Electromagnetic field quantization in absorbing dielectrics

TLDR: The electromagnetic field is quantized in dielectric media that show both loss and dispersion in the form of Langevin forces in the forms of noise current operators.

Abstract: The electromagnetic field is quantized for normal transmission of incident waves through a parallel-sided dielectric slab. The dielectric material is dispersive and it acts as a linear amplifier over limited ranges of the frequency and as a linear attenuator at the remaining frequencies. The field operators derived for the three spatial regions within and on either side of the slab are shown to satisfy the canonical commutation relations. The noise fluxes emitted by the slab are evaluated and shown to satisfy the general requirements for the minimum noise associated with linear amplifiers and attenuators. The behavior of the amplifier gain profile on the approach to the lasing threshold of the slab is determined, but the results are restricted to the below-threshold state of the system. The spectra of the electric-field fluctuations are evaluated for the three spatial regions and for amplifying and attenuating frequencies.