Source-linked AI summary
Effective mode volumes and Purcell factors for leaky optical cavities
Philip Trøst Kristensen, Cole Van Vlack, Stephen Hughes
TL;DR
Finite-dissipation optical cavities are quasinormal modes with outgoing-wave boundary conditions, making the problem non-Hermitian and the common effective mode volume ambiguous. The paper introduces a corrected mode volume that accounts for long-distance behavior and can be evaluated with standard cavity-mode calculations.
Problem
For finite-Q cavities, the common effective mode-volume definition based on Hermitian inner products is ambiguous and formally diverges with integration volume.
Method
The paper defines cavity modes as quasinormal modes with outgoing-wave boundary conditions and introduces an inner product that accounts for their long-distance behavior.
Results
The corrected effective mode volume converges quickly and agrees with the correct value within the single-mode approximation, whereas the common definition increases with domain size.
Takeaways & Limitations
The corrected mode volume provides an unambiguous basis for describing light–matter interaction and computing Purcell factors in leaky optical cavities.
Takeaways & Limitations
The single-mode approximation has limited validity, with observable discrepancies for low-Q examples such as N=1 and N=2.
Abstract
from arXiv · showhide
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.