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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 17, Iss. 12 — Dec. 1, 2000
  • pp: 2431–2439

Wavelet operators for nonlinear optical pulse propagation

Iestyn Pierce, Paul Rees, and K. Alan Shore  »View Author Affiliations


JOSA A, Vol. 17, Issue 12, pp. 2431-2439 (2000)
http://dx.doi.org/10.1364/JOSAA.17.002431


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Abstract

A method that uses discrete wavelet transforms for the solution of evolution equations that describe optical pulse propagation in nonlinear media is presented. The theory of orthogonal wavelet transforms is outlined and applied to the representation of optical pulses. Wavelet transform representations of propagation operators are presented and applied to the nonlinear Schrödinger equation, yielding results that are indistinguishable from traditional Fourier-based simulations. The compression properties of wavelet representations of optical pulses permit significant improvement in execution speed compared with that of the split-step Fourier method.

© 2000 Optical Society of America

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.4370) Nonlinear optics : Nonlinear optics, fibers

History
Original Manuscript: March 1, 2000
Revised Manuscript: August 21, 2000
Manuscript Accepted: August 30, 2000
Published: December 1, 2000

Citation
Iestyn Pierce, Paul Rees, and K. Alan Shore, "Wavelet operators for nonlinear optical pulse propagation," J. Opt. Soc. Am. A 17, 2431-2439 (2000)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-12-2431


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References

  1. M. J. Ablowitz, P. A. Clarkson, Solitons, Nonlinear Evolution Equations, and Inverse Scattering (Cambridge U. Press, Cambridge, UK, 1991).
  2. T. R. Taha, M. J. Ablowitz, “Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation,” J. Comp. Physiol. 55, 203–230 (1984). [CrossRef]
  3. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed., Optics and Photonics Series (Academic, Orlando, Fla., 1995).
  4. R. W. Ramirez, The FFT, Fundamentals and Concepts (Prentice-Hall, Englewood Cliffs, N.J., 1985).
  5. C. Van Loan, Computational Frameworks for the Fast Fourier Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1992).
  6. M. Y. Hong, Y. H. Chang, A. Dienes, J. P. Heritage, P. J. Delfyett, “Subpicosecond pulse amplification in semiconductor laser amplifiers: theory and experiment,” IEEE J. Quantum Electron. 30, 1122–1131 (1994). [CrossRef]
  7. Ref. 3, p. 51.
  8. D. Yevick, B. Hermansson, “New fast Fourier transform and finite element approaches to the calculation of multiple-stripe-geometry laser modes,” J. Appl. Phys. 59, 1769–1771 (1986). [CrossRef]
  9. H. J. A. da Silva, J. J. O’Reilly, “Optical pulse modeling with Hermite–Gaussian functions,” Opt. Lett. 14, 526–528 (1989). [CrossRef] [PubMed]
  10. G. Strang, T. Q. Nguyen, Wavelets and Filter Banks (Wellesley Cambridge Press, Wellesley, Mass., 1996).
  11. I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, Philadelphia, Mass., 1992).
  12. J. D. Villasenor, B. Belzer, J. Liao, “Wavelet filter evaluation for image compression,” IEEE Trans. Image Process. 4, 1053–1060 (1995). [CrossRef] [PubMed]
  13. G. Beylkin, R. Coifman, V. Rokhlin, “Fast wavelet transforms and numerical analysis. I,” Commun. Pure Appl. Math. 44, 141–183 (1991). [CrossRef]
  14. W. H. Press, S. A. Teukolsky, W. H. Vetterling, B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).
  15. G. Beylkin, “On the representation of operators in bases of compactly supported wavelets,” SIAM J. Numer. Anal. 29, 1716–1740 (1992). [CrossRef]
  16. B. Jawerth, W. Sweldens, “An overview of wavelet based multiresolution analyses,” SIAM Rev. 36, 377–412 (1994). [CrossRef]
  17. P. Charton, V. Perrier, “Rapid matrix-vector products using wavelet transform—application to numerical-solution of partial-differential equations,” Model. Math. Anal. Numer. 29, 701–747 (1995).

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