An efficient algorithm for strongly focused optical beams propagating in Kerr media

Due to the lens-induced quadratic phase factor from converging lens, the beam-propagation method (BPM) is computationally expensive in simulations by the sampling theorem for lens-induced strongly focused beams propagating in nonlinear media. In the paper, we present a modified approach (MA) based on the separate envelope and lens-induced phase to only compute the envelope in the whole focal region. Then we demonstrate the correctness of MA analytically by the propagation of focused Gaussian beam and numerically by that of focused Super-Gaussian beam in linear media. Numerical simulations of strongly focused beams based on MA are in good agreement with those of BPM when propagating in Kerr media. The sampling requirement of MA which is similar with no lens-induced phase beam is lower than that of BPM which increases with the lens-induced chirp parameter and the propagation distance. Thus the computational efficiency can be greatly improved.