We present a numerical model to deal with optical nonlinear processes at a strong focusing situation where general methods possibly fail to work. We find a special curvilinear coordinate system through which a new paraxial wave equation set is developed and its eigenmode transmission solutions are derived. On the basis of the wave equations, a detailed algorithm for second-harmonic generation is proposed with the Fourier-space method. Numerical results in non-walk-off and walk-off cases show that the new model can handle wave interactions on the strong focusing L/b>>1 condition within a relative small sampling grid, with which traditional methods will lose efficiency, and can provide unique features in comparison with the model in a Cartesian coordinate system. Concrete assessment of the new model is rendered by error analysis.
© 2006 Optical Society of America
Original Manuscript: July 5, 2005
Manuscript Accepted: January 29, 2006
Jin Jer Huang, Xiao Yong Hu, De Ming Ren, and Yan Chen Qu, "Simulation of three-wave interactions for focused beams with an assistant curvilinear coordinate system," J. Opt. Soc. Am. B 23, 1312-1322 (2006)