Mapping complex mode volumes with cavity perturbation theory

K G Cognée,D Balestri,A F Koenderink,F La China,M Gurioli,F Intonti,W Yan,P Lalanne

doi:10.1364/optica.6.000269

Abstract

Microcavities and nanoresonators are characterized by their quality factors Q and mode volumes V. While Q is unambiguously defined, there are still questions on V and in particular on its complex-valued character, whose imaginary part is linked to the non-Hermitian nature of open systems. Helped by cavity perturbation theory and near field experimental data, we clarify the physics captured by the imaginary part of V and show how a mapping of the spatial distribution of both the real and imaginary parts can be directly inferred from perturbation measurements. This result shows that the mathematically abstract complex mode volume in fact is directly observable.

Highlights

Where ε is the permittivity of the unperturbed cavity, ε0 and μ0 are vacuum permittivity and permeability, and Ẽ and Hare the unperturbed-cavity-mode electric and magnetic fields
We have introduced the mode volume V, the classical real quantity used throughout in quantum electrodynamics [8,9] that gauges the coupling of an emitting dipole with the cavity mode
With the recent advent of theoretical results on the normalization of leaky resonator modes [8,19,20], it becomes evident that cavity perturbation theory cannot rely a normalization based on energy but on quasinormal-mode (QNM) formalism to account for the non-Hermitian character of the problem

Summary

Introduction

Where ε is the permittivity of the unperturbed cavity, ε0 and μ0 are vacuum permittivity and permeability, and Ẽ and Hare the unperturbed-cavity-mode electric and magnetic fields. The perturbation results in a modification ∆ωof the initial complex resonance frequency ω ≡ ω0 + i γ0⁄2 of the unperturbed cavity mode, Re(Δω) and Im(Δω) respectively representing the frequency shift and linewidth change. We rather consider a spatially-dependent mode volume to directly take into account the dependence of ∆ωwith the perturber position.

Results

Conclusion