improved couple mode theory

An improved coupled mode theory, grounded in the field matching technique, has been devised and validated for photonic devices with gradually varying structures, such as tapers. This novel approach addresses a limitation of traditional coupled mode theory, which approximates varying structures by dividing them into several uniform sections with different waveguide widths. This segmentation often leads to unphysical field reflections at the interfaces between adjacent sections, impacting both power propagation and reflection coefficients of the devices. To mitigate this issue, this paper introduces an improved formula that incorporates a coefficient matrix at the interfaces to seamlessly balance field discontinuities. Simulation results clearly show that this method significantly enhances both computational accuracy and efficiency compared to the conventional coupled mode theory approach