OSA's Digital Library

Journal of Lightwave Technology

Journal of Lightwave Technology

| A JOINT IEEE/OSA PUBLICATION

  • Vol. 30, Iss. 10 — May. 15, 2012
  • pp: 1405–1421

Optimal Design of Dispersion Filter for Time-Domain Split-Step Simulation of Pulse Propagation in Optical Fiber

Yang Zhu and David V. Plant

Journal of Lightwave Technology, Vol. 30, Issue 10, pp. 1405-1421 (2012)


View Full Text Article

Acrobat PDF (1505 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations
  • Export Citation/Save Click for help

Abstract

The nonlinear Schrödinger equation can be solved by split-step methods, where in each step, linear dispersion and nonlinear effects are treated separately. This paper considers the optimal design of an FIR filter as the time-domain implementation for the linear part. The objective is to minimize the integral of the squared error between the FIR frequency response and the desired dispersion characteristics over the band of interest. This least square (LS) problem is solved in two approaches: the normal equation approach gives the explicit solution, whereas the singular value decomposition approach, which is based on the theory of discrete prolate spheroidal sequences, provides geometrical insights and reveals that the normal equation could be ill-conditioned. In addition, the frequency response might exhibit singular behaviors such as overshoot. We propose two filters that both can mitigate these shortcomings: the regularized LS filter achieves this by adding a regularization term to the objective function; the quadratically constrained quadratic programming-based filter addresses overshooting more efficiently by imposing a maximum magnitude constraint on the frequency response. Numerical results show that these filters can suppress the overshoots, control the squared error, reduce the filter length and lower the computational complexity. For both single channel and wavelength-division multiplexing channels, the proposed methods generate similar outputs as the standard split-step Fourier method.

© 2012 IEEE

Citation
Yang Zhu and David V. Plant, "Optimal Design of Dispersion Filter for Time-Domain Split-Step Simulation of Pulse Propagation in Optical Fiber," J. Lightwave Technol. 30, 1405-1421 (2012)
http://www.opticsinfobase.org/jlt/abstract.cfm?URI=jlt-30-10-1405


Sort:  Year  |  Journal  |  Reset

References

  1. B. Hermansson, D. Yevick, "Numerical investigation of soliton interaction," Electronics Lett. 19, 570-571 (1983).
  2. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).
  3. R. Hardin, F. Tappert, "Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations," SIAM Rev. 15, 423 (1973).
  4. Q. Chang, E. Jia, W. Sun, "Difference schemes for solving the generalized nonlinear Schrödinger equation," J. Comput. Phys. 148, 397-415 (1999).
  5. O. Sinkin, Z. Holzlöhner, R. , C. J. Menyuk, "Optimization of the split-step Fourier method in modeling optical-fiber communications systems," J. Lightw. Technol. 21, 61-68 (2003).
  6. Q. Zhang, M. Hayee, "Symmetrized split-step Fourier scheme to control global simulation accuracy in fiber-optic communication systems," J. Lightw. Technol. 26, 302-316 (2008).
  7. A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto, "A time-domain optical transmission system simulation package accounting for nonlinear and polarization-related effects in fiber," IEEE J. Sel. Areas Commun. 15, 751-765 (1997).
  8. T. Kremp, W. Freude, "Fast split-step wavelet collocation method for WDM system parameter optimization," J. Lightw. Technol. 23, 1491-1502 (2005).
  9. L. R. Watkins, Y. R. Zhou, "Modeling propagation in optical fibers using wavelets," J. Lightw. Technol. 12, 1536-1542 (1994).
  10. M. Delfour, M. Fortin, G. Payr, "Finite-difference solutions of a non-linear Schrödinger equation," J. Comput. Phys. 44, 277-288 (1981).
  11. K. Peddanarappagari, M. Brandt-Pearce, "Volterra series approach for optimizing fiber-optic communications system designs," J. Lightw. Technol. 16, 2046-2055 (1998).
  12. X. Li, X. Chen, M. Qasmi, "A broad-band digital filtering approach for time-domain simulation of pulse propagation in optical fiber," J. Lightw. Technol. 23, 864-875 (2005).
  13. K. He, X. Li, "An efficient approach for time-domain simulation of pulse propagation in optical fiber," J. Lightw. Technol. 28, 2912-2918 (2010).
  14. L. Zhu, X. Li, E. Mateo, G. Li, "Complementary FIR filter pair for distributed impairment compensation of WDM fiber transmission," IEEE Photon. Technol. Lett. 21, 292-294 (2009).
  15. L. Trefethen, "Householder triangularization of a quasimatrix," IMA J. Numer. Anal. 30, 887-897 (2010).
  16. D. Slepian, "Prolate spheroidal wave functions, Fourier analysis, and uncertainty—V: The discrete case," Bell Syst. Tech. J. 57, 1371-1430 (1978).
  17. A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics (Springer-Verlag, 2007).
  18. Y. Ye, Interior Point Algorithms: Theory and Analysis (Wiley, 1997).
  19. S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge Univ. Press, 2004).
  20. T. Taha, M. Ablowitz, "Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation," J. Comput. Phys. 55, 203-230 (1984).
  21. G. W. Stewart, Afternotes Goes to Graduate School (SIAM, 1998).
  22. Z. Battles, L. Trefethen, "An extension of MATLAB to continuous functions and operators," SIAM J. Sci. Comput. 25, 1743-1770 (2004).
  23. J. Hunter, B. Nachtergaele, Applied Analysis (World Scientific, 2001).
  24. W. Rudin, Real and Complex Analysis (McGraw-Hill, 1987).
  25. J. Nocedal, S. Wright, Numerical Optimization (Springer-Verlag, 2006).
  26. N. Levinson, "The Wiener RMS error criterion in filter design and prediction," J. Math. Phys. 25, 261-278 (1947).
  27. G. Golub, C. Van Loan, Matrix Computations (Johns Hopkins Univ. Press, 1996).
  28. Å. Björck, Numerical Methods for Least Squares Problems (SIAM, 1996).
  29. Y. Zhu, Optimal design of dispersion filter for time-domain implementation of split-step method in optical fiber communication Master's thesis McGill Univ.MontrealCanada (2011).
  30. E. Phan-Huy Hao, "Quadratically constrained quadratic programming: Some applications and a method for solution," Math. Meth. Oper. Res. 26, 105-119 (1982).
  31. "YALMIP wiki," http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Main.HomePage.
  32. M. Grant, S. Boyd, "CVX: Matlab software for disciplined convex programming," http://sedumi.ie.lehigh.edu/.
  33. "SeDuMi: A Matlab toolbox for optimization over symmetric cones," [Online]. Available: http://sedumi.ie.lehigh.edu/.
  34. A. V. Oppenheim, R. W. Schafer, J. R. Buck, Discrete-Time Signal Processing (Prentice Hall, 1999).
  35. H. Fu, "Revisiting large-scale convolution and FFT on parallel computation platforms," (2010) http://www.stanford.edu/~haohuan/pdf/ncar_talk.pdf.
  36. R. Farhoudi, K. Mehrany, "Time-domain split-step method with variable step-sizes in vectorial pulse propagation by using digital filters," Opt. Commun. 283, 2518-2524 (2010).
  37. S. Savory, "Digital filters for coherent optical receivers," Opt. Exp. 16, 804-817 (2008).

Cited By

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