Multimode Quantum Light Scattering: Method of Characteristic Modes

We developed a theory of multimode quantum light scattering based on the characteristic modes, which are widely used in classical electrodynamics. The concept of characteristic mode photons is introduced as a main element of novelty of our analysis. It is shown, that representation of the field operators in the basis of characteristic modes satisfies the canonical commutative relations. As an example, we consider the problem of scattering of two single-photon orthogonal beams by a perfectly conducting circular cylinder. A manifestation of the Hong-Ou-Mandel effect is demonstrated. The theory is promising for a variety of applications including quantum radars, antennas, detectors, sensors, and other quantum devices.