A Quantum Theory for Propagation of Electromagnetic Waves through Lossy Dielectrics in Presence of Third Order Dispersion

In this paper, we present a quantum theory for field propagation through a three dimensional dielectric when the third order dispersion and the attenuation coefficients are included. A unique Lagrangian is defined leading to the correct equation of motion and the classical Hamiltonian. It is assumed that the dielectric has a combination of inhomogeneity, dispersion and nonlinearity. By employing constraint quantization approach the final Hamiltonian is expanded in terms of properly defined annihilation and creation operators. We obtain the quantum fields (quantum photon-polaritons fields) for propagation through the dielectric in the presence of the third order dispersion and the attenuation coefficients by using these annihilation and creation operators. The number operator in the final Hamiltonian indicates the number of photon-polaritons in the medium. The nonlinear part of the Hamiltonian could be derived by defining displacement field operator in terms of annihilation and creation operators. As a simple example, the present quantum theory is applied to field propagation through a one dimensional slab.