J. Eur. Opt. Society-Rapid Publ. 22, 23( 2026) 233
Fig. 1. Dependence of the Fano parameter q on the phase shift of the continuum mode, with the resulting line shapes: asymmetric for q ± 1 and quasi-Lorentzian for q = 0. interferometers( FPI), and Bragg gratings. Fano resonance was first demonstrated by Ugo Fano in his investigation of inelastic electron scattering by helium [ 12 ], revealing an asymmetric line shape with a high-quality factor. It was established that this resonance arises when a discrete mode spectrum interferes with a continuous mode spectrum. This interaction is described by the spectrum r( E), as expressed in equation( 1) [ 13 ].
rðEÞ ¼ 4 sin 2 ðq þ XÞ2 /
1 þ X: ð1Þ 2
Here, q = cot / is the Fano parameter, with / the continuum phase shift and E the spectral energy. The dimensionless variable X = 2( E – E₀)/ C is defined by the resonance energy E₀ and linewidth C. Originally introduced for absorption spectra, the model also describes transmission, reflection, and scattering, highlighting its versatility in optical devices. The parameter q governs spectral asymmetry: for q ± 1, strong discrete – continuum coupling produces asymmetric line shapes, while for | q | 1orq 0, weaker coupling yields Lorentzian-like profiles. In Figure 1 shows the dependence of the Fano parameter q on the phase shift.
3 Historical overview
Between 2005 and 2015, only a limited number of papers were published in this field, reflecting the exploratory nature of Fano resonance at the time and the early emergence of its application in fiber-based structures. Figure 2 presents a timeline of the annual number of articles on Fano resonance in fiber-optic systems published between 2005 and 2025.
Chiba et al. [ 14 ] reported that Fano resonances can be induced in a multimode tapered fiber waveguide coupled with a high-Q microspherical cavity, without requiring any additional elements such as reflectors or delay optics. Steinvurzel et al. [ 15 ] demonstrated that the scattering resonances of a single cylinder correspond to Fano resonances, which indeed appear in the loss spectra of solid-core photonic bandgap fibers( PBFs). Totsuka et al. [ 16 ] performed Fano resonance to yield coupled-resonator-induced transparency. Vincetti and Setti [ 17 ] reported that Fano resonances between hollow-core modes and higher-order dielectric modes occur within the transmission bands. Li et al. [ 18 ] observed Fano resonances in a single whispering-gallery microresonator. Furthermore, Vincetti and Setti [ 19 ] showed that the additional losses in Kagome fiber designs arise from Fano resonances between core modes and cladding modes exhibiting strong spatial dependence. Chang and Solgaard [ 20 ] presented Fano resonances in integrated silicon Bragg reflectors, highlighting their potential for sensing applications. Finally, Yu et al. [ 21 ] reported the control of Fano resonances in photonic crystal structures and demonstrated their application in ultrafast optical switching. Yang et al. [ 22 ] demonstrated an aerostatically tuned microbubble whispering-gallery resonators to obtain an electro-magnetic-induced transparency and Fano-like lineshapes to sensing application. Over the last decade, Figure 3 highlights a marked increase in the use of resonant waveguide structures in optical fibers, underscoring a strong potential that remains not yet fully explored in this field.
In 2016, Miao et al. [ 23 ] reported the evolution of Fano resonance in a thin fiber taper – coupled cylindrical microcavity. Unlike enclosed microcavities, the cylindrical configuration supported both localized whispering gallery modes( WGMs) and delocalized radiation modes. Zhao et al. [ 24 ] demonstrated a simple method to achieve Fano-like resonance by coupling a microsphere resonator with a fiber Mach – Zehnder interferometer( FMZI). In their configuration, a tapered microfiber was integrated into one arm of the interferometer to enable evanescent coupling with the microsphere resonator. Gu et al. [ 25 ] investigated a fiber loop laser stabilized by Fano resonance in a metallic grating – coupled resonator, demonstrating improved spectral stability. Liao et al. [ 26 ] developed a technique to reduce the spectral density of a microbottle resonator( MBR) by depositing UV-curable adhesive droplets near the resonator’ s central region, effectively degrading the Q-factors of high-order bottle modes and enhancing resonance selectivity.
In 2017, several studies expanded the understanding and applications of Fano resonance in optical systems. Lin et al. [ 27 ] proposed a novel microstructured optical fiber( MOF) for multichannel sensing based on Fano resonance among different WGMs propagating through the fiber. The proposed MOF comprised multiple capillary channels of varying diameters arranged within a tubular framework. Miao et al. [ 28 ] demonstrated a ring fiber laser structure based on a thin fiber taper – coupled microcylinder system functioning as a transmissive optical filter that selectively allowed narrowband modes to propagate. Li et al. [ 29 ] carried out theoretical and numerical investigations of three distinct types of Fano resonances, each arising from different physical mechanisms, in a plasmonic resonator composed of two circular cavities. Zhang et al. [ 30 ] proposeda cone-shaped inner-wall coupler to efficiently excite WGMs in a microsphere resonator, while Zhang et al. [ 31 ] reported