Accurate Computation of b-Coefficients in Nonlinear Fourier Transform for the Manakov Equation

Abstract

In recent years, nonlinear Fourier transform (NFT) has been intensely researched as a scheme for communication over the nonlinear optical fiber and characterizing dynamics in nonlinear optical systems. For the accurate computation of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> -coefficients on discrete eigenvalues, the bidirectional algorithm has been proposed where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> -coefficients are calculated at a cutting point within the temporal window rather than two boundaries. The performance of the bidirectional algorithm depends severely upon the selection criterion of the cutting-point, which has been investigated in nonlinear Schrodinger equation and Korteweg–De Vries equation but not yet in Manakov equation accounting for the dual-polarization signals over optical fiber. In this paper, we propose a cutting-point criterion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> -coefficients for the bidirectional algorithm of Manakov equation and compare it with existing criteria. Numerical results show that, the resulting algorithm has much better accuracy compared with existing criteria, especially for signals containing a large number of eigenvalues with large imaginary parts. The bidirectional algorithm with the proposed criterion is useful for decoding the dual-polarization nonlinear frequency division multiplexing (DP-NFDM) signals for communication and characterization of vector soliton dynamics in Manakov equation described systems.