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7 pages, 7 figures.-- PACS number(s): 42.55.Px, 42.60.Mi, 42.65.-kWe 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.This work was funded by the European project IOLOS\udProject No. IST-2005-34743 and Spanish projects PhoDeCC\udProject No. TEC2006-10009/MIC, FISICOS Project No.\udFIS2007-60327, and ECusCo Project No. 2008501047. A.S.\udacknowledges Ramón y Cajal program by Spanish MEC.Peer reviewe

Noise spectra of a semiconductor ring laser in the bidirectional regime