Regularization of the Spectral Singularity in 𝒫𝒯-Symmetric Systems by All-Order Nonlinearities: Nonreciprocity and Optical Isolation

Spectral singularities are ubiquitous with 𝒫𝒯 symmetry leading to infinite transmission and reflection coefficients. Since physical systems cannot have singularities, these must be the artifact of some missing physics. The singularities imply the divergence of the fields in the medium, thereby breaking the very assumption of the linearity of the medium used to obtain such singularities. We show how the incorporation of the correct all-order nonlinear behavior of the medium regularizes the spectral singularity. The all-order nonlinear 𝒫𝒯-symmetric device is shown to exhibit very effective isolation or optical diode action since transmission through such a system is nonreciprocal. In contrast, a linear system or a system with Kerr nonlinearity is known to have only reciprocal transmission.