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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 10 — May. 16, 2005
  • pp: 3822–3834

Uncertainty relation for the optimization of optical-fiber transmission systems simulations

A. A. Rieznik, T. Tolisano, F. A. Callegari, D. F. Grosz, and H.L. Fragnito  »View Author Affiliations


Optics Express, Vol. 13, Issue 10, pp. 3822-3834 (2005)
http://dx.doi.org/10.1364/OPEX.13.003822


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Abstract

The mathematical inequality which in quantum mechanics gives rise to the uncertainty principle between two non commuting operators is used to develop a spatial step-size selection algorithm for the Split-Step Fourier Method (SSFM) for solving Generalized Non-Linear Schrödinger Equations (G-NLSEs). Numerical experiments are performed to analyze the efficiency of the method in modeling optical-fiber communications systems, showing its advantages relative to other algorithms.

© 2005 Optical Society of America

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

ToC Category:
Research Papers

History
Original Manuscript: April 4, 2005
Revised Manuscript: May 3, 2005
Published: May 16, 2005

Citation
A. Rieznik, T. Tolisano, F. A. Callegari, D. Grosz, and H. Fragnito, "Uncertainty relation for the optimization of optical-fiber transmission systems simulations," Opt. Express 13, 3822-3834 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-10-3822


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References

  1. G. P. Agrawal, Nonlinear Fiber Optics (London, U.K. Academic, 1995).
  2. Oleg V. Sinkin, Ronald Holzlöhner, John Zweck, and Curtis Menyuk, �??Optimization of the Split-Step Fourier Method in Modeling Optical-Fiber Communications Systems�?? IEEE J. of Lightwave Technol. 21, 61-68 (2003). [CrossRef]
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  6. Eq. (6) is a variant of the so-called Baker-Hausdorff formula. See, for example, G.H. Weiss and A.A. Maraudin, J. Math. Phys, 3, 771-777 (1962).
  7. E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970).
  8. Although N is a non-linear operator, it involves only a multiplication operation and is considered constant in each interval. Eq. (10) follows from applying the Schwartz inequality to the functions [D �?? <D>]A and [N �?? <N>]A. Actually, this rigorous derivation determines an even smaller upper bound than that stated by eq. (10): where <C>2, the �??quantum covariance,�?? is given by ...
  9. This is a straightforward consequence of Parseval�??s theorem. In quantum mechanics the Fourier transform of an operator is nothing but the same operator expressed in the conjugate representation. Of course, the QM average value of an observable operator can not depend on the representation.
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  12. B. Fornberg and T. A. Driscoll, �??A fast spectral algorithm for nonlinear wave equations with linear dispersion,�?? J. Comp. Phys. 155, 456-467 (1999). [CrossRef]
  13. Q. Chang, E. Jia, and W. Suny, �??Difference schemes for solving the generalized nonlinear Schrödinger equation,�?? J. Comp. Phys. 148, 397-415 (1999). [CrossRef]

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