Impact of mode regularization for quasinormal mode perturbation theories

Abstract

We give insight into the critical problem of an open resonator that is subject to a perturbation outside of its cavity region. We utilize the framework of quasinormal modes (QNMs), which are the natural mode solutions to the open boundary problem with complex eigenfrequencies. We first highlight some fundamental problems with currently adopted formulas using QNM perturbation theory, when perturbations are added outside the resonator structure and present a first potential step for solving this problem connected to a regularization of the QNMs. We then show an example for a full three-dimensional plasmonic resonator of arbitrary shape and complex dispersion and loss, clearly displaying the divergent nature of the first-order mode change predicted from QNM perturbation theory. Subsequently, we concentrate on the illustrative case of a one-dimensional dielectric barrier, where analytical QNM solutions are possible. We inspect the change of the mode frequency as function of distance between the cavity and another smaller barrier structure. The results obtained from a few QNM expansion are compared with exact analytical solutions from a transfer matrix approach. We show explicitly how regularization prevents a problematic spatial divergence for QNM perturbations in the far field, though eventually higher-order effects and multimodes can also play a role in the full scattering solution, and retaining a pure discrete QNM picture becomes questionable in such situations, since the input-output coupling ultimately involves reservoir modes.

17 pages, 11 figures

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Cited by in corpus (7)

• Classical Purcell factors and spontaneous emission decay rates in a linear gain medium
• Quantization of optical quasinormal modes for spatially separated cavity systems with finite retardation
• Extending completeness of the eigenmodes of an open system beyond its boundary, for Green's function and scattering-matrix calculations
• Rigorous theory of coupled resonators
• Gain-modified emission dynamics between two quantum emitters in a plasmonic gain cavity system
• Green's function expansion for multiple coupled optical resonators with finite retardation using quasinormal modes
• Position-Resolved Resonance Quantization for Lossy Cavities