Analysis of linear and nonlinear coupled dielectric waveguides

Graduation date: 1993Multiport network functions, such as impedance matrix\ud parameters and scattering parameters, of general multiple\ud coupled slab waveguides are derived in terms of the normal\ud mode parameters of the system. These characteristic normal\ud mode parameters include the propagation constants, the\ud modal impedances, and the eigenvector matrices. It is\ud shown that the results of the analysis for four and six\ud port optical directional couplers based on this approach\ud are in good agreement with those based on the conventional\ud coupled mode theory for matched systems. In addition,\ud unlike the coupled mode theory, this approach allows for\ud the inclusion of the structure terminations or the boundary\ud conditions and can be readily used to calculate the near\ud and far end crosstalk in optical interconnects. Examples of general asymmetric two-waveguide and symmetric three-waveguide\ud couplers are included to demonstrate the\ud applications and usefulness of this method.\ud The conventional matrix method algorithm which has\ud been used to study graded index and nonlinear waveguides is\ud modified here for enhanced accuracy and efficiency. This\ud enhanced algorithm is used to investigate the propagation\ud characteristics and the nonlinear switching behavior of\ud general five-layer waveguide structures with self-defocusing\ud nonlinear coupling media. The saturation\ud effects of the nonlinear media are incorporated by using a\ud two-level saturation model. The numerical results obtained\ud for a multiple quantum well directional coupler are shown\ud to be in agreement with published experimental data. This\ud method is also applied to analyze a nonlinear three-waveguide\ud coupler with self-defocusing coupling media. The\ud results show the power dependent switching characteristics\ud when the light is coupled to the input of an outside guide,\ud whereas a quasi-linear switching behavior is obtained for\ud excitation to the center guide