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Solution of the Scalar Helmholtz Wave Equation by Lanczos Reduction

By J. A. Fleck, Jr.

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Citation:
J. A. Fleck, Jr., "Solution of the Scalar Helmholtz Wave Equation by Lanczos Reduction," Progress In Electromagnetics Research, Vol. 11, 103-141, 1995.
http://www.jpier.org/PIER/pier.php?paper=9403219

References:
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

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

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.
doi:10.1364/AO.17.003990

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

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

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

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

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

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

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

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.
doi:10.1016/0021-9991(91)90137-A

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

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

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

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

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

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

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.


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