Analysis of anti-resonant reflecting optical waveguide grating using the method of lines

This research work is related to the modeling of integrated optical waveguides, waveguide discontinuities and gratings using the Method of Lines (MoL). The basic three-point central-difference approximation of the ∂2/∂ x2 operator used in the MoL is extended to five-point and seven-point approximations with appropriate interface conditions for the E and H fields. This gives us improved numerical accuracy and reduced matrix size. It is applied to find the modal field and effective indices of the TE and TM Modes in different multi-layer optical waveguldes. Single and multiple waveguide discontinuity problems are solved using the MoL. The Perfectly Matched Layer (PML) absorber is used to absorb the radiated fields from discontinuities. The MoL is applied to periodic waveguide gratings and their reflection and transmission spectra are calculated. A fast and stable Cascading and Doubling Algorithm Z'S used to model long gratings having thousands of periods. The MoL is applied to model a multi-layer ARROW structure. Periodic corrugations are introduced on the top surface of ARROW for possible optical filtering applications. The reflection and transmission spectra of the resulting ARROW Grating are calculated for different amount of loss in the ARROW with different number of grating periods and different groove depths.