Spectral Collocation and FDTD Approaches for the Design of Focusung Grating Couplers

Theoretical and numerical investigations on sub-wavelength waveguide focusing grating couplers are presented. The analyses are based on two approaches, the spectral collocation method and the finite-difference time-domain method. The methods solve the full-vectorial time-domain Maxwell equations. Their applicability to study the properties of general diffractive optical elements with complex features in the sub-wavelength regime is demonstrated, and their performance is compared. The design of a focusing coupler, integrated in multilayer planar waveguide technology is demonstrated numerically, and the optical diffraction physics are discussed, as classical methods based on scalar geometrical ray optics fail to predict the nearfield optical electromagnetic characteristics when local modulation changes in the surface profile are significant, altering the propagation of the fundamental mode.Key words: Diffractive Optics, focusing grating couplers, sensors, omputational models in Optics.