We have developed a modified Arnoldi method that includes a complex square-
root approximation, which excels at modeling the propagation of highly dive
rging beams in various media. Simulations of one transverse dimensional bea
m with an ultranarrow width and of cylindrical Gaussian beams with various
divergence angles reveal the strength of this nonparaxial-beam propagation
method. (C) 2001 Optical Society of America.