Noise properties of semiconductor ring lasers

We analyze a rate equation model in the Langevin formulation for the two modes of the electric field and the carrier density, modelling the spontaneous emission noise in a semiconductor ring laser biased in the bidirectional regime. We analytically investigate the influence of complex backscattering coefficient when the two modes are reinterpreted in terms of mode-intensity sum (I-Spectrum) and difference (D-spectrum). The D-spectrum represents the energy exchange between the two counterpropagating modes and it is shaped by the noisy precursor of a Hopf bifurcation influenced mainly by the conservative backscattering. The I-Spectrum reflects the energy exchange between the total field and the medium and behaves similarly to the standard relative intensity noise for single-mode semiconductor lasers. Good agreement between analytical approximation and numerical results is found.