Unidirectional lasing in nonlinear Taiji microring resonators

We develop a general formalism to study laser operation in active microring resonators supporting two counterpropagating modes. Our formalism is based on the coupled-mode equations of motion for the field amplitudes in the two counterpropagating modes and a linearized analysis of the small perturbations around the steady state. We show that the devices including an additional S-shaped waveguide establishing a unidirectional coupling between both modes--the so-called "Taiji" resonators--feature a preferred chirality on the laser emission and can ultimately lead to unidirectional lasing even in the presence of sizable backscattering. The efficiency of this mode selection process is further reinforced by the Kerr nonlinearity of the material. This stable unidirectional laser operation can be seen as an effective breaking of -reversal symmetry dynamically induced by the breaking of the symmetry of the underlying device geometry. This mechanism appears as a promising building block to ensure nonreciprocal behaviors in integrated photonic networks and topological lasers without the need for magnetic elements.