Coupled-Mode Theory Of Optical Waveguide Under Random Disturbances

Coupled-mode theory (CMT) has been developed from the orthogonal CMT to the nonorthogonal one as well as from the scalar CMT to the vector one during these scores of years. It was applied extensively in guided-wave optics as an effective mathematical tool for the analysis of the coupling between the modes. However, as far as we know, there has not been any report of the rigorous vectorial CMT in the relative publication at home and abroad. So, it is looked forward to being more perfect.In this thesis, beginning with the Maxwell Equation, we mainly do the following work based on the rigorous mathematical analysis:Firstly, we present the rigorous nonorthogonal vectorial CMT for the isotropic waveguide under isotropic disturbances and anisotropic disturbances respectively. During the derivation, it is fully reflected the property of the vector and the universal fitness without any approximation. When the isotropic waveguide is under the isotropic disturbances, the coupling term due to polarization, which is presented in the coupled-mode theory of the Wei-Ping Huang, isn't included in this rigorous vectorial coupled-mode theory, exactly, the rigorous vectorial CMT doesn't contain the coupling term due to polarization which is include in the scalar coupled-mode theory because this term is counteracted with the other coupling term neglected under weakly guiding approximation. As for anisotropic disturbances, we get the coupled-mode equations with arbitrary dielectric tensors. From them, we obtain the coupled-mode equations of the slowly varying term C (Z) which is more simplicity. Additionally, the single-mode fiber is taken as an example to judge which of the terms in the coupling coefficient should be retained under different conditions.Secondly, we derive the scalar CMT for the anisotropic optical waveguide under random disturbances from the Helmholtz equation. The physical meaning for each of the term in the coupling coefficient is stated. In particular,we advance firstly (as far as our knowledge), that the birefringence can cause additional coupling for the directional coupler. Then, taking the Ti-diffused LiNbO3 directional coupler and the Ti-diffused LiNbO3 with gradient refractive index for examples, we make the numerical simulation for the coupling coefficient or the propagation constant, which prove that the birefringence has played a crucial effect on the propagation constant and the coupling between the modes that we can not neglect.