Propagation of nonparaxial beams with a modified Arnoldi method

We have developed a modified Arnoldi method that includes a complex square-root approximation, which excels at modeling the propagation of highly diverging beams in various media. Simulations of one transverse dimensional beam with an ultranarrow width and of cylindrical Gaussian beams with various divergence angles reveal the strength of this nonparaxial-beam propagation method.