An integral split-step fourier method for digital back propagation to compensate fiber nonlinearity

In optical fiber transmission systems, the split-step Fourier method (SSFM) has been widely used in digital back propagation (DBP) to compensate fiber nonlinearity. In this paper, by using the Lagrange's Integral Mean Value Theorem (LIMVT), we derive an analytical expression to calculate the optimal value of the nonlinearity calculation position (NLCP) for different systems and we propose an integral SSFM (I-SSFM) based on the expression. The I-SSFM can be performed more accurately and efficiently without parameter optimization. Simulations of various transmission links show that the I-SSFM outperforms the conventional asymmetric SSFM (A-SSFM) and the symmetric SSFM (S-SSFM) significantly, especially when we employ less amount of steps to ensure computation efficiency. The computation effort of the I-SSFM reaches as low as 50% of that of the S-SSFM.