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IEEE Journal of Quantum Electronics

Spectral broadening of stochastic light intensity-smoothed by a saturated semiconductor optical amplifier

M. Munroe, J. Cooper, M. G. Raymer

Published Mar 1, 1998• 26 citations
Publisher

Abstract

We present calculations of the intensity smoothing of stochastic light by a semiconductor optical amplifier (SOA). We predict spectral changes of the light that are due to amplitude-to-phase coupling in the gain medium. The intensity smoothing of noisy optical signals with an SOA carries a penalty of spectral broadening (increased phase noise) that increases with increasing alpha parameter (linewidth enhancement factor). The spectral broadening also increases with increasing strength of the intensity fluctuations being smoothed.

DOI
10.1109/3.661465

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We present calculations of the intensity smoothing of stochastic light by a semiconductor optical amplifier (SOA). We predict spectral changes of the light that are due to amplitude-to-phase coupling in the gain medium. The intensity smoothing of noisy optical signals with an SOA carries a penalty of spectral broadening (increased phase noise) that increases with increasing alpha parameter (linewidth enhancement factor). The spectral broadening also increases with increasing strength of the intensity fluctuations being smoothed.
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.
We numerically investigate the effect of inhomogeneous broadening caused by quantum-dot (QD) size fluctuations on the gain and phase recovery of QD semiconductor optical amplifiers (SOAs). We establish 1088 coupled rate equations to simulate the carrier dynamics of the inhomogeneously broadened QD ensembles as inhomogeneous broadening increases. When all the QD ensembles are identical and inhomogeneous broadening becomes zero, eight coupled rate equations are solved for the homogeneous QDs. The gain and phase recovery responses are calculated when an ultrashort pump pulse is injected into a QD SOA. As the inhomogeneous broadening increases, the slow component of the phase recovery at the QD ground state increases due to the enlarged contribution from the slow phase recovery of carrier reservoirs such as the QD excited states. By separately calculating the gain and phase recovery responses of the homogeneous QDs with different sizes, we identify how increasing inhomogeneous broadening affects the enlarged slow phase recovery components from carrier reservoirs. We also demonstrate that the effect of inhomogeneous broadening on the temporal variation of the α-factor is more significant compared to the injection pump power.
Statistical moments of laser intensity passing through an amplifier with stochastic gain are evaluated. This situation happens when turbulent flows exist in the gain medium, which is assumed to be a two-level atomic system. Also, it is assumed that the turbulence structure is fully characterized by a stochastic process. This gain medium is assumed to be partially homogeneously broadened and slightly saturated. In the derivations, the paraxial approximation is combined with the perturbation method to solve for the random laser field inside the amplifier. For mathematical simplicity, a plane wave is propagated through the gain medium which contains only weak turbulence fluctuations. Dependences of the average laser intensity and contrast on turbulence fluctuation strength, characteristic length of the turbulence, and gain saturation and numerically demonstrated. It is found that the turbulence fluctuations make both average intensity and contrast stronger. Also, the gain saturation reduces both average intensity and contrast. In addition, it is shown that the contrast increases as the characteristic length of turbulence is increased.>
In contrast to absorbers, where the delay time via wave mixing saturates to its maximum with increasing device length due to decay of pump power along the device, in semiconductor optical amplifiers (SOAs) the delay time increases with the device length and is limited by the corresponding growth of the SOA gain, which can lead to unacceptable amplified stimulated emission in the SOA. The number of pulses which can be stored in an SOA, defined by the gain and group velocity dispersion, also is given ultimately by this SOA gain limitation, and is estimated between one and two.
The slow light effect in SOAs has many applications in microwave photonics such as phase shifting and filtering. Models are needed to predict slow light in SOAs and its dependence on the bias current, optical power and modulation index. In this paper we predict the slow light characteristics of a tensile-strained SOA by using a detailed time-domain model. The model includes full band-structure based calculations of the material gain, bimolecular recombination and spontaneous emission, a carrier density rate equation and travelling wave equations for the input signal and amplified spontaneous emission. The slow light effect is caused by coherent population oscillations, whereby beating between the spectral components of an amplitude modulated lightwave causes carrier density oscillations at the beat frequency, leading to changes in the group velocity. The resulting beat signal at the SOA output after photodetection, is phase shifted relative to the SOA input beat signal. The phase shift can be adjusted by controlling the optical power and bias current. However the beat signal gain is low at low frequencies, leading to a poor beat signal output signal-to-noise ratio. If the optical input and SOA drive current are simultaneously modulated, this leads to forced population oscillations that greatly enhance the low frequency beat signal gain. The model is used to determine the improvement in gain and phase response and its dependency on the optical power, bias current and modulation index. Model predictions show good agreement with experimental trends reported in the literature.