Dept. of Elec. Eng., Queen's Univ., Kingston, ON K7L 3N6, Canada
In this talk, the Lanczos procedure is applied to the high-order alternative wide-angle propagation operator. This operator is obtained by approximating [radical 1+(epsilon)+(mu)[radical , where (epsilon)=n[sup 2](Z)-1 and (mu)=k[sub 0][sup -2](cursive beta)/(cursive beta)z[sup 2], by the expression [radical 1+(epsilon)+(mu)[radical =-1+[radical 1+(epsilon)[radical +[radical 1+(mu)[radical -1/8((epsilon)(mu)+(mu)(epsilon))+1/16[((epsilon)+(mu))[sup 3]-(epsilon)[sup 3]-(mu)[sup 3]]+... . The exponential of the first three terms on the right-hand side of the above expression correspond to the Thomson--Chapman propagator and can be evaluated with the standard split-step Fourier algorithm. The remaining correction terms can be implemented either through standard Pade approximants or with the Lanczos procedure. Unlike the Pade formalism, the perturbative Lanczos scheme can be implemented equally efficiently in both two and three spatial dimensions. The procedure further does not suffer from the previously documented convergence difficulties associated with the Lanczos evaluation of the full square-root operator [Hermansson et al., IEEE J. Light. Technol. 10, 772--776 (1992)] and is therefore highly computationally efficient. Finally, it is verified that the Lanczos method yields highly accurate results for a leaky surface duct test case.