Abstract

The five eigenvalues of the linear stability analysis of the single-mode laser model have been monitored as functions of laser detuning and laser excitation. With sufficient detuning there are two pairs of complex conjugate eigenvalues corresponding to two different kinds of eigenvector. For large detunings and high excitations, these pairs of eigenvalue may collide below the instability threshold. For detunings below the critical value for the collision, one pair of eigenvalues is responsible for the instability. For detunings above the critical value for collision, the other pair of eigenvalues is responsible for the instability. As one pair arises in resonance purely from amplitudes and the other pair corresponds to evolution of the relative phases of the field and polarization, we have investigated the eigenvectors in the detuned case and the time evolution of the solutions for evidence of qualitative changes in the nature of the instabilities near the steady-state solutions or in the long-term pulsing solutions. The collision of the eigenvalues appears to have little to do with the presence or absence of small amplitude oscillations near the instability threshold but does seem to provide information on the stability of the relative phase of the solutions.

© 1986 Optical Society of America