Stability and modulation properties of a semiconductor laser with weak optical feedback from a distant reflector

Abstract

We analyse the stability of the steady-state solutions of the compound system formed by a single-longitudinal-mode semiconductor laser and an external reflector. Of the large number of these external cavity modes (ECMs) created in pairs of modes and antimodes by moderate feedback, the antimodes are always unstable, while the modes may be stable or unstable when created. The ECMs that have a large positive frequency shift with respect to the emission frequency of the solitary laser are unstable when created. In contrast, the ECMs that have a large, negative frequency shift are stable on creation and remain stable over a relatively large feedback range. For sufficiently large feedback an ECM that is created stable gives way to a time-dependent solution (limit cycle or torus) that is localized in phase space around the ECM; several time-dependent attractors may coexist. Approximating the dynamical equations, taking into account terms up to second order, we obtain relations for the amplitudes of the oscillations of the laser variables for these attractors. The external cavity length and the injection current are key parameters which determine these amplitudes. Our approximations are in good agreement with numerical simulations, and hold even far from the bifurcation points where these attractors originate.