Theoretical analysis of a bimode laser

Abstract

We study analytically the dynamical behaviors of class $A$ and $B$ lasers operating on two transverse modes. A generalization of the well-known multimode model of Lamb, taking into account the transverse hole burning effects as well as nonlinear phase couplings, is considered. Taking as a control parameter the difference between the empty cavity eigenfrequency of the modes, the main developments of this article are the following. The existence and stability of stationary patterns related to (i) single-mode stationary states and (ii) locked bimode phase-sensitive solutions are analyzed. (iii) Unlocked periodic behavior and frequency pushing or pulling effects are characterized in a fully analytical description. Our analysis puts in evidence the qualitative differences of stationary as well as periodic behaviors for class $A$ and $B$ bimodal lasers. Moreover, we show that the laser response is strongly dependent on the symmetry properties, or on the relative spatial parity, of the modes involved: The dynamical properties of opposite or equal parity modes laser are introduced and investigated here.