Abstract

Transverse effects in nonlinear optics have recently attracted considerable attention because of the intriguing process of pattern formation and especially for potential future applications. Laser models of Maxwell-Bloch equations have been among the first systems analysed in detail in the spatio-temporal domain in order to detect and organise the complicate dynamical behaviour of spatial structures. The original models^[1] have been integrated both as partial differential equations^{[2, 3]} and via modal expansion in Gauss-Laguerre modes.^{[4, 5]} One common feature in the progressive complication of the laser output appears to be the presence and interaction of optical vortices, i.e. points in the transverse plane where the gradient of the field phase is singular while the field amplitude vanishes. In Ref. ⁴ some of us have studied the formation of static crystals of optical vortices. Later, dynamical behaviour of laser vortices has been described by both intergrating the partial differential equations^[3] and a suitable modal expansion.^[5]

© 1992 IQEC