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Physical Review A

Photoelectron statistics of solitons corrupted by amplified spontaneous emission

Takayuki Yoshino, Govind Prasad Agrawal

Published Feb 1, 1995• 1 citation
Publisher

Abstract

The probability density function (PDF) of photoelectron counts is investigated theoretically for a fundamental soliton corrupted by the spontaneous-emission noise that is generated by optical amplifiers employed along a fiber-optic transmission line. An analysis based on the orthogonal expansion of the light amplitude makes it possible to find the exact PDF that includes the influence of the soliton width, the hyperbolic-secant pulse shape, and a Lorentzian bandpass optical filter. The derived PDF is applicable to any cascaded chain of amplifiers and, as a practical example, is calculated for a receiver equipped with an optical preamplifier. The pulse width significantly affects photoelectron statistics when the product of the filter bandwidth and the counting interval is small. By comparing our exact PDF with the commonly used approximate Gaussian and Laguerre PDFs, we find that such approximations introduce large errors (by several orders of magnitude) in the tail of the PDF that is relevant for calculation of bit error rates in soliton communication systems.

DOI
10.1103/physreva.51.1662

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The probability density function (PDF) of photoelectron counts is investigated theoretically for a fundamental soliton corrupted by the spontaneous-emission noise that is generated by optical amplifiers employed along a fiber-optic transmission line. An analysis based on the orthogonal expansion of the light amplitude makes it possible to find the exact PDF that includes the influence of the soliton width, the hyperbolic-secant pulse shape, and a Lorentzian bandpass optical filter. The derived PDF is applicable to any cascaded chain of amplifiers and, as a practical example, is calculated for a receiver equipped with an optical preamplifier. The pulse width significantly affects photoelectron statistics when the product of the filter bandwidth and the counting interval is small. By comparing our exact PDF with the commonly used approximate Gaussian and Laguerre PDFs, we find that such approximations introduce large errors (by several orders of magnitude) in the tail of the PDF that is relevant for calculation of bit error rates in soliton communication systems.
The Fokker-Planck approach is used to study the statistics of an optical pulse propagating in semiconductor optical amplifiers in which the amplified spontaneous emission noise dominates. The probability density functions (pdfs) of the pulse peak sample are calculated for different saturation levels. Analytical results are possible for an ideal linear amplifier and when the simplest first-order approximation for nonlinear amplification is used. In other cases, we solve numerically the Fokker-Planck equation and the appropriate Langevin equation. Multicanonical Monte Carlo simulations ensure efficient calculations of the pdfs whose high- and low-power tails deviate from noncentral chi-square statistics for moderate and deep saturation levels, thus implying that the electric field process is not Gaussian.
We present a theoretical analysis and an experimental study of the statistical properties of the noise accompanying an optical pulse propagating in a nonlinear semiconductor optical amplifier. Several degrees of gain saturation corresponding to different levels of optical signal-to-noise ratios (OSNRs) are examined. We employ the Heun numerical procedure to ensure proper convergence to the Stratonovich solution of the multiplicative propagation equation. This algorithm takes also into account the effect of gain saturation due to the amplified spontaneous emission noise. Moreover, the multicanonical Monte Carlo algorithm is used to efficiently calculate the probability density functions (pdfs), including the tails, of the peak of a pulse which emerges at the output of a saturated semiconductor optical amplifier. The results are compared to the corresponding pdfs obtained in a linear amplification system (where the optical noise is additive and Gaussian) having the same gain and under identical OSNR levels. We demonstrate that the pdf of the saturated amplifier is shifted toward lower power levels and is narrower, or equivalently, the mean and variance for the saturated amplifier case are smaller. Also, the difference between the two configurations increases with the degree of gain saturation. The theoretical predictions are confirmed by a series of experiments in which the pdfs at the output of the linear amplification scheme and saturated semiconductor optical amplifier are measured for an optical pulse of /spl sim/ 70-ps duration.
The bit error rate (BER) performance of an optical soliton communication system is analyzed. Based on the jitter variance equation and the chi-square distribution for the amplified spontaneous emission noise, an analytic expression for the BER calculation is obtained. We have investigated the effects of Gordon-Haus jitter, which is due to the random phase shift of the soliton individual central wavelength induced by the amplified spontaneous emission noise of the amplifiers. Very good agreement has been obtained between our theory and the reported experimental results.
An equation for the distribution of the number of photoelectrons at the output of a radiation detector of an optical receiver with a preamplifier is derived for the case of a Poisson distribution of the incident photons. An analysis is given of the noise in a glass-fiber preamplifier. A computer calculation is reported of the probability of transmission of a signal for a given probability of spurious operation. This calculation is made for the case of an amplifier generating few modes. The results are given of an experimental investigation of a receiver with a neodymium glass-fiber amplifier. These results support the calculations.
The eigenvalue of the eigenvalue equation associated to the nonlinear Schrödinger equation is constant regardless of the propagation distance, so it’s an ideal information carrier that is not affected by the dispersion and the nonlinearity of optical fiber. However, the eigenvalue is affected by noise added to the signal. In this paper, we study the influence of the amplified spontaneous emission noise caused by optical amplifiers inserted at equal intervals in optical transmission system. The theoretical analysis result is consistent with computer simulated and experimental results.
This article presents an application of a recently published probablistic model for traveling wave optical amplification. Both optical signal and amplified spontaneous emission (ASE) noise are modeled as bunches of photons traveling along the amplifying region with size varying according to simple random rules. The results of the theory enable one to obtain a complete and accurate characterization of the signal and noise counting at the amplifier output. On the basis of the above statistics, we find a realistic evaluation of the limits imposed by both quantum and ASE noise on the performances of a receiver including an optical amplifier at a preamplifier stage.