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IEEE Journal of Quantum Electronics

Noise in resonant optical amplifiers of general resonator configuration

E.L. Goldstein, Malvin Carl Teich

Published Jan 1, 1989• 14 citations
Publisher

Abstract

The population-statistical description of a linear optical amplifier, extended to include both a resonant optical cavity and explicit input and output photon fluxes, is shown to yield three useful noise relationships. Despite the treatment's plainly particulate character, it provides an expression for the variance of the time-integrated output-photon-detection process in which terms associated with interferometrically generated beat noise are prominent. For systems whose photodetector electrical bandwidth B is much smaller than the amplifier's optical bandwidth Delta v, as is almost invariably the case for semiconductor amplifiers in lightwave-communication systems, the time-integrated photocurrent variance can be written in a simple, physically intuitive form. Two quotients are of central importance: ( Delta nu /B) and the ratio (/) of mean amplified-signal power to mean amplified-spontaneous-emission power. In the usual case of interest for optical amplifiers in communication systems where>>, the signal-to-noise ratio of the integrated photocurrent, on which the error probability in an on-off-keyed system depends, is approximately=1/2( Delta v/B) ((n/sub S/)/(n/sub ASE/)).>

DOI
10.1109/3.42058

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The population-statistical description of a linear optical amplifier, extended to include both a resonant optical cavity and explicit input and output photon fluxes, is shown to yield three useful noise relationships. Despite the treatment's plainly particulate character, it provides an expression for the variance of the time-integrated output-photon-detection process in which terms associated with interferometrically generated beat noise are prominent. For systems whose photodetector electrical bandwidth B is much smaller than the amplifier's optical bandwidth Delta v, as is almost invariably the case for semiconductor amplifiers in lightwave-communication systems, the time-integrated photocurrent variance can be written in a simple, physically intuitive form. Two quotients are of central importance: ( Delta nu /B) and the ratio (/) of mean amplified-signal power to mean amplified-spontaneous-emission power. In the usual case of interest for optical amplifiers in communication systems where>>, the signal-to-noise ratio of the integrated photocurrent, on which the error probability in an on-off-keyed system depends, is approximately=1/2( Delta v/B) ((n/sub S/)/(n/sub ASE/)).>
The inverted population model of a linear optical amplifier is extended to incorporate explicit input and output photon fluxes. The input field is assumed to be incoherently coupled to the internal field of the amplifier, thus permitting a population statistical description of the complete system, including photon detection. Steady-state behavior and intensity amplification are simultaneously realizable. The integrated statistics of the photoelectron count at the detector are obtained and employed to evaluate a suitably defined signal-to-noise ratio for the system. The conditions under which signal enhancement can occur are derived and discussed for the case in which the input field photocount is Poisson distributed.
Introduction Most of the lightwave transmission systems operating today benefit fully from extensive deployment of optical amplifiers (OA). These components perform the amplification of optical intensity directly in the optical domain, without resorting to any electrical-domain regeneration. Optical amplifiers increase the average number of output photons per unit time by several orders of magnitude compared with the incoming signal intensity. However, as with every amplifying process, optical amplification cannot be achieved without paying back for the unavoidable noise power added to the signal intensity. As we will see in detail in Chapter 6, the optical amplification process comes with optical noise generated by spontaneous emission inside the active medium. The intensity of the optical signal is represented by the flux of the signal photon population. Conversely, the photons generated by the spontaneous emission process inside the optical cavity represent the noise photon population. The fundamental phenomenon supporting optical amplification is stimulated emission. The basic property of stimulated emission, making the great difference from spontaneous emission and enabling optical amplification, is the coherent nature of the photon generation process. Accordingly, both signal and noise photons go through the same multiplication process by means of stimulated emission. Unless the optical cavity where the stimulated emission takes place (the active cavity) presents selective features for enhancing the signal photon population relative to the spontaneous one, there is no way to avoid noise photons going through stimulated emission, filling most of the cavity population. As a consequence, both photon populations increase, leading respectively to amplified signal intensity and to amplified spontaneous emission intensity. It should be apparent that every noise photon can create a new identical noise photon as a result of stimulated emission, effectively increasing the noise intensity in the active optical cavity. This is the well-known mechanism of amplified spontaneous emission (ASE) noise in optical amplification. Any improvement in the optical amplifier structure devoted to increasing stimulated over spontaneous emission will probably increase the optical signal-to-noise ratio (OSNR) at the cavity output. The spectrum of gain characteristic of the optical active medium is usually wide enough to support an efficient amplification of the broadband spontaneous emission spectrum, leading to the broadband ASE noise power spectral density.
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 authors present a rigorous and self-contained noise analysis of an optical amplifier based on the statistics of the input source field and the amplified spontaneous emission field of the amplifier. The method enables us to obtain the frequency dependence of the output electrical noise power, which has not been derived in previous studies of optical amplifier noise based on the photon-statistics master equation. The authors characterise for the first time the noise of an optical amplifier in combination with a super-fluorescent source, taking into account the frequency dependence of the gain and the presence of optional optical filters.
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.