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We present an eigenmode based method to calculate the scattering-matrix and the optical cross-section of resonators. The eigenmodes of the system of interest are calculated via perturbation of an analytically solvable basis system using the resonant-state expansion (RSE). The eigenmodes form a complete set, and one can construct the Green’s function as a Mittag-Leffler series. The scattering-matrix can be uniquely linked to the Green’s function, and from it the cross-section can be found [2]. The non-resonant contribution to the scattering-matrix is fully taken into account via the Green’s function, thus there is no need for further fitting or other approximations. This method eliminates the overlap integrals between the excitation and the mode fields used in other approaches, making it computationally highly efficient. For illustration, the cross-section of a dielectric sphere and a cylinder is calculated over a broad frequency range. The perturbed modes form a complete set inside the basis system, both inside and outside of the resonator [3]. The impact of this on the scattering calculation and on other applications is also discussed.
[1] Muljarov, E.A., Langbein, W. and Zimmermann, R., 2010. Brillouin-Wigner perturbation theory in open electromagnetic systems. EPL (Europhysics Letters), 92(5), p.50010.
[2] Lobanov, S.V., Langbein, W. and Muljarov, E.A., 2018. Resonant-state expansion of three-dimensional open optical systems: Light scattering. Physical Review A, 98(3), p.033820.
[3] Sztranyovszky, Z., Langbein, W. and Muljarov, E.A., 2025. Extending completeness of the eigenmodes of an open system beyond its boundary, for Green's function and scattering-matrix calculations. Physical Review Research, 7(1), p.L012035.