OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 14, Iss. 5 — May. 1, 1997
  • pp: 1207–1212

Effect of the second-derivative paraxial term in the scalar Maxwell's equation on amplitude losses and reflections in optical fibers

Ilya Vorobeichik, Nimrod Moiseyev, and Daniel Neuhauser  »View Author Affiliations

JOSA B, Vol. 14, Issue 5, pp. 1207-1212 (1997)

View Full Text Article

Enhanced HTML    Acrobat PDF (268 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The scalar Maxwell's equation, including the often-neglected second-derivative paraxial term, is solved. This term is shown to increase the loss of the amplitude of the light beam inside a single-mode optical fiber. The reflected (backward-traveling) wave that is due to the second-derivative term is obtained from the calculation of the scattering matrix as formulated in quantum-mechanical dynamical problems.

© 1997 Optical Society of America

Ilya Vorobeichik, Nimrod Moiseyev, and Daniel Neuhauser, "Effect of the second-derivative paraxial term in the scalar Maxwell's equation on amplitude losses and reflections in optical fibers," J. Opt. Soc. Am. B 14, 1207-1212 (1997)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. W. Snyder and S. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  2. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  3. R. E. Prange and S. Fishman, “Experimental realization of kicked quantum chaotic systems,” Phys. Rev. Lett. 63, 704 (1989). [CrossRef] [PubMed]
  4. M. D. Feit, J. A. Fleck, and A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Compu. Phys. 47, 412 (1982); M. D. Feit and J. A. Fleck, Jr., “Simple spectral method for solving propagation problems in cylindrical geometry with fast Fourier transforms,” Opt. Lett. 14, 662 (1989). [CrossRef] [PubMed]
  5. R. Kosloff, in Time-Dependent Quantum Molecular Dynamics, NATO ASI Series B299, J. Broeckhave and L. Lathouwers, eds. (Plenum, New York, 1992), p. 92.
  6. I. Vorobeichik, U. Peskin, and N. Moiseyev, “Modal losses and design of modal irradiance patterns in an optical fiber by the complex scaled (t, t) method,” J. Opt. Soc. Am. B 12, 1133 (1995); “Propagation of light beam in optical fiber by the (t, t) method,” Non-Linear Opt. 11, 79 (1995); [CrossRef]
  7. See, for example, recent simulations of large-scale strongly coupled scattering problems (as occur in four-center reactions) involving millions of basis functions: U. Manthe, T. Seideman, and W. H. Miller, “Full-dimensional quantum mechanical calculation of the rate constant for the H2+OH→H2O+H reaction,” J. Chem. Phys. 99, 10078 (1193); D. H. Zhang and J. Z. H. Zhang, “Full-dimensional time-dependent treatment for diatom–diatom reaction—the H2+OH reaction,” J. Chem. Phys. 101, 1146 (1994); D. Neuhauser, “Fully quantal initial-state-selected reaction probabilities (j=0) for a four-atom system—H2(v= 0, 1, j=0)+OH(v=0, 1, j=0)→H + H2O,” J. Chem. Phys. JCPSA6 100, 9272 (1994). [CrossRef]
  8. U. Peskin and N. Moiseyev, “The solution of the time-dependent Schrödinger equation by the (t, t) method—theory, computational algorithm and applications,” J. Chem. Phys. 99, 4590 (1993). [CrossRef]
  9. R. Ratowsky and J. A. Fleck, “Accurate numerical solution of the Helmholtz equation by iterative Lanczos reduction,” Opt. Lett. 16, 787 (1991). [CrossRef] [PubMed]
  10. Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335 (1990). [CrossRef]
  11. G. R. Hadley, “Multistep method for wide-angle beam propagation,” Opt. Lett. 17, 1743 (1992). [CrossRef] [PubMed]
  12. U. Peskin, W. H. Miller, and Å Edlund, “Quantum time evolution in time-dependent fields and time-independent reactive-scattering calculations via an efficient Fourier grid preconditioner,” J. Chem. Phys. 103, 10030 (1995). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited