Approach to calculate normal modes by decomposing the dyadic Green’s function

Abstract

Normal mode is a very fundamental notion in quantum and classical optics. In this paper, we present a method to calculate normal modes by decomposing dyadic Green's function, where the modes are excited by dipoles. The modes obtained by our method can be directly normalized and their degeneracies can be easily removed. This method can be applied to many theoretical descriptions of cavity electrodynamics and is of interest to nanophotonics.

Regularized quasinormal modes for plasmonic resonators and open cavities

“…Regarding the issue of obtaining the complexfrequency Green function in FDTD, there has been some work for studying Casimir effects 61,62 , where a mathematically modified permittivity function is used to map the problem onto a complex frequency space, but it is limited to positive imaginary parts for the frequencies and therefore cannot be adopted to complex frequencies associated with QNMs. In an earlier attempt to extract leaky mode behaviour in FDTD 63 , a simple dipole-response normalization technique was proposed for leaky photonic crystal cavities, but a normal mode picture was taken; indeed, a real-valued mode function was obtained that is known to lack the correct modal phase information (of an open cavity), and the method was cited to apply to dielectric structures only, for reasons that were not explained. The phase of the QNM is a necessity, e.g., for obtaining the correct Purcell factor as a function of position, particularly in plasmonics where very low quality factors are involved.…”

Leaky-mode expansion of the electromagnetic field inside dispersive spherical cavity

“…The main conceptual difference form the standard approach to the completeness problem 29,30 is that we analyze the convergence of the series directly, without invoking any properties of Green's functions. 28,34 The advantage of the present method is that it is more general. Specifically, we do not need to assume that the function to be represented as a resonant-state expansion is a product of time-evolution in the system (i.e., optical cavity in the present case or a Hamiltonian in the quantum case) with modified, outgoing boundary conditions.…”

“…There are also some technical issues that are subject to debate and different treatments. For instance, various ways of mode-volume calculation 26 and quasi-normalization 27,28 have been described and contrasted in the literature, oftentimes re-inventing methods established previously or in different fields.…”