Applications of the SDTD method to the analysis and design of couplers for optical interconnects and optical communications

The main topic of this Thesis is the analysis of diffractive optical couplers by use of the Finite-Difference Time Domain Method (FDTD). The FDTD method is developed using the total-field scattered-field formalism (TF-SF) in conjunction with perfect matching absorbing layers (PML). In the same framework the spatially higher order FDTD (HO-FDTD) is developed and techniques (permittivity smoothing) for improving the accuracy of the FDTD and HO-FDTD are applied. The scattering problem of holographic and surface-relief gratings of finite length with finite-width incident beams is solved using the FDTD and HO-FDTD methods and the results are compared with the FDFD (Finite-Difference Frequency Domain Method) for the holographic gratings, and with the BEM (Boundary Element Method) for the surface relief gratings. In addition the FDTD results are compared with the RCWA (Rigorous Coupled Wave Analysis) method in the limit that the grating length and the beam width increases. Using the above FDTD methods holographic and surface-relief grating output couplers are analyzed with respect to their performance and directivity and the results are compared with the RCWA/LM (Rigorous CoupledWave Analysis/Leaky- Mode) method. Improved accuracy in the FDTD results is observed using the permittivity smoothing methods. The FDTD method with permittivity smoothing is also used for the study of input and output preferential grating couplers. In particular the volume holographic grating coupler: VHGC, the slanted surface relief grating coupler: SSRGC, the double corrugated surface relief grating coupler: DCSRGC and the reflecting stack surface relief grating coupler: RSSRGC are analyzed. Finally the FDTD method is generalized for nonlinear materials with dispersion, based on the GVADE (General Vector Auxiliary Differential Equation) algorithm in conjunction with the TF-SF technique and the CPML (Convolutional Perfect Matching Layers). Several test cases for soliton propagation of the new algorithm propagation are presented