Scattering of the quantized electromagnetic waves from a bi-anisotropic absorbing magneto-dielectric slab

Abstract

A canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric slab is provided. The quantized Maxwell’s equations in the presence of the slab are exactly solved and the time-space dependence of the quantized electric and magnetic fields are obtained. The Fock space of the total system is introduced. The scattering matrix of the bi-anisotropic magneto-dielectric slab is obtained in terms of the susceptibility tensors of the slab. The scattering matrix relates the annihilation operators of the outgoing quantized electromagnetic waves from the slab to the annihilation operators of the incoming quantized electromagnetic waves to the slab. The Fresnel’s coefficients of the bi-anisotropic magneto-dielectric slab are obtained in terms of the susceptibility tensors of the slab. The Fresnel’s coefficients relate the powers radiated by the outgoing quantized electromagnetic waves from the slab to the powers radiated by the incoming quantized electromagnetic waves to the slab. The radiated powers by the outgoing quantized electromagnetic waves are calculated in the special cases that the slab is in the thermal state and the incoming quantized electromagnetic waves to the slab are in the vacuum state and the coherent state.