Modal Purcell factor in PT -symmetric waveguides

Abstract

We study the spontaneous emission rate of a dipole emitter in PT-symmetric environment of two coupled waveguides using the reciprocity approach generalized to nonorthogonal eigenmodes of non-Hermitian systems. Considering emission to the guided modes, we define and calculate the modal Purcell factor composed of contributions of independent and interfering nonorthogonal modes leading to the emergence of cross-mode terms in the Purcell factor. We reveal that the closed-form expression for the modal Purcell factor within the coupled mode theory slightly alters for the non-Hermitian coupled waveguide compared to the Hermitian case. It is true even near the exceptional point, where the eigenmodes coalesce and the Petermann factor goes to infinity. This result is fully confirmed by the numerical simulations of active and passive PT-symmetric systems being the consequence of the mode nonorthogonality.