Numerical studies of beam and pulse propagation in lasers and nonlinear media: Transverse pattern dynamics and nonparaxial effects

A review of recent work in numerical modelling of transverse pattern formation and dynamics in lasers and nonparaxial beam propagation is presented. The algorithms developed involve the field decomposition in terms of the Gaussian-Laguerre modes. Three models are discussed in detail. In the first one, the transverse pattern evolution of a short pulse in a ring unidirectional laser with a homogeneously broadened optically thin active medium is considered under the approximation of transversely synchronous pulse. The pulse-train envelope and transverse pattern dynamics are studied numerically using more than 200 empty cavity modes. In the second model the limitation of thin active medium is removed, and the propagation of self-acting beam through the active medium of arbitrary thickness is taken into account solving the conventional paraxial wave equation. Stationary regimes with deformed modes, quasi-periodic oscillations, and mode-locking regimes are observed. Phase singularities (optical vortices) in the transverse field pattern are demonstrated. In the third model, the Gauss-Laguerre decomposition is used to solve the Helmholtz equation describing wide-angle (nonparaxial) beam propagation in nonlinear media. The role of backward waves in wide-angle Kerr self-focusing is discussed.