A Discrete Transmission-Matrix Method for Modeling the Distributed Feedback Arising from Continuously Varying Refractive Index Profiles

摘要

Several methods exist for modeling the Fresnel reflectance arising from arbitrary refractive index profiles. In many cases, the calculation can be done analytically; however, a numerical method must be employed for more complicated scenarios. The transmission matrix is an analytic method which is well suited for modeling reflection at abrupt interfaces. In this work, we develop a numerical approach, relying on the transmission matrix method, which can properly model the reflection and transmission properties of a continuously varying index profile. This approach has been applied to high power semiconductor lasers by modeling the built-in distributed feedback arising from the continuously mismatched wave impedance along the cavity length caused by a non-uniform temperature profile.