Noise properties in Semiconductor Ring Lasers Antonio P´ erez S., Roberta Zambrini, Alessandro Scir` e and Pere Colet Instituto de F´ ısica Interdisciplinar y Sistemas Complejos, IFISC, CSIC-UIB, Campus UIB, Ctra. Valldemossa km. 7.5, E-07122 Palma de Mallorca, Spain. ABSTRACT 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. Keywords: Semiconductor lasers, ring lasers, laser dynamics 1. INTRODUCTION Semiconductor ring lasers (SRLs) 1 gained interest due to their peculiar properties from both fundamental and applicative point of view. SRLs exhibit different operating regimes ranging from bidirectional-continuous wave regime, to a bidirectional with alternate oscillations regime, to a bistable regime, to mode locking and chaos. 3–7 These variety of operating regimes makes them promising candidates for wavelength filtering, unidirectional travelling wave operation, and multiplexing/demultiplexing applications. In particular the bistable regime is interesting for applications in optical logics, optical gating and reshaping, 8 whereas the bidirectional regime is also interesting for rotation sensing applications. 9 From a fundamental point of view, the interaction of fluctuations and two-mode nonlinear system unveiled interesting physics and new phenomena, e.g. the phenomenon of stochastic resonance was demonstrated in a ring dye laser. 10 Also, fluctuations are important in applications for ring lasers, as they determine the performance of the ring laser gyroscope, 11 or induce spontaneous switching in a bistable SRL. 12 The main noise source of a semiconductor laser is represented by spontaneous emission, which yields to fluctuations of the emitted intensity an frequency. 13 Different examples of how to model the spontaneous emission noise are shown in. 14–16 While SRL share some general characteristics with other kinds of ring lasers, they also have some distinctive features such as phase/amplitude coupling, which is known to enhance phase noise, 13 and strong intermodal gain crossaturation, which induces anticorrelated dynamics in the mode-power distribution. 3 Also, for technological reasons, SRLs experience conservative backscattering stronger than dissipative one as in gas or dye ring lasers. 17 We address here how these features influence the noise spectra of SRL. We consider the effects of the spontaneous emission noise in a two mode rate equation model, for a SRL operating in the bidirectional regime. We analytically calculate noise-spectra and correlations properties when the two modes are reinterpreted in terms of mode-intensity sum and difference taking into account the fluctuations on the phase of the fields. On one side the total intensity and carrier density show a noise spectrum (I-spectrum) characterized by a resonance induced by the typical field-medium exchange processes (relaxation oscillations) and the global phase invariance induced by the Goldstone mode, so as far as those variables are concerned, it behaves as a standard single-mode Fabry-Perot semiconductor laser. Besides, the degree of freedom associated to the simultaneous presence of two counterpropagating modes allows for a further process of energy exchange between the two modes. Our analysis unveiled that such process presents a resonance interpreted as a ’noisy precursor’ of a Hopf bifurcation 18 influenced mainly by the backscattering parameters. Email: antonio@ifisc.uib.es