How to calculate the pole expansion of the optical scattering matrix from the resonant states

Abstract

We present a formulation for the pole expansion of the scattering matrix of open optical resonators, in which the pole contributions are expressed solely in terms of the resonant states, their wave numbers, and their electromagnetic fields. Particularly, our approach provides an accurate description of the optical scattering matrix without the requirement of a fit for the pole contributions, or the restriction to geometries, or systems with low Ohmic losses. Hence, it is possible to derive the analytic dependence of the scattering matrix on the wave number with low computational effort, which allows for avoiding the artificial frequency discretization of conventional frequency-domain solvers of Maxwell's equations and for finding the optical far-and near-field response based on the physically meaningful resonant states. This is demonstrated for three test systems, including a chiral arrangement of nanoantennas, for which we calculate the absorption and the circular dichroism.

Modeling electromagnetic resonators using quasinormal modes

“…The problem is closely connected to that of scattering calculations, which have been treated in a number of ways in Refs. [68,54,69,41,70]. Similar to the divergence at large distances, the dramatic increase of the electromagnetic feedback close to metal surfaces cannot be captured by a single QNM.…”

“…As we have seen in Section 3.4, the QNMs are intimately related to the poles of the Green tensor. Therefore, in general, it is possible to use the QNMs to calculate the scattered field resulting from a given input field, an exercise generally referred to as the construction of the scattering matrix [68,41,69] and directly related to calculations of experimentally relevant quantities such as scattering and extinction cross sections [54,70]. Instead of treating the problem in a scattering framework, one can also take the point of view, that the electromagnetic resonator can act as a temporal energy storage when excited by an incoming pulse.…”

Modeling Optical Materials at the Single Scatterer Level: The Transition from Homogeneous to Heterogeneous Materials

“…In this paper, we have focused on random nanocomposites that contain nanospheres at volume fractions below because this range is experimentally accessible [ 43–49 ] and offers an unprecedented control of the magnitude and dispersion of the effective refractive index. [ 19 ] However, our approach can be readily generalized: First, to other types of scatterers, including atoms, molecules, [ 22 ] as well as nanoparticles with other shapes [ 8,29–31,65,66 ] and, second, also to other kinds of particle distributions. Specifically, both random packings [ 13,67–70 ] as well as the transition regime between ordered and disordered packings [ 71–74 ] exhibit a fascinating complexity.…”

Full electromagnetic Green's dyadic of spherically symmetric open optical systems and elimination of static modes from the resonant-state expansion

“…The electromagnetic dyadic Green's function (GF), introduced by Schwinger more than 70 years ago, is a tensor determining the electric and magnetic fields generated by a point-like source, such as a dipole, an oscillating charge, or a current. The GF contains a complete information about the physical system and provides access to any observable, such as electromagnetic near and far field distributions [1,2], total radiation intensity and Purcell's factor [3,4], optical scattering matrix and scattering cross sections [5,6].…”

“…In particular, the quality factor of a RS is given by half of the ratio of real to imaginary part of its eigenfrequency. The concept of RSs has recently become a powerful tool widely used in the literature for studying the spectral properties of open optical systems and for describing resonances observed in the optical spectra in a mathematically rigorous way [4][5][6][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”