Fast split-step wavelet collocation method for WDM system parameter optimization

To meet rapidly increasing bandwidth requirements, extensive numerical simulations are an important optimization step for optical networks. Using a basis of cardinal functions with compact support, a new split-step wavelet collocation method (SSWCM) was developed as a general solver for the nonlinear Schro/spl uml/dinger equation describing pulse propagation in nonlinear optical fibers. With N as the number of discretization points, this technique has the optimum complexity O(N) for a fixed accuracy, which is superior to the complexity O(Nlog/sub 2/N) of the standard split-step Fourier method (SSFM). For the simulation of a large 40-Gb/s dense-wavelength-division-multiplexing (DWDM) system with 64 channels, the SSWCM requires less than 40% of computation time compared with the SSFM. This improvement allows a systematic optimization of wavelength-division-multiplexing (WDM) system parameters to achieve a minimum bit-error rate.

[1]  L. R. Watkins,et al.  Modeling propagation in optical fibers using wavelets , 1994 .

[2]  Ole Møller Nielsen,et al.  Wavelets in scientific computing , 1998 .

[3]  B. Hermansson,et al.  The unitarity of split-operator finite difference and finite-element methods: Applications to longitudinally varying semiconductor rib waveguides , 1990 .

[4]  Stéphane Mallat,et al.  A Wavelet Tour of Signal Processing, 2nd Edition , 1999 .

[5]  Gilles Deslauriers,et al.  Symmetric Iterative Interpolation Processes , 1989 .

[6]  Hans-Jürgen Reinhardt.  Analysis of Approximation Methods for Differential and Integral Equations , 1985 .

[7]  Tristan Kremp.  Split-step Wavelet-Kollokationsmethoden zur Simulation linearer und nichtlinearer optischer Wellenausbreitung (Split-step Wavelet Collocation Methods for Linear and Nonlinear Optical Wave Propagation) , 2004, it Inf. Technol..

[8]  G. Beylkin.  On the representation of operators in bases of compactly supported wavelets , 1992 .

[9]  Govind P. Agrawal,et al.  Nonlinear Fiber Optics , 1989 .

[10]  Wolfgang Freude,et al.  Fast wavelet collocation method for WDM system parameter optimization , 2003, OFC 2003 Optical Fiber Communications Conference, 2003..

[11]  John G. Proakis,et al.  Digital Communications , 1983 .

[12]  P. Humblet,et al.  On the bit error rate of lightwave systems with optical amplifiers , 1991 .

[13]  Masanori Koshiba,et al.  Split-step finite-element method applied to nonlinear integrated optics , 1990 .

[14]  Dirk Schulz,et al.  Improved split-step method for efficient fibre simulations , 2001 .

[15]  Arieh Iserles.  How Large is the Exponential of a Banded Matrix , 1999 .

[16]  Jau Tang.  The multispan effects of Kerr nonlinearity and amplifier noises on Shannon channel capacity of a dispersion-free nonlinear optical fiber , 2001 .

[17]  Partha P. Mitra,et al.  Nonlinear limits to the information capacity of optical fibre communications , 2000, Nature.

[18]  C.R. Menyuk,et al.  A mean field approach for simulating wavelength-division multiplexed systems , 2000, IEEE Photonics Technology Letters.

[19]  Andreas Rieder,et al.  Split-Step Wavelet Collocation Method for Nonlinear Optical Pulse Propagation , 2002, CLEO 2002.

[20]  Langis Gagnon,et al.  Symmetric Daubechies' wavelets and numerical solution of NLS equations , 1994 .

[21]  Hugo E. Hernandez-Figueroa,et al.  Improved all-optical switching in a three-slab nonlinear directional coupler with gain , 1994 .

[22]  B. Finlayson.  The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer , 1972 .

[23]  W. Rosenkranz,et al.  Efficient numerical simulation of multichannel WDM transmission systems limited by XPM , 2003, IEEE Photonics Technology Letters.

[24]  Jean-Michel Poggi,et al.  Wavelets and their applications , 2007 .

[25]  A. Carena,et al.  Suppression of spurious tones induced by the split-step method in fiber systems simulation , 2000, IEEE Photonics Technology Letters.

[26]  R. Scarmozzino,et al.  Numerical techniques for modeling guided-wave photonic devices , 2000, IEEE Journal of Selected Topics in Quantum Electronics.

[27]  S. Goedecker.  Wavelets and Their Application: For the Solution of Partial Differential Equations in Physics , 1998 .

[28]  C. Francia,et al.  Constant step-size analysis in numerical simulation for correct four-wave-mixing power evaluation in optical fiber transmission systems , 1999, IEEE Photonics Technology Letters.

[29]  C.J. Rasmussen.  Simple and fast method for step size determination in computations of signal propagation through nonlinear fibres , 2001, OFC 2001. Optical Fiber Communication Conference and Exhibit. Technical Digest Postconference Edition (IEEE Cat. 01CH37171).

[30]  Unconditionally stable procedure to propagate beams through optical waveguides using the collocation method. , 1991, Optics letters.

[31]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[32]  Gilles Deslauriers,et al.  Symmetric iterative interpolation processes , 1989 .

[33]  I. Miller.  Probability, Random Variables, and Stochastic Processes , 1966 .

[34]  Wolfgang J. R. Hoefer,et al.  A wavelet formulation of the finite-difference method: full-vector analysis of optical waveguide junctions , 2001 .

[35]  I Pierce,et al.  Wavelet operators for nonlinear optical pulse propagation. , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.