Non-Hermitian Hamiltonian approach for electromagnetic wave propagation and dissipation in dielectric media

Using the formal analogy between a certain class of Maxwell equations and the Schrdinger equation, we derive the effective Hamiltonian operator that governs the propagation of electromagnetic (EM) wave modes inside nonconducting linear media, which include a large range of nanophotonic and plasmonic waveguides. It turns out that this Hamiltonian is essentially non-Hermitian, and thus requires a special treatment. We formulate the density operator approach for dynamical systems with non-Hermitian Hamiltonians, and derive a master equation that describes the statistical ensembles of EM wave modes. The method provides a theoretical instrument which can be used when designing the next generation of quantum EM devices for sensitive and non-invasive measurements.