Optimally designed narrowband guided-mode resonance reflectance filters for mid-infrared spectroscopy

An alternative to the well-established Fourier transform infrared (FT-IR) spectrometry, termed discrete frequency infrared (DFIR) spectrometry, has recently been proposed. This approach uses narrowband mid-infrared reflectance filters based on guided-mode resonance (GMR) in waveguide gratings, but filters designed and fabricated have not attained the spectral selectivity (≤ 32 cm^-1) commonly employed for measurements of condensed matter using FT-IR spectroscopy. With the incorporation of dispersion and optical absorption of materials, we present here optimal design of double-layer surface-relief silicon nitride-based GMR filters in the mid-IR for various narrow bandwidths below 32 cm^-1. Both shift of the filter resonance wavelengths arising from the dispersion effect and reduction of peak reflection efficiency and electric field enhancement due to the absorption effect show that the optical characteristics of materials must be taken into consideration rigorously for accurate design of narrowband GMR filters. By incorporating considerations for background reflections, the optimally designed GMR filters can have bandwidth narrower than the designed filter by the antireflection equivalence method based on the same index modulation magnitude, without sacrificing low sideband reflections near resonance. The reported work will enable use of GMR filters-based instrumentation for common measurements of condensed matter, including tissues and polymer samples.