Near-field to far-field transformations of optical quasinormal modes and efficient calculation of quantized quasinormal modes for open cavities and plasmonic resonators
Juanjuan Ren, Sebastian Franke, Andreas Knorr, Marten Richter, Stephen Hughes
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 (in regimes where this is possible), and we demonstrate several order of magnitude improvement for the calculation runtimes. We also introduce an efficient pole approximation for computing the quantized quasinormal mode parameters. Using this approach, we show how to compute regularized quasinormal modes and quantum optical parameters for a full 3D metal dimer (with various material losses) 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, designed to yield a Purcell factor in excess of 1 million. In the latter example, we show how to compute the quantized mode 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.