Abstract
We report a theoretical framework to explain the characteristics of Fabry-Perot (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.
Highlights
Many sensors operate as resonators with the analyte perturbing the resonant conditions
From a conceptual point of view the present sensor differs from sensors such as an Surface Plasmon Resonance (SPR) sensors in that the inherent tradeoffs in such systems do not apply in the open resonator structure
In an SPR sensor the gold layer forms the sensor surface only responds to the changes in the external environment whereas in the present system the resonant structure itself changes with the analyte
Summary
Many sensors operate as resonators with the analyte perturbing the resonant conditions. There is a mode cut-off for the FP modes occurring at the incident wave vector labeled as ‘neff’ as shown in the figures This incident angle the effective medium does not support propagating modes for the 0th order, so the structure does not function as a resonant cavity, so the FP approximation breaks down. Sufficiently large index contrast and a near-wavelength grating period condition more than one Bloch mode is present and the situation strongly deviates from the effective medium condition To analyze this effect, two sets of grating structures with identical parameters except the refractive index of grating material n2 were different with the n2 of 1.4283 and 3.48 for the low contrast and the high contrast cases respectively; varying hg, dm of 48 nm, λg of λ0 (near-wavelength condition), fill factor of 0.5, n3 of 1.00, =0 and TM polarization light. We confine our discussion of sensor applications to low contrast structures
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