Electromagnetic field quantization in planar absorbing heterostructures

Abstract

The quantization scheme for the electromagnetic field in planar absorbing heterostructures has been developed. The scheme is based on the field expansion over a complete set of orthonormal modes. We used two types of the field modes. The first one is defined as the field created by a plane wave incident at the surface of the structure from the non-absorbing half space. The second type of modes corresponds to the field generated by electric current fluctuations in the absorbing media. To normalize the field modes, the following conditions were used: 1) the time-averaged Poynting vector attributed to the incident wave equals the density of energy flow of elementary quanta of the field energy; 2) for the given frequency and polarization, the total time-averaged Poynting vector equals to zero. The theory is applied to calculate the rate of spontaneous transitions between electron subbands in a quantum well placed near the absorbing layer that can support the surface phonon or plasmon polaritons.