J. Eur. Opt. Society-Rapid Publ. 22, 23( 2026) 237
Fig. 5. Typical configurations of WGM resonators coupled to optical fibers to excite Fano resonance.
parameters for obtaining a well-defined Fano spectrum on an optical spectrum analyzer( OSA). Based on these simulations, the structure’ s performance as a refractive-index sensor was demonstrated both theoretically and experimentally, highlighting its advantages as a sensing element and showcasing the potential of this new configuration to the scientific community.
Fig. 6. Dynamic behavior of the Fano-FBG structure, where the interference between Fresnel and Bragg reflections results in the emergence of a Fano-like reflected spectrum.
ity [ 91 ]. Another approach relies on Fabry – Pérot interferometers( FPIs) coupled to a WGM microsphere [ 42 ], or combined with FBGs [ 49, 92, 93 ], where the interaction between the two elements induces a Fano-like resonance. FPI-based schemes have also been enhanced by integrating a gold plasmonic metasurface on the facet [ 94 ]. In contrast, Sagnac interferometers are less commonly used to induce Fano resonance in optical fibers, being more frequently reported in silicon waveguides [ 95 ].
4.4 Bragg gratings structures
This review briefly addresses one of the most recent works in optical fiber sensors, published in 2024, which proposes a Fano-like FBG structure, as illustrated in Figure 6 [ 53 ]. This FBG structure is a phase-shift grating operated in reflection, in which the last period is modified to introduce the phase shift; that is, its periodicity is shorter than the nominal FBG period. This study investigated a Fano- FBG configuration in which the reflectivity at the fiber end was kept fixed while the FBG reflectivity was varied. The inverse case was then analyzed: the FBG reflectivity was held constant, and the fiber-tip reflectivity was varied externally. The objective was to identify the optimal
4.4.1 An analytical approach to modeling the Fano-like FBG
The interferometric phenomenon that yields the FBG spectrum can be described using coupled-mode theory, as presented by Sakhabutdinov et al. [ 49 ]. Another possibility is to study the interaction between the incident electric field amplitude E and the grating structure. In this approach, the model is based on summing the contributions of the waves reflected at each refractive-index perturbation introduced by the grating modulation. The grating period between the successive reflective points K introduces a phase shift of u = b( 2K), where b = 2pn eff / k 0 the propagation coefficient, n eff the effective refractive index, and k 0 the vacuum wavelength. To model the superposition of reflections, N reflective points are defined to simulate the FBG, each characterized by transmission and reflection coefficients of t K = 2n 1 n 2 / n 1 + n 2 and r K =( n 1 � n 2)/( n 1 + n 2), respectively, where n 1 is the optical fiber core refractive index and n 2 is the grating refractive index.
The Fano-like resonance arises from interference between a discrete spectrum and a continuum spectrum. In this framework, a spacing is introduced between the grating’ slastpitchandthefiber tip, with a length ranging from 0andK. The continuum mode originates itself from the Fresnel reflection at the fiber tip across this final spacing,, with reflection coefficient of R U = [( n eff � n e)/( n eff + n e)] 2, wheren e is the environment RI. The phase shift is determined by this specific length U, which in turn controls the tuning of the Fano asymmetry parameter q. Equations( 2) and( 3) provide the mathematical model obtained by summing the reflected electromagnetic waves, that reproduces the Fano-like asymmetrical spectrum generated by the Fano-FBG. In this numerical model, the FBG response is expressed as a geometric series, with the