Splitted-mode dynamics in 1-defect semiconductor ring laser

This study addresses the problem of an active circular semiconductor cavity with an arbitrary reflection point, characterized by a complex reflection and transmission coefficients. The cold cavity eigenfunctions and eigenfrequencies of the optical system are calculated in a Maxwell-Bloch framework, with suitable boundary conditions. Results show that the reflection point has the effect of splitting each longitudinal mode of the unperturbed cavity in two closely-spaced longitudinal modes, termed as splitted modes (SMs). Depending on the reflection and transmission coefficients the mode splitting and the cavity losses difference between the two SMs of each couple can be controlled. When considering the effect of the active semiconductor medium, the non-linear gain couples the various SMs one to each other. In many practical cases, the gain curve would limit the lasing action to the couple of SMs closest to the gain peak. Moreover, a full analytical theory for the dynamic of two coupled SMs is developed, whereas the multi-SMs case is analyzed through numerical simulations.