Abstract

A broad-band digital filtering approach for the simulation of pulse propagation in the optical fiber has been developed. Unlike the most popular frequency-domain split-step method, the pulse propagation is realized by letting the signal samples pass through a preextracted digital filter where the convolution is simply made by a series of operations that consist of shift and multiplication only. It also differs from the existing time-domain split-step method in a sense that the digital filter is extracted to match the frequency-domain fiber linear transfer function in the full bandwidth range rather than in a reduced portion. This approach is verified through comparisons made with the conventional frequency-domain split-step method and is applied to the simulation of multiple-channel narrow-pulse propagation over the long-haul fiber. The main advantage brought by this approach lies in that the simulator is fully realized in a"data-flow"fashion; that is, the signal (long sample stream) is treated sample by sample, rather than block (a collection of neighboring samples) by block. Matching the fiber frequency-domain response over the full bandwidth does not require any further reduction on the propagation step since the error can be controlled through the filter length. The authors' preliminary effort on the filter length reduction on a given error reveals that a savings on both memory and computation time is also achievable in comparison with the frequency-domain split-step method.

© 2005 IEEE

PDF Article

References

  • View by:
  • |

  1. G. P. Agrawal, Nonlinear Fiber Optics, New York: Academic, 2001.
  2. N. Yajima and A. Outi, "A new example of stable solitary waves", Prog. Theor. Phys., vol. 45, no. 6, pp. 1997-1998, Jun. 1971.
  3. R. H. Hardin and F. D. Tappert, "Applications of the split step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations", SIAM Rev. Chronicle, vol. 15, p. 423, 1973.
  4. R. A. Fisher and W. K. Bischel, "The role of linear dispersion in plane-wave self-phase modulation", Appl. Phys. Lett., vol. 23, pp. 661-663, 1973.
  5. I. S. Greig and J. L. Morris, "A hopscotch method for the Korteweg-de-Vries equation", J. Comput. Phys., vol. 20, pp. 64-80, 1976.
  6. M. Delfour, M. Fortin and G. Payre, "Finite-difference solutions of a nonlinear Schrödinger equation", J. Comput. Phys., vol. 44, pp. 277-288, 1981.
  7. L. R. Watkins and Y. R. Zhou, "Modeling propagation in optical fibers using wavelet", J. Lightw. Technol., vol. 12, no. 9, pp. 536-1542, Sep. 1994.
  8. K. V. Peddanarapagari and M. Brandt-Pearce, "Volterra series approach for optimizing fiber-optic communications system designs", J. Lightw. Technol. , vol. 16, no. 11, pp. 2046-2055, Nov. 1998.
  9. Q. Chang, E. Jia and W. Sun, "Difference schemes for solving the generalized nonlinear Schrodinger equation", J. Comput. Phys., vol. 148, pp. 397-415, 1999.
  10. O. V. Sinkin, R. Holzlohner, J. Zweck and C. R. Menyuk, "Optimization of the split-step Fourier method in modeling optical fiber communication systems", J. Lightw. Technol. , vol. 21, no. 1, pp. 61-68, Jan. 2003.
  11. G. P. Agrawal, Applications of Nonlinear Fiber Optics, New York: Academic, 2001.
  12. X. Zhang and H. Iwakura, "Design of IIR digital allpass filters based on eigenvalue problems", IEEE Trans. Signal Process., vol. 47, no. 2, pp. 554-559, Feb. 1999.
  13. C. R. Menyuk, "Stability of solitons in birefringent optical fibers, II Arbitrary amplitudes", J. Opt. Soc. Amer. A, Opt. Image Sci. , vol. A5, pp. 392-402, 1988.
  14. A. Carema, V. Curri, R. Gaudino, P. Poggiolini and S. Benedetto, "A time-domain optical transmission system simulation package accounting for nonlinear and polarization-related effects in fiber", IEEE J. Select. Areas Commun., vol. 15, no. 4, pp. 751-764, May 1997.
  15. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes, Cambridge: U.K.: Cambridge Univ. Press, 2001.
  16. M. C. Jeruchim, P. Balaban and K. S. Shanmugan, Simulation of Communication Systems, Norwell, MA: Kluwer Academic, 2000.
  17. M. Kahn, M. S. Mackisack, M. R. Osborne and G. K. Smyth, "On the consistency of Prony's method and related algorithms", J. Comput. Graphical Statistics, vol. 1, pp. 329-349, 1992.
  18. A. V. Oppenhem, A. S. Willsky and S. H. Nawab, Signals and Systems, Englewood Cliffs, NJ: Prentice-Hall, 1997.
  19. A. V. Oppenheim and R. W. Schafer, Discrete Time Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1999.
  20. A. Lowery and P. C. R. Gurney, "Two simulators for photonic computer-aided design", Appl. Opt., vol. 37, no. 26, pp. 6066-6077, Sep. 1998.
  21. A. Lowery, O. Lenzmann, I. Koltchanov, R. Moosburger, R. Freund, A. Richter, S. Georgi, D. Breuer and H. Hamster, "Multiple signal representation simulation of photonic devices, systems and networks", IEEE J. Select. Topics Quantum Electron. , vol. 6, no. 2, pp. 282-296, Mar. 2000.

Other (21)

G. P. Agrawal, Nonlinear Fiber Optics, New York: Academic, 2001.

N. Yajima and A. Outi, "A new example of stable solitary waves", Prog. Theor. Phys., vol. 45, no. 6, pp. 1997-1998, Jun. 1971.

R. H. Hardin and F. D. Tappert, "Applications of the split step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations", SIAM Rev. Chronicle, vol. 15, p. 423, 1973.

R. A. Fisher and W. K. Bischel, "The role of linear dispersion in plane-wave self-phase modulation", Appl. Phys. Lett., vol. 23, pp. 661-663, 1973.

I. S. Greig and J. L. Morris, "A hopscotch method for the Korteweg-de-Vries equation", J. Comput. Phys., vol. 20, pp. 64-80, 1976.

M. Delfour, M. Fortin and G. Payre, "Finite-difference solutions of a nonlinear Schrödinger equation", J. Comput. Phys., vol. 44, pp. 277-288, 1981.

L. R. Watkins and Y. R. Zhou, "Modeling propagation in optical fibers using wavelet", J. Lightw. Technol., vol. 12, no. 9, pp. 536-1542, Sep. 1994.

K. V. Peddanarapagari and M. Brandt-Pearce, "Volterra series approach for optimizing fiber-optic communications system designs", J. Lightw. Technol. , vol. 16, no. 11, pp. 2046-2055, Nov. 1998.

Q. Chang, E. Jia and W. Sun, "Difference schemes for solving the generalized nonlinear Schrodinger equation", J. Comput. Phys., vol. 148, pp. 397-415, 1999.

O. V. Sinkin, R. Holzlohner, J. Zweck and C. R. Menyuk, "Optimization of the split-step Fourier method in modeling optical fiber communication systems", J. Lightw. Technol. , vol. 21, no. 1, pp. 61-68, Jan. 2003.

G. P. Agrawal, Applications of Nonlinear Fiber Optics, New York: Academic, 2001.

X. Zhang and H. Iwakura, "Design of IIR digital allpass filters based on eigenvalue problems", IEEE Trans. Signal Process., vol. 47, no. 2, pp. 554-559, Feb. 1999.

C. R. Menyuk, "Stability of solitons in birefringent optical fibers, II Arbitrary amplitudes", J. Opt. Soc. Amer. A, Opt. Image Sci. , vol. A5, pp. 392-402, 1988.

A. Carema, V. Curri, R. Gaudino, P. Poggiolini and S. Benedetto, "A time-domain optical transmission system simulation package accounting for nonlinear and polarization-related effects in fiber", IEEE J. Select. Areas Commun., vol. 15, no. 4, pp. 751-764, May 1997.

W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes, Cambridge: U.K.: Cambridge Univ. Press, 2001.

M. C. Jeruchim, P. Balaban and K. S. Shanmugan, Simulation of Communication Systems, Norwell, MA: Kluwer Academic, 2000.

M. Kahn, M. S. Mackisack, M. R. Osborne and G. K. Smyth, "On the consistency of Prony's method and related algorithms", J. Comput. Graphical Statistics, vol. 1, pp. 329-349, 1992.

A. V. Oppenhem, A. S. Willsky and S. H. Nawab, Signals and Systems, Englewood Cliffs, NJ: Prentice-Hall, 1997.

A. V. Oppenheim and R. W. Schafer, Discrete Time Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1999.

A. Lowery and P. C. R. Gurney, "Two simulators for photonic computer-aided design", Appl. Opt., vol. 37, no. 26, pp. 6066-6077, Sep. 1998.

A. Lowery, O. Lenzmann, I. Koltchanov, R. Moosburger, R. Freund, A. Richter, S. Georgi, D. Breuer and H. Hamster, "Multiple signal representation simulation of photonic devices, systems and networks", IEEE J. Select. Topics Quantum Electron. , vol. 6, no. 2, pp. 282-296, Mar. 2000.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.