Publications

FDM Helmholtz Modeling of Finite Grating and Waveguide Width Effects on Resonant Subwavelength Grating Reflectivity

Peters, D.W.; Kemme, S.A.; Hadley, G.R.

Resonant subwavelength gratings (RSGs) may be used as narrow-band wavelength and angular reflectors. Rigorous coupled wave analysis (RCWA) predicts 100% reflectivity at the resonant frequency of an incident plane wave from an RSG of infinite extent. For devices of finite extent or for devices illuminated with a finite beam, the peak reflectivity drops, coupled with a broadening of the peak. More complex numerical methods are required to model these finite effects. We have modeled finite devices and finite beams with a two-dimensional finite difference Helmholtz equation. The effect of finite grating aperture and finite beam size are investigated. Specific cases considered include Gaussian beam illumination of an infinite grating, Gaussian illumination of a finite grating, and plane wave illumination of an apertured grating. For a wide grating with a finite Gaussian beam, it is found that the reflectivity is an exponential function of the grating width. Likewise, for an apertured grating the reflectivity shows an exponential decay with narrowing aperture size. Results are compared to other methods, including plane wave decomposition of Gaussian beams using RCWA for the case of a finite input beam, and semi-analytical techniques for the case of the apertured grating.