Quantum Input-Output theory in an Arbitrary Magneto-Dielectric

We developed a macroscopic quantum electrodynamic (QED) framework by utilizing the classical first-order Green’s function to formulate the quantum input-output relation in dispersive and absorptive magneto-dielectric structures. The formalism relies on a symplectic six-vector representation of the electromagnetic (EM) fields, resulting in compact adjoint identities for time-reversal symmetry, reciprocity, and the Stratton-Chu relation. These identities help bind together the boundary, surface, and volume fields.

We show that the output electromagnetic mode operators can be expressed as a linear combination of input EM modes and Langevin noise sources, leading to a scattering matrix, defined in terms of the first-order Maxwell Green’s function. The Langevin noise term encodes the absorption of the medium, ensuring consistency with the fluctuation–dissipation theorem. Moreover, numerically derived Green’s function kernel accounts for the intricate effects of spatial inhomogeneity, material dispersion, and absorption. Thus, by accounting for both boundary effects and volumetric losses, this framework goes beyond conventional QED, making it applicable to a wide range of engineered photonic environments.