Fano Approximation as a Fast and Effective Way for Estimating Resonance Characteristics of Surface Plasmon Structures

Developing efficient methods for evaluating resonance characteristics of resonance structures is of particular importance in sensing, spectroscopy, and optical filtration. In the past, the resonance characteristics were evaluated using exact approaches with time-consuming data post-processing algorithms. In this work, using the Fano approximation of the resonance line shapes appearing in spectra of planar plasmonic structures, we obtain analytical expressions for the surface field enhancement, resonance width and height, and sensitivity as functions of structural optical parameters. Approximate data for three-layer Au-, Ag-, Cu-, and Al-based structures in aqueous environment are compared with exact values to estimate the approximation error in the visible and infrared regions. We obtain overall good fits of the approximated estimations to the exact data over the wavelength regions considered, which ensure the validity of the Fano-based approach. Furthermore, by applying the Fano-based approach to gas sensing, we demonstrate that in the angular spectra of the three-layer structures, the excitation of propagating plasmons in the infrared region leads to narrower resonance line shapes due to the decrease in the plasmonic mode damping, resulting in higher sensitivities to changes in air environment. The Fano-based expressions tangibly increase the speed of calculations, provide an insight into fundamental aspects of resonance physics, and can be used for designing efficient sensing structures and characterizing optical changes in the environment.