Effect of dielectric constant tuning on a photonic cavity frequency and Q-factor.

For practical applications in quantum electrodynamics, it has been proposed to produce frequency tuning or Q-switching by dynamically changing the dielectric constant around a nano-cavity. Local changes in the dielectric constant of a photonic cavity with finite-lifetime, may affect not only the frequency of electromagnetic cavity modes but also their quality-factor (Q). Thus, it is important to have prediction capability regarding the combined effect of these changes. Here perturbation theory, usually applied to eigenmodes with real eigenvalues, is formulated in the complex domain, in which the eigen-frequency imaginary part is related to the Q-factor. Normalizable leaky modes, and bi-orthogonality in a finite volume are the basis for such a formulation. We introduce such capabilities by presenting semi-analytical expressions of first order perturbation analysis for a 3D cavity with radiation losses. The obtained results are in good agreement with numerical calculations.