Modeling of Multimodal Scattering by Conducting Bodies in Quantum Optics: the Method of Characteristic Modes

We propose a numerical technique for modeling the quantum multimode light scattering by a perfectly conducting body. Using the novel quantization technique, we give the quantum adaptation of the characteristic mode approach widely used in the classical electrodynamics. The method is universal with respect to the body's configuration, as well as its dimensions relative to the wavelength. Using this method and calculating the first- and the second-order field correlation functions, we demonstrate how scattering affects quantum-statistical features of the field. As an example, we consider scattering of the two single-photon incident Gaussian beams on the cylinder with circular cross-section. We show that the scattering is accompanied by the two-photon interference and demonstrates the Hong-Ou-Mandel effect. It is shown, that the scattered two-photon field and its correlations are able to manifest a varying directive propagation, which is controllable by various means (angles of incidence, configuration of the body, relations between its sizes with the frequency). We expect that this method will be useful for designing quantum-optical devices.