Effective mode volumes and Purcell factors for leaky optical cavities

TL;DR

This paper redefines the concept of effective mode volume in leaky optical cavities with dissipation, providing a rigorous and unambiguous way to compute Purcell factors and related optical effects.

Contribution

It introduces a new definition of effective mode volume suitable for non-Hermitian, leaky cavities, resolving ambiguities in traditional approaches.

Findings

Proposes an alternative mode volume definition applicable to dissipative cavities.

Enables accurate calculation of Purcell factors in leaky optical systems.

Provides a practical method compatible with existing mode calculation techniques.

Abstract

We show that for optical cavities with any finite dissipation, the term "cavity mode" should be understood as a solution to the Helmholtz equation with outgoing wave boundary conditions. This choice of boundary condition renders the problem non-Hermitian, and we demonstrate that the common definition of an effective mode volume is ambiguous and not applicable. Instead, we propose an alternative effective mode volume which can be easily evaluated based on the mode calculation methods typically applied in the literature. This corrected mode volume is directly applicable to a much wider range of physical systems, allowing one to compute the Purcell effect and other interesting optical phenomena in a rigorous and unambiguous way.