Split-Step Wavelet Collocation Method for Nonlinear Optical Pulse Propagation

Tristan KREMP  Alexander KILLI  Andreas RIEDER  Wolfgang FREUDE  

IEICE TRANSACTIONS on Electronics   Vol.E85-C   No.3   pp.534-543
Publication Date: 2002/03/01
Online ISSN: 
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Issue on Signals, Systems and Electronics Technology)
Category: Optical Transmission Radio on Fiber
WDM system,  nonlinear Schrodinger equation,  partial differential equation,  wavelet,  collocation method,  

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With the emerging technology of photonic networks, careful design becomes necessary to make most of the already installed fibre capacity. Appropriate numerical tools are readily available. Usually, these are based on the split-step Fourier method (SSFM), employing the fast Fourier transform (FFT). With N discretization points, the complexity of the SSFM is O(N log2N). For real-world wavelength division multiplexing (WDM) systems, the simulation time can be of the order of days, so any speed improvement would be most welcome. We show that the SSFM is a special case of the so-called collocation method with harmonic basis functions. However, for modelling nonlinear optical waveguides, various other basis function systems offer significant advantages. For calculating the propagation of single soliton-like impulses, a problem-adapted Gauss-Hermite basis leads to a strongly reduced computation time compared to the SSFM . Further, using a basis function system constructed from a scaling function, which generates a compactly supported wavelet, we developed a new and flexible split-step wavelet collocation method (SSWCM). This technique is independent of the propagating impulse shapes, and provides a complexity of the order O(N) for a fixed accuracy. For a typical modelling situation with up to 64 WDM channels, the SSWCM leads to significantly shorter computation times than the standard SSFM.