Broadening the angular tolerance in two-dimensional grating resonance structures at oblique incidence

Abstract

Broadening of the angular response of two-dimensional (2D) guided mode resonant spectral filters at oblique incidence is investigated. Coupling into multiple fundamental guided resonant modes having the same propagation constant but propagating in different planes (inherent multiple-plane diffraction by 2D gratings) is shown to significantly broaden the angular tolerance while maintaining narrow linewidth. Resonances have symmetric and broad angular responses when the incident wave is coupled to four resonant modes in a structure with a hexagonal grating pattern. Further broadening is implemented by enhancing the second Bragg diffraction of the 2D grating structure. Resonance with a narrow spectral linewidth $\left(\Delta {\lambda }_{\text{FWHM}}\sim 1.6\times {10}^{-4}{\lambda }_0\right)$ and angularly tolerant to an $\sim 6\mu \text{m}$ beam diameter is obtained. A second approach utilizing a dual 2D grating configuration with a second grating on the substrate side is shown to increase the lateral confinement, causing the merging of two successive resonant bands. This results in further improvement of the angular∕spectral linewidth ratio by $\sim 80\%$.