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Quantum Electronics

Amplified spontaneous emission spectrum at the output of a diode amplifier saturated by an input monochromatic wave

Alexander P. Bogatov, Alexander E. Drakin, N V D'yachkov, T I Gushchik

Published Aug 22, 2016• 3 citations
Publisher

Abstract

Expressions for the amplitudes of amplified spontaneous emission waves in a diode amplifier near the frequency of a 'strong' input monochromatic wave have been derived in terms of a random function of a stationary Gaussian process. We have found expressions for the spectral density of the amplitudes and shown that, on the red side of the spectrum with respect to frequency , spontaneous emission waves obtain additional nonlinear gain, induced by the strong wave, whereas on the blue side of the spectrum an additional loss is induced. Such behaviour of the amplitudes of amplified waves agrees with previous results.

DOI
10.1070/qel16130

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Expressions for the amplitudes of amplified spontaneous emission waves in a diode amplifier near the frequency of a 'strong' input monochromatic wave have been derived in terms of a random function of a stationary Gaussian process. We have found expressions for the spectral density of the amplitudes and shown that, on the red side of the spectrum with respect to frequency , spontaneous emission waves obtain additional nonlinear gain, induced by the strong wave, whereas on the blue side of the spectrum an additional loss is induced. Such behaviour of the amplitudes of amplified waves agrees with previous results.
Spectral line broadening due to resonance absorption and induced emission is investigated for general spectral distributions of the radiation field using the frequency-dependent relaxation operator method. An analytic self-consistent solution is found for the case of equal spectral profiles of field and radiative cross sections. The often-assumed Gaussian distribution of the field in saturated amplifiers is shown to yield symmetrical doublet structure for the radiative cross sections if the induced rates are larger than or comparable to the Gaussian width. A similar calculation was therefore performed for double Gaussian field spectra that reproduces such doublet structure for the cross sections in the case of narrowly spaced Gaussians. Self-consistent solutions of gain and line-broadening equations are accordingly expected to favor the sidebands, and at very high powers and gains amplified-spontaneous-emission lines should generally split into two lines of equal intensity separated by an averaged Rabi frequency. Since the cross-section profiles vary along the amplifier, the overall gain may be diminished, although the local cross sections have enhanced maxima at high powers.
The intensity fluctuations in the output of a saturable optical amplifier are studied as the amplifier length is increased. Characteristics are determined by calculation of the diagonal elements of the density matrix of the optical field. Saturation affecting both upper-state and lower-state atomic populations is considered. Spontaneous emission distributed along the amplifier causes the "photon-number" distribution to approach a Bose-Einstein distribution during linear amplification if the input field is not Bose-Einstein. The onset of saturation reduces the relative fluctuations of the optical field both by introducing nonlinear gain and by reducing the spontaneous emission. Limiting solutions show that strong saturation leads to a major reduction in the fluctuations causing the photon-number distribution to approach a Poisson distribution.
The output of pulsed, homogeneously broadened amplified spontaneous emission (ASE) lasers operating under conditions of strong saturation is considered. An expression for the maximum power (energy) per unit volume that may be extracted from steady-state (pulsed) systems is derived and shown to be independent of the saturation intensity. Numerical calculations of the temporal evolution of the populations in the laser levels and the growth in the ASE fluence, peak intensity, and spectral width are presented for three types of laser system: quasi steady state, short pump pulses, and self-termination. In all cases the growth in the fluence of the ASE pulse is found to agree with an analytic solution derived for conditions of strong saturation. The calculated growth in intensity of the ASE pulse is compared with expressions derived by Pert [J. Opt. Soc. Am. B11, 1425 (1994)] for the steady-state case. As expected, good agreement is found for the quasi-steady-state system, but in the limit of strong saturation significant differences occur for the short pump pulse and self-terminating laser systems considered. For all cases considered, the variation of the spectral width of the ASE pulse is found to be in reasonable agreement with that predicted by Pert for steady-state conditions.
Paraxial Maxwell-Bloch theory is used to describe amplified spontaneous emission (ASE) in strongly inverted media. Counterpropagation of waves coupled through gain saturation and diffraction, and pumping by a laser beam which propagates transverse to the amplifier are included in the treatment. The reactive part of the medium polarization is calculated by population-rate equations in the limit of rapid dephasing of the atomic dipoles. The spontaneous emission noise source needed for the numerical simulation of Maxwell's equations is derived from microscopic theory by coarse-graining, thereby establishing the compatibility of the spherically symmetric microscopic source with paraxial propagation theory. The three coupled Maxwell equations for the counterpropagating ASE waves and the transversely propagating pump wave are solved numerically in time and two spatial dimensions. This simulation is used to calculate the longitudinal profile of the transverse fluorescence, which measures the saturation of the gain, the longitudinal profile of the transmitted pump wave, which measures the saturation of pump absorption, and the transverse coherence function of the radiation emitted from the ends of the amplifier.
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.