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 f ormation and dynamics in lasers and nonparaxial beam propagation is pr esented. The algorithms developed involve the field decomposition in t erms of the Gaussian-Laguerre modes. Three models are discussed in det ail. In the first one, the transverse pattern evolution of a short pul se in a ring unidirectional laser with a homogeneously broadened optic ally thin active medium is considered under the approximation of trans versely synchronous pulse. The pulse-train envelope and transverse pat tern dynamics are studied numerically using more than 200 empty cavity modes. In the second model the limitation of thin active medium is re moved, and the propagation of self-acting beam through the active medi um of arbitrary thickness is taken into account solving the convention al paraxial wave equation. Stationary regimes with deformed modes, qua si-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 (nonparaxia l) beam propagation in nonlinear media. The role of backward waves in wide-angle Kerr self-focusing is discussed.