FDM Helmholtz modeling of finite grating and waveguide width effects on resonant subwavelength grating reflectivity

David W Peters; Shanalyn A Kemme; G. Ronald Hadley

doi:10.1117/12.506119

10 November 2003 FDM Helmholtz modeling of finite grating and waveguide width effects on resonant subwavelength grating reflectivity

David W Peters, Shanalyn A Kemme, G. Ronald Hadley

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Proceedings Volume 5177, Gradient Index, Miniature, and Diffractive Optical Systems III; (2003) https://doi.org/10.1117/12.506119
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

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 a semi-analytical techniques for the case of the apertured grating.

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David W Peters, Shanalyn A Kemme, and G. Ronald Hadley "FDM Helmholtz modeling of finite grating and waveguide width effects on resonant subwavelength grating reflectivity", Proc. SPIE 5177, Gradient Index, Miniature, and Diffractive Optical Systems III, (10 November 2003); https://doi.org/10.1117/12.506119

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