Coupled Cavity Model: Correctness and Limitations

TL;DR

This paper analyzes the correctness and limitations of the classical Coupled Cavity Model, revealing the existence of spurious solutions in infinite resonator chains that hinder certain approximation methods.

Contribution

It identifies the presence of spurious solutions in the model's characteristic equation and discusses their impact on analytical approaches.

Findings

Spurious solutions exist in the characteristic equation for infinite resonator chains.

These solutions do not affect numerical calculations but complicate approximate methods.

Limitations of the classical model are highlighted for chains with varying parameters.

Abstract

Results of analysis of correctness and limitations of the classical Coupled Cavity Model are presented in the paper. It is shown that in the case of an infinite chain of resonators, there are spurious solutions of the characteristic equation. These spurious solutions do not violate the correctness of direct numerical calculations, but their existence makes it difficult (or even impossible) to use approximate WKB methods for analyzing chains with slowly varying parameters.