Dynamics of radiation from a wide-aperture laser under conditions of coherent interaction of the radiation with a medium

The dynamics of the radiation from a wide-aperture laser is investigated taking account of the finite response time of the polarisation of the active medium. This radiation is described by the Maxwell — Bloch equations, which are simplified for the case of fast relaxation of the polarisation. The methods of a qualitative theory of nonlinear dynamics systems are used to find the conditions for instability of the steady-state homogeneous laser radiation field in a Fabry — Perot cavity. It is shown that, as a rule, the system becomes unstable via an Andronov — Hopf bifurcation and the transverse profile of the optical field is modulated by a travelling self-wave. The main parameters of these self-waves are determined and their growth increment is found. It is shown that each of the roots of the characteristic equation of the system can be used to estimate the stability range of the self-wave solutions. The laser equations are also solved numerically and the results obtained are in good agreement with the conclusions of the qualitative theory. The numerical results predict harmonic and quasi-harmonic self-waves (with multiplication of their period) and also behaviour resembling chaos.