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Quantum-statistical effects occur during the propagation of electromagnetic(EM) waves inside the dielectric media or metamaterials, which include a largeclass of nanophotonic and plasmonic waveguides with dissipation and noise.Exploiting the formal analogy between the Schrodinger equation and the Maxwellequations for dielectric linear media, we rigorously derive the effectiveHamiltonian operator which describes such propagation. This operator turns outto be essentially non-Hermitian in general, and pseudo-Hermitian in somespecial cases. Using the density operator approach for general non-HermitianHamiltonians, we derive a master equation that describes the statisticalensembles of EM wave modes. The method also describes the quantum dissipativeand decoherence processes which happen during the wave's propagation, and,among other things, it reveals the conditions that are necessary to control theenergy and information loss inside the above-mentioned materials.

Quantum-statistical approach to electromagnetic wave propagation and dissipation inside dielectric media and nanophotonic and plasmonic waveguides