Output Power PDF of a Saturated Semiconductor Optical Amplifier: Second-Order Noise Contributions by Path Integral Method

Abstract

Abstract-We have developed a second-order small-signal model for describing the nonlinear redistribution of noise in a saturated semiconductor optical amplifier. In this paper, the details of the model are presented. A numerical example is used to compare the model to statistical simulations. We show that the proper inclusion of second-order noise terms is required for describing the change in the skewness (third-order moment) of the noise distributions. The calculated probability density functions are described far out in the tails and can hence describe signals with very low bit error rate (BER). The work is relevant for describing the noise distribution and BER in, for example, optical regeneration.

Multicanonical Evaluation of the Tails of the Probability Density Function of Semiconductor Optical Amplifier Output Power Fluctuations

“…Our method yields the pdf reliably even for values as low as . Finally, the MMC results for the pdf are shown to agree with calculations from analytic expressions in [17] when all second-order noise contributions are taken into account.…”

“…1. Based on the analysis in [17], we expect the pdf to be well approximated by the noncentral -distribution (12) where is a modified Bessel function of the first kind, and is given in terms of the power by (13) Here is the output power in the absence of noise ( ), and ( ) is the right side of (55) in [17] for ( ). The filter transfer function is in our case equal to .…”

“…The complex electric field , with longitudinal coordinate in the SOA waveguide, is normalized such that is the power. The equations governing the time dependence of the electric field amplitude and gain are assumed to be of the standard form [17]- [19] (1) (2) Here is the modal gain, is the spontaneous carrier lifetime, is the linewidth enhancement factor, and is the waveguide loss. The function is a Langevin noise term, which describes the spontaneous emission noise.…”

“…The factors are independent Gaussian complex random variables with unit width and is given by (8) Here is the population inversion factor. As in [17], we approximate by , where is the steady-state gain. The sampling of noise contributions with sampling time models a -shaped spontaneous emission spectrum with bandwidth .…”

“…The field at the output facet, , is given by (7) for . It may be filtered to model an optical filter [17], but in the present article, we only include electronic filtering of the output power to model the receiver. The filtered output is (9) where is the filter response function.…”