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IEEE Journal of Quantum Electronics

Noise spectra of semiconductor optical amplifiers: relation between semiclassical and quantum descriptions

Mark Shtaif, B. Tromborg, Gad Eisenstein

Published May 1, 1998• 57 citations
Publisher

Abstract

The paper presents a comparison between a semiclassical and a quantum description of the output noise spectra of semiconductor optical amplifiers. The noise sources are represented by Langevin noise functions or operators and by the vacuum field operator, and the analysis takes into account the effects of increasing gain saturation along the amplifier waveguide. It is shown that the difference between the semiclassical and quantum descriptions sums up to a shot noise term and to a correction to the semiclassical autocorrelation relation for the carrier noise. A discussion is given of the shapes of the noise spectra, the relative importance of various noise contributions, and their dependence on input power.

DOI
10.1109/3.668775

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The paper presents a comparison between a semiclassical and a quantum description of the output noise spectra of semiconductor optical amplifiers. The noise sources are represented by Langevin noise functions or operators and by the vacuum field operator, and the analysis takes into account the effects of increasing gain saturation along the amplifier waveguide. It is shown that the difference between the semiclassical and quantum descriptions sums up to a shot noise term and to a correction to the semiclassical autocorrelation relation for the carrier noise. A discussion is given of the shapes of the noise spectra, the relative importance of various noise contributions, and their dependence on input power.
Using the semiclassical approach the gain and noise powers, associated to signal and, generated in optical Raman amplifiers, are estimated for forward and backward configurations. Because it combines a corpuscular approach to a phase-amplitude description of the optical field and of the associated noise, this classical formalism allows to identify, to distinguish and to evaluate the respective noise contributions linked, first, to incident fields, such as input zero-point fluctuations, and relative intensity noise associated to the pump, and to the amplifier itself due to the electron momentum fluctuations at the optical frequency. The contribution of Rayleigh backscattering and pump depletion effects are taken into account. For both configurations, the effects of gain and pump power distribution on noise generation are underlined. The determination of the origin and of the amount of intensity noise at the output constitutes a first step toward the amplification of signal with reduced noise amount in Raman amplifiers.
Using the semiclassical approach the gain and the noise powers, associated to signal and, generated in optical Raman amplifiers, are estimated for forward and backward configurations. Because it combines a corpuscular approach to a phase-amplitude description of the optical field and of the associated noise, this classical formalism allows to identify, to distinguish and to evaluate the respective noise contributions linked, first, to incident fields, such as input zero-point fluctuations, and relative intensity noise associated to the pump, and to the amplifier itself due to the electron momentum fluctuations at the optical frequency. The contribution of Rayleigh backscattering and pump depletion effects are taken into account. For both configurations, the effects of gain and pump power distribution on noise generation are underlined. The determination of the origin and of the amount of intensity noise at the output constitutes a first step toward the amplification of signal with reduced noise amount in Raman amplifiers.
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.
We present a detailed analytical model describing the noise properties of quantum-dot (QD) optical amplifiers operating in the linear and saturated regimes. We describe the dependence of the optical noise on the main physical parameters characterizing the QD gain medium as well as on operating conditions. The optical noise at the amplifier output shows a broad-band spectrum with an incoherent spectral hole due to the gain inhomogeneity. A coherent spectral dip stemming from noise-signal nonlinear interactions is superimposed on that broad-band spectrum. The broad-band incoherent component is also calculated using an approximate model which makes use of an equivalent inhomogeneous population inversion factor. The validity of the approximation is examined in detail. We also calculate the electrical relative intensity noise and observe a spectral hole corresponding to the spectral shape of the optical noise. The most important characteristics of the optical and electrical noise spectra are determined by the degree of inhomogeneous broadening and by the fast carrier dynamics of QD amplifiers. The fast dynamics causes a very wide noise spectral hole which has important potential consequences for detection of fast data and for all optical signal processing.
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.