Guided-mode Resonance Filter for Micro-optic Spectrometer

Spectrometers are usually composed of diffraction gratings and prisms, and become large in size for high wavelength resolution. High-density integration of narrowband-pass filters of different wavelengths on a substrate can be expected to produce an ultra-compact spectrometer. We focused on guided-mode resonance (GMR) filters as such filters. The GMR filter consists of a thin-film waveguide and a sub-wavelength grating. GMR filters of different filtering wavelengths can be integrated in the same substrate because their periodic structure in refractive index spread along in-plane direction. On the other hand, GMR filter normally needs an aperture size and beam diameter of hundreds of microns and is not suitable for high-density integration. In this study, we proposed and investigated a GMR filter of a single-layer cross grating for a compact narrowband-pass filter. Different guided modes contributing to the broadband and narrowband reflection propagate orthogonally each other. By using simultaneously these guided modes, both reflections are cancelled at the competing wavelengths, resulting in high transmittance. In this paper, design examples with numerical simulation results are presented. It was predicted that a passband of 15 nm was obtained in the stopband of 200 nm for an incident beam of a 10-micron diameter.