Enhanced Stability and Exceptional Points in Active Photonic Couplers

We consider active photonic couplers consisting of two coupled dissimilar waveguides with gain and loss. We show that under generic conditions, not restricted by parity-time or other types of symmetry, there exist finite-power, constant-intensity Nonlinear Supermodes, resulting from the balance between gain, loss, nonlinearity, coupling, and dissimilarity. These Nonlinear Supermodes are characterized by the amplitude ratio and the phase difference of the two electric wave fields, which can be tuned to have almost any desired value, by appropriate parameter selection. The asymmetry of the system is shown to result in non-reciprocal dynamics enabling directed power transport functionality. In turn, we systematically investigate the dynamical response of such asymmetric coupler in the context of a set of single-mode equations with gain/loss saturation included. Additionally, we point and map, in the parameter and in the solution space of this photonic structure, a rich set of Exceptional Points, corresponding to non-Hermitian degeneracies where two eigenvalues and eigenvectors coalesce. The importance of the Exceptional Points is crucial for the system response under noisy perturbations or other modulations as well as for sensing applications.