 Optical Society of America.
Figure 40.
Figure 40. (a) Fano cavity consisting of a waveguide with a fully reflecting mirror in the left end and a Fano mirror in the right end. (b) Squared modulus (orange solid) and phase (gray dotted) of the Fano mirror reflectivity. (c) Level structure of quantum emitter ($| e \rangle$ and $| g \rangle$) and phonon modes along with optical LDOS, $J$. (d) The photonic structure is mapped to a generic configuration, $\mathcal{E}^\prime$, consisting of two coupled discrete modes, dissipating into a common reservoir. Figure 1 reprinted with permission from Denning et al., Phys. Rev. B 100, 214306 (2019) [195]. Copyright 2019 by the American Physical Society.
Figure 41.
Figure 41. (a) Frequency dependence of the LDOS, $J/{\Gamma _0}$, (black solid line) and the spectral density, $J^\prime /{\Gamma _0}$, generated by the mapped structure (green dotted line, shaded area). (b) LDOS as a function of frequency and coupling rate. (c) Photon indistinguishability (color scale) for varying emitter frequency, ${\omega _{\rm{eg}}}$, and nanocavity coupling rate, ${\gamma _{\rm F}}$. The dotted white line traces the peak of the LDOS in panel (b). (d) Emission spectrum (solid orange line and shaded area) for optimal parameters with $\delta = {0.010}$ corresponding to the white dot line in panel (c) along with the LDOS (gray dashed line) and the bulk emission spectrum (blue solid line). All quantities are normalized to their peak value. (e) Emission spectrum for parameters corresponding to the black dot in panel (c) where phonons reduce the indistinguishability by driving transitions between the polaritons. Figures 2 and 3 reprinted with permission from Denning et al., Phys. Rev. B 100, 214306 (2019) [195]. Copyright 2019 by the American Physical Society.
Figure 42.
Figure 42. (a),(b) SEM images of kirigami fabricated by global FIB irradiation: (a) twisted triple Fibonacci spiral and (b) window-decoration-type nanobarriers. Scale bars: 1 µm. [200]. (c),(d) SEM images of 3D metamaterials with Fano resonances [201,202]. (e) reproduction of the painting “Mother and Son,” printed by Dong Wang. The colors in Reproduction are generated by the ${{\rm TiO}_2}$ nanostructures [203]. (f) Scattering cross-section spectrum of the hetero-metallodielectric octamer cluster in both a-GST and c-GST phases of the surrounding nanoparticles. The inset is the schematic representation of the octamer assembly [207]. (g) Schematic of the Fabry–Perot–nanoantenna hybrid: a dipole emitter close to a plasmonic nanoparticle (zoomed in size) is embedded in a Fabry–Perot cavity [208]. (a) and (b) From Liu et al., Sci. Adv. 4, eaat4436 (2018) [200]. Reprinted with permission from AAAS. (c) Reprinted with permission from Springer Nature, Creative Commons Attribution 4.0 International License: Liu et al., Sci. Rep. 7, 8010 (2017) [201]. (d) Reprinted with permission from Springer Nature, Creative Commons Attribution 4.0 International License: Liu et al. Sci. Rep. 6, 27817 (2016) [202]. (e) Yang et al., Adv. Opt. Mater. 6, 1701009 (2018) [203]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission. (f) Reprinted from Ahmadivand et al., Opt. Mater. 84, 301–306 (2018) [214]. Copyright 2018, with permission from Elsevier. (g) Reprinted with permission from Gurlek et al., ACS Photon. 5, 456–461 (2018) [208]. Copyright 2018 American Chemical Society.

Equations (30)

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( ω 1 ω i γ 1 g g ω 2 ω i γ 2 ) ( x 1 x 2 ) = i ( f 1 f 2 ) ,
| x 1 ( Ω ) | 2 | f 1 2 | γ 1 2 ( ω 1 ω 2 ) 2 + γ 1 2 ( q + Ω ) 2 1 + Ω 2 ,
Ω = [ ω ω 2 + ( g 2 γ 1 ) ( ω 1 ω 2 ) 1 + q 2 ] γ 1 ( 1 + q 2 ) g 2 .
σ ( E ) = D 2 ( q + Ω ) 2 1 + Ω 2 ,
E n J n ( x ε 2 ) + A n H n ( 1 ) ( x ε 2 ) = D n J n ( x ε 1 ) ,
ε 1 E n r J n ( x ε 2 ) + ε 1 A n r H n ( 1 ) ( x ε 2 ) = ε 2 D n r J n ( x ε 1 ) ,
a n = ε 2 J n ( x ε 2 ) r J n ( x ε 1 ) ε 1 r J n ( x ε 2 ) J n ( x ε 1 ) ε 1 r H n ( 1 ) ( x ε 2 ) J n ( x ε 1 ) ε 2 H n ( 1 ) ( x ε 2 ) r J n ( x ε 1 ) ,
d n = J n ( x ε 2 ) r H n ( 1 ) ( x ε 2 ) H n ( 1 ) ( x ε 2 ) r J n ( x ε 2 ) J n ( x ε 1 ) r H n ( 1 ) ( x ε 2 ) ε 2 ε 1 H n ( 1 ) ( x ε 2 ) r J n ( x ε 1 ) .
| a n | 2 = 1 ( 1 + q n ( a ) 2 ) ( ϵ n ( a ) + q n ( a ) ) 2 ( 1 + ϵ n ( a ) 2 ) , | b n | 2 = 1 ( 1 + q n ( b ) 2 ) ( ϵ n ( a ) + q n ( b ) ) 2 ( 1 + ϵ n ( b ) 2 ) .
q n ( a ) = χ n ( x ) ψ n ( x ) , q n ( b ) = χ n ( x ) ψ n ( x ) ,
H = ( ω 1 k k ω 2 ) i ( γ 1 γ 1 γ 2 γ 1 γ 2 γ 2 ) .
k ( γ 1 γ 2 ) = ( ω 1 ω 2 ) γ 1 γ 2 ,
Q t o t 1 = Q r a d 1 + Q m a t 1 ,
P 2 ω = α k 2 Q 2 L 2 k 12 [ Q 1 L 1 k 1 P ω ] 2 .
t o u t = E o u t E