Efficient near-field to far-field transformations for quasinormal modes of optical cavities and plasmonic resonators

TL;DR

This paper introduces an efficient method for transforming near-field to far-field data of optical quasinormal modes, enabling rapid computation of quantum optical parameters in complex nanostructures with high accuracy.

Contribution

The authors develop a novel near-field to far-field transformation technique for quasinormal modes, significantly improving computational efficiency and enabling practical analysis of complex 3D nanostructures.

Findings

Achieved several orders of magnitude faster calculations compared to Dyson equation methods.

Successfully computed quantum optical parameters for complex structures in under one minute.

Validated results with full Maxwell dipole simulations showing excellent agreement.

Abstract

We describe an efficient near-field to far-field transformation for optical quasinormal modes, which are the dissipative modes of open cavities and plasmonic resonators with complex eigenfrequencies. As an application of the theory, we show how one can compute the reservoir modes (or regularized quasinormal modes) outside the resonator, which are essential to use in both classical and quantum optics. We subsequently demonstrate how to efficiently compute the quantum optical parameters necessary in the theory of quantized quasinormal modes [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)]. To confirm the accuracy of our technique, we directly compare with a Dyson equation approach currently used in the literature (in regimes where this is possible), and demonstrate several order of magnitude improvement for the calculation run times. We also introduce an efficient pole approximation for computing the quantized quasinormal mode parameters, since they require an integration over a range of frequencies. Using this approach, we show how to compute regularized quasinormal modes and quantum optical parameters for a full 3D metal dimer in under one minute on a standard desktop computer. Our technique is exemplified by studying the quasinormal modes of metal dimers and a hybrid structure consisting of a gold dimer on top of a photonic crystal beam. In the latter example, we show how to compute the quantum optical parameters that describe a pronounced Fano resonance, using structural geometries that cannot practically be solved using a Dyson equation approach. All calculations for the spontaneous emission rates are confirmed with full-dipole calculations in Maxwell's equations and are shown to be in excellent agreement.