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Quantum Electronics

Self-wave processes in a bistable laser

Sergey V. Fedorov, Nikolai N Rozanov

Published May 31, 1999• 1 citation
Publisher

Abstract

The stability of transversely one-dimensional laser autosolitons in nonlinear media with a finite rate of relaxation of two-level atoms is analysed. It is shown that, when the stability limits are crossed, oscillating autosolitons and/or autosolitons moving along an aperture are formed. The conditions for bistability between moving autosolitons and giant travelling pulses are determined.

DOI
10.1070/qe1999v029n05abeh001507

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The stability of transversely one-dimensional laser autosolitons in nonlinear media with a finite rate of relaxation of two-level atoms is analysed. It is shown that, when the stability limits are crossed, oscillating autosolitons and/or autosolitons moving along an aperture are formed. The conditions for bistability between moving autosolitons and giant travelling pulses are determined.
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Abstract We analyse the simplest model that describes the dynamics of a two-level, optically bistable system in a ring cavity, and incorporates a Gaussian radial variation of the electric field. We find that the most favourable situation to achieve self-pulsing instabilities is that of atomic and cavity detunings with opposite sign. The results are compared with those of plane-wave theory. We show that noise plays a primary role at the onset of self-oscillatory instabilities, and that its effects are governed by an equation formally identical to the Risken equation for the laser.
Analytical traveling-wave self-pulsing solutions of a homogeneously broadened ring laser are presented in the limit that the dipole relaxation rate is much greater than the atomic inversion relaxation rate. The phase velocity v(\ensuremath{\Lambda}) as a function of the normalized pump \ensuremath{\Lambda} is given explicitly. This function has a simple relation with the upper boundary ${\ensuremath{\alpha}}_{\mathrm{max}(\mathrm{\ensuremath{\Lambda}}}$) of the Risken-Nummedal-Graham-Haken (RNGH) instability domain in the (\ensuremath{\alpha},\ensuremath{\Lambda}) plane, where \ensuremath{\alpha} is the wave vector of the perturbations. The self-pulsing may appear in different ways, depending on how the stationary solution becomes unstable. If the instability of the stationary solution is caused by an unstable mode touching upon the upper boundary of the RNGH-instability domain in the (\ensuremath{\alpha},\ensuremath{\Lambda}) plane, the self-pulsing is supercritical; if the unstable mode lies on the lower boundary, a subcritical self-pulsing arises, and the system is bistable. This rule provides new signatures of the self-pulsing phenomena and will be helpful to experimental identification of the self-pulsing arising from the RNGH instability. The linear stability analysis reveals two kinds of instabilities for these self-pulsing solutions. One kind of instability is rooted in the RNGH instability of the stationary solution and may occur even when the amplitude of the self-pulsing solution approaches zero. The other kind of instability occurs when the oscillating amplitude of the self-pulsing solution becomes large. Above this large-amplitude instability threshold no traveling-wave self-pulsing can be stable any longer. The results for the corresponding Lorenz model are also presented.
The regions of stability of homogeneous generation regimes in a wide-aperture laser with a saturable absorber, including a semiconductor laser with a vertical output of radiation, are determined depending on the relative relaxation rate of carriers in active and passive media and on the frequency detunings of working transitions in these media with a resonant frequency of radiation, taking into account its polarization state. The excitation thresholds for relaxation and polarization oscillations are determined within the four-level model. Keywords: wide-aperture laser, saturable absorber, relaxation and polarization oscillations