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

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