Abstract

We present a novel linearization method to calculate accurate eye diagrams and bit error rates (BERs) for arbitrary optical transmission systems and apply it to a dispersion-managed soliton (DMS) system. In this approach, we calculate the full nonlinear evolution using Monte Carlo methods. However, we analyze the data at the receiver assuming that the nonlinear interaction of the noise with itself in an appropriate basis set is negligible during transmission. Noise-noise beating due to the quadratic nonlinearity in the receiver is kept. We apply this approach to a highly nonlinear DMS system, which is a stringent test of our approach. In this case, we cannot simply use a Fourier basis to linearize, but we must first separate the phase and timing jitters. Once that is done, the remaining Fourier amplitudes of the noise obey a multivariate Gaussian distribution, the timing jitter is Gaussian distributed, and the phase jitter obeys a Jacobi- θ distribution, which is the periodic analogue of a Gaussian distribution. We have carefully validated the linearization assumption through extensive Monte Carlo simulations. Once the effect of timing jitter is restored at the receiver, we calculate complete eye diagrams and the probability density functions for the marks and spaces. This new method is far more accurate than the currently accepted approach of simply fitting Gaussian curves to the distributions of the marks and spaces. In addition, we present a deterministic solution alternative to the Monte Carlo method.

[IEEE ]

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J. Lightwave Technol. (7)

D. Marcuse, "Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers", J. Lightwave Technol., vol. 8, pp. 1816-1823, Dec. 1990 .

P. A. Humblet and M. Azizog˜lu, "On the bit error rate of lightwave systems with optical amplifiers", J. Lightwave Technol., vol. 9, pp. 1576-1582, Nov. 1991.

R. Hui, M. O'Sullivan, A. Robinson and M. Taylor, "Modulation instability and its impact in multispan optical amplified IMDD system: Theory and experiments", J. Lightwave Technol., vol. 15, pp. 1071-1081, July 1997 .

M. Midrio, "Analytical performance evaluation of nonreturn-to-zero transmission systems operating in normally dispersive nonlinear fibers", J. Lightwave Technol., vol. 15, pp. 2038-2051, Nov. 1997 .

V. S. Grigoryan, C. R. Menyuk and R.-M. Mu, "Calculation of timing and amplitude jitter in dispersion-managed optical fiber communications using linearization", J. Lightwave Technol., vol. 17, pp. 1347-1356, Aug. 1999 .

J.-S. Lee and C.-S. Shim, "Bit-error-rate analysis of optically preamplified receivers using an eigenfunction expansion method in optical frequency domain", J. Lightwave Technol., vol. 12, pp. 1224-1229, July 1994 .

E. Forestieri, "Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre-and postdetection filtering", J. Lightwave Technol., vol. 18, pp. 1493-1503, 2000.

Opt. Lett. (2)

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