Coupled-mode theory (CMT) can be modeled by properties of uncoupled resonant and/or guided mode without any complicated mathematical derivations. This provides for an intuitive grasp and a physical insight into the structural parameters for the efficient design and analysis of optical devices. The coupling between two waveguides is modeled through the formalism of a coupling-in-space and a resonant mode coupling with one or more ports in coupling-in-time. Rigorous mathematical derivations of CMT based on perturbation theory provide an accurate prospect of coupling properties.
In this thesis, the author designed various optical devices, which had a high performance, using coupled mode theory. In the model of the directional coupling of a resonant mode with two ports, the broadband absorption enhancement of a monolayer graphene embedded in the center of a cavity was experimentally demonstrated by using prism coupling to meet the critical coupling conditions. The experimental results were comparable to theoretical calculations in the visible range. A compact opto-electronic coupler between the side-polished fiber and the silicon waveguide was used to enhance the graphene. It had a wavelength selectivity and a low insertion loss that were suitable for a course wavelength division multiplexer (CWDM) photodetector and was modeled as a contra-directional coupler through periodic gratings. The ultra-wideband reflector was designed by using a new approach that tailors Fano resonance between the single guided mode resonance (GMR) mode and the Fabry-Perot resonance (FPR) background mode in the high contrast grating structure (HCGs). Analysis of the new method was based on a coupled mode theory for designing reflectors provided a more intuitive understanding of the device properties in comparison to previous methods.
Most of the previous investigations were conducted through modal analysis and modeling of coupled mode theory; and were verified through various numerical methods such as the transfer matrix method (TMM), the finite element method (FEM), and the rigorous coupled wave analysis (RCWA). The TMM calculated the absorption and reflectance of monolayer graphene through prism coupling into the dielectric mode. The FEM simulated the transmittance and absorption of two guided mode couplers and modal analysis. RCWA simulated the reflectance and transmittance of a wideband reflector using HCGs.