J. A. Fleck, Jr.,
"Solution of the Scalar Helmholtz Wave Equation by Lanczos Reduction," ,
Vol. 11, 103-141, 1995.
doi:10.2528/PIER94032109
1. Fleck, Jr., J. A., J. R. Morris, and M. D. Feit, "Time-dependent propqation of high energy laser beams through the atmosphere," Appl. Phys., Vol. 10, 129-160, 1976.
doi:10.1007/BF00896333 Google Scholar
2. Huang, W. P., S. T. Chu, A. Goss, and S. K. Chaudhmi, "A scalar finite-difference time-domain approach to guided wave optics," IEEE Photonics Tech. Lett., Vol. 3, 524-526, 1991.
doi:10.1109/68.91022 Google Scholar
3. Claerbout, J. F., findamentals of Geophysical Data Processing with Applications to Petrolelum Prospecting, McGraw-Hill, 1976.
4. Lee, D., Y. Saad, M, and H. Schultz, "An efficient method for solving the three-dimensional wide angle wave equation," Computational Acoustics, Vol. 1 --- Wave Propagation, Eds. D. Lee, R. L. Sternberg, and M. H. Schultz, North Holland, Amsterdam, 1988. Google Scholar
5. Feit, M. D., J. A. Fleck, and Jr., "Light propagation in gradedindex optical fibers," Appl. Opt., Vol. 17, 3990-3998, 1978.
doi:10.1364/AO.17.003990 Google Scholar
6. Van Roey, J., J. van der Donk, and P. E. Lagasse, "Beam propagation method: Analysis and assessment," J. Opt. Soc. Amer., Vol. 71, 803-810, 1981.
doi:10.1364/JOSA.71.000803 Google Scholar
7. Feit, M. D., J. A. Fleck, and Jr., "Beam paraxiality, filament formation, and beam breakup in the self-focusing of optical beams," J. Opt. Soc. Amer. B, Vol. 5, 633-640, 1988.
doi:10.1364/JOSAB.5.000633 Google Scholar
8. Thomson, D. J. and N. R. Chapman, "A wide-angle split-step algorithm for the parabolic equation," J. Acoust. Soc. Amer., Vol. 74, 1848-1854, 1983.
doi:10.1121/1.390272 Google Scholar
9. Thylen, L. and C. M. Lee, "Beam-propagation method based on matrix diagonalization," J. Opt. Soc. Am. A, Vol. 9, 143-146, 1992.
doi:10.1364/JOSAA.9.000142 Google Scholar
10. Gerdes, J. and R. Pregla, "Beam propagation algorithm based on the method of lines," J. Opt. Soc. Am. B, Vol. 8, 389-395, 1991.
doi:10.1364/JOSAB.8.000389 Google Scholar
11. Lanczos, C., "An iteration method for the solution of the eigenvalue problem of linear differential and integral operators," J. Res. Nut Bur. Standards, Vol. 45, 255-282, 1950.
doi:10.6028/jres.045.026 Google Scholar
12. Park, T. J. and J. C. Light, "Unitary quantum time evolution by iterative Lanczos reduction," J. Chem. Phys., Vol. 85, 5870-5876, 1986.
doi:10.1063/1.451548 Google Scholar
13. Sehmi, B. S., Large Order Stmctuml Eigenanalysis for Finite Element Systems, Halsted, 1989.
14. Leforestier, C., R. H. Bisseling, C. Cerjan, M. D. Feit, R. Friesner, A. Goldberg, A. Hmerich, G. Jolicard, W. Karrlein, H. D. Meyer, N. Lipkin, 0. Roncero, and R. Kosloff, "A comparison of different propagation schemes for the time dependent Schrodinger equation," J. Comp. Phys., Vol. 94, 59-80, 1991.
doi:10.1016/0021-9991(91)90137-A Google Scholar
15. Ratowsky, R., J. A. Fleck, and Jr., "Accurate numerical solution of the Helmholtz equation by iterative Lanczos reduction," Opt. Lett., Vol. 16, 787-789, 1991.
doi:10.1364/OL.16.000787 Google Scholar
16. Ratowsky, R., J. A. Fleck, Jr., and M. D. Feit, "Helmholtz beam propagation in rib waveguides and couplers by iterative lanczos reduction," J. Opt. Soc. Amer. A, Vol. 9, 265-273, 1992.
doi:10.1364/JOSAA.9.000265 Google Scholar
17. Ratowsky, R., J. A. Fleck, Jr., and M. D. Feit, "Accurate solution of the Helmholtz equation by Lanczos orthogonalization for media with loss or gain," Opt. Lett., Vol. 17, 10-12, 1992.
doi:10.1364/OL.17.000010 Google Scholar
18. Hermansson, B., D. Yevick, W. Bardyszewski, and M. Glasner, "A comparison of Lanczos electric field propagation methods," J. Lightwave Technol., Vol. 10, 772-776, 1992.
doi:10.1109/50.143077 Google Scholar
19. Feit, M. D., J. A. Fleck, Jr., and A. Steiger, "Solution of the Schrodinger equation by a spectral method," J. Comp. Phys., Vol. 47, 412-433, 1982.
doi:10.1016/0021-9991(82)90091-2 Google Scholar
20. Feit, M. D., J. A. Fleck, Jr., and , "Computation of mode eigenfunctions in graded-index optical fibers by the propagating beam method," Applied Opt., Vol. 19, 2240-2246, 1980.
doi:10.1364/AO.19.002240 Google Scholar
21. Ratowsky, R., J. A. Fleck, Jr., and M. D. Feit, "Accurate description of ultra wide-angle beam propagation in homogeneous media by Lanczos orthogonalization," Opt. Lett., in press. Google Scholar
22. Born, M. and E. Wolf, Principles of Optics, 560, Pergamon, 1970.