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

TL;DR

This paper develops a quantum theoretical framework for electromagnetic wave propagation in lossy dielectrics with third order dispersion, incorporating inhomogeneity and nonlinearity, and applies it to a one-dimensional slab example.

Contribution

It introduces a novel quantum theory including third order dispersion and attenuation in dielectric media, with a unique Lagrangian and Hamiltonian formulation.

Findings

Derived quantum photon-polariton fields in lossy dispersive media.

Quantized the Hamiltonian with annihilation and creation operators.

Applied the theory to a one-dimensional dielectric slab.

Abstract

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.