Spatiotemporal mode locking in quadratic nonlinear media

A theoretical model is developed to characterize spatiotemporal mode locking (ML) in quadratic nonlinear media. The model is based on the two-dimensional nonlinear Schrodinger equation with coupling to a mean term (NLSM) and constructed as an extension of the master mode-locking model. It is numerically demonstrated that there exists steady-state soliton solutions of the ML-NLSM model that are astigmatic in nature. A full stability analysis and bifurcation study is performed for the ML-NLSM model, and it is manifest that spatiotemporal ML of the astigmatic steady-state solutions is possible in quadratic nonlinear media.