Coupled mode theory in non-Hermitian optical cavities

We study the coupling of mode in time for non-Hermitian cavities. Using variational principle, we provide a self-consistent approach to study the mode hybridization in non-Hermitian cavities from the first-principle of Maxwell's equations. We first extend the reaction concept for time reversal adjoint system using the scalar inner product. We apply our theory to the non-Hermitian parity-time symmetric cavities, and obtain excellent agreement with results obtained by finite element fullwave simulations. In contrast, the conventional coupled mode theory using complex inner product fails to capture the bifurcation of the dispersion of parity-time symmetric cavities, as non-Hermicity increases. Our theory may have potential applications in non-Hermitian optical systems.