Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 11 > pp. 103-141

Solution of the Scalar Helmholtz Wave Equation by Lanczos Reduction

By J. A. Fleck, Jr.

Full Article PDF (1,585 KB)

J. A. Fleck, Jr., "Solution of the Scalar Helmholtz Wave Equation by Lanczos Reduction," Progress In Electromagnetics Research, Vol. 11, 103-141, 1995.

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.

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.

3. Claerbout, J. F., findamentals of Geophysical Data Processing with Applications to Petrolelum Prospecting, McGraw-Hill, New York, 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.

5. Feit, M. D., J. A. Fleck, and Jr., "Light propagation in gradedindex optical fibers," Appl. Opt., Vol. 17, 3990-3998, 1978.

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.

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.

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.

9. Thylen, L. and C. M. Lee, "Beam-propagation method based on matrix diagonalization," J. Opt. Soc. Am. A, Vol. 9, 143-146, 1992.

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.

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.

12. Park, T. J. and J. C. Light, "Unitary quantum time evolution by iterative Lanczos reduction," J. Chem. Phys., Vol. 85, 5870-5876, 1986.

13. Sehmi, B. S., Large Order Stmctuml Eigenanalysis for Finite Element Systems, Halsted, New York, 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.

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.

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.

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.

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.

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.

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.

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.

22. Born, M. and E. Wolf, Principles of Optics, 560, Pergamon, New York, 1970.

© Copyright 2014 EMW Publishing. All Rights Reserved