Noise Spectra of a semiconductor ring laser in the bidirectional regime

We analytically investigate the influence of complex backscattering coefficients and pump current on the noise spectra of a two-mode model for semiconductor ring laser in the Langevin formulation. The system features in the bidirectional regime are naturally described in terms of the two mode-intensity sum (I spectrum) and difference (D spectrum). The I spectrum reflects the energy exchange between the total field and the medium and behaves similarly to the relative intensity noise for single-mode semiconductor lasers. The D spectrum represents the energy exchange between the two counterpropagating modes and is shaped by the noisy precursor of a Hopf bifurcation induced by the complex backscattering.