2024/11/12 by Jonathan Lin, Lin, Jonathan
Engineering · Physics and Astronomy · #FOS: Physical sciences #Gyrotron and Vacuum Electronics Research #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Optics (physics.optics) #Particle Accelerators and Free-Electron Lasers #Particle accelerators and beam dynamics
paper · pdf · doi:10.48550/arxiv.2411.08118
openalex publication_date 2024/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Coupled-mode theory (CMT) is a powerful tool for simulating near-harmonic systems. In telecommunications, variations of the theory have been used extensively to study waveguides, both analytically and through numerical modelling. Analogous mathematical techniques to the CMT are also widely used in quantum mechanics. The purpose of this work is to collect different formulations of the CMT and their underlying connections to quantum mechanical techniques, and to showcase their utility in modelling slowly varying waveguides including directional couplers and photonic lanterns. My choice of example waveguides is motivated by the astronomical applications of such devices in starlight nulling, wavefront sensing, and high-resolution spectroscopy. I first provide a brief review of the standard form of the CMT, applicable for waveguides with fixed eigenmodes. Next, I show that the CMT also applies for slowly varying waveguides, and demonstrate the close relation between the CMT and several well-known approximation methods from quantum mechanics, as well as concepts like geometric phase. Finally, I present a verification of my analysis, in the form of the numerical package cbeam.