Analysis of Open Grating-Based Fabry–Pérot Resonance Structures With Potential Applications for Ultrasensitive Refractive Index Sensing

Abstract

We report a theoretical framework to explain the characteristics of Fabry-Pérot (FP) resonances excited in a thin film-based grating consisting of a thin gold layer and a rectangular dielectric grating in the sub-wavelength and near-wavelength grating regimes. The zeroth-order diffraction inside the grating layer forms an FP resonant cavity with effective refractive index arising from an averaging effect between the refractive indices of the grating material and the filling material between the grating grooves. A simplified model based on Fresnel equations and phase matching condition is proposed to predict the FP resonant mode for the grating structure, this is compared with rigorous coupled-wave analysis to determine its range of validity. We also compare the performance of the proposed structure with other thin film-based interferometers for refractive index sensing applications, in terms of, sensitivity, full width at half maximum, figure of merit and dynamic range. The proposed structure has a full width at half maximum around 10 times to 60 times narrower than conventional surface plasmon resonance and conventional FP resonators. Thus, the figure of merit is higher than Kretschmann based surface plasmon resonance and FP structures by a factor of 20 and 2 respectively with a wider dynamic range. The total energy stored in the grating resonant cavity is 5 and 20-fold greater than the surface plasmon resonance configuration and the conventional FP structures. Since the resonator discussed here is an open structure, it is far better suited for liquid sensing compared to a closed FP structure.

Fabry–Perot Resonance in 2D Dielectric Grating for Figure of Merit Enhancement in Refractive Index Sensing

“…In Sasivimolkul et al [ 13 ], we have recently reported an effective refractive index model that the FP mode position excited through 1D grating can be located using an asymmetric FP condition as expressed in Equation (3), where the grating layer can be simplified by a homogeneous layer of effective refractive index ( n eff ) and the layer thickness h g as depicted in Figure 4 . …”

“…The n eff for the 1D grating can be expressed as shown in Equation (5) [ 13 ]. It is crucial to point out that this n eff equation allows us to calculate and predict the mode position with no need for grating simulation software.…”

“…Recently, in Sasivimolkul et al [ 13 ], we have reported that the optimum gold thickness for the minimum reflectance dip was different for the TM polarization and TE polarization due to the different loss of energy dissipation of each polarization [ 13 ]. Therefore, the optimum gold thicknesses for TM polarization and TE polarization d g of 48 nm and 38 nm, respectively, were employed in this study.…”

“…At present, there are several types of resonators, including thin-film resonators [ 10 ], ring resonators [ 11 ], and grating waveguides [ 12 ]. Our previous work [ 13 ] has identified that subwavelength and near wavelength dielectric grating can serve as Fabry–Perot (FP) resonant cavity. The FP resonances excited in a thin film-based grating consisting of a thin gold layer and a one-dimensional (1D) rectangular dielectric grating, as shown in Figure 1 a.…”

“…In our previous work [ 13 ], we reported that the thin film-based grating resonator gave a narrow full-width at half maximum (FWHM) and better figure of merit (FOM), which leads to better refractive index sensing capability for small changes in the sample refractive index region. However, it has slightly lower sensitivity than the SPR, as shown in Figure 1 c.…”