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Optics Letters

Generalized noise analysis of spatially inhomogeneous laser amplifiers

Guang–Hua Duan

Published Feb 15, 1993• 7 citations
Publisher

Abstract

A classical approach for treating the noise properties of spatially inhomogeneous laser amplifiers is presented. Based on the Green’s function method, the amplifier output is related to the input and the amplified spontaneous emission noise. By using the correlation properties of spatially distributed spontaneous emission, the amplifier noise variance is obtained in a rigorous way. Compared with the density operator method, this approach can easily take into account the influence of spatially inhomogeneous amplifier structures, such as in the case of erbium-doped fiber amplifiers and distributed-feedback semiconductor amplifiers. The results show that the canonical expression of noise variance is valid for any type of amplifier if one defines an effective gain and noise power density, which can be accurately calculated by this approach.

DOI
10.1364/ol.18.000275

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A classical approach for treating the noise properties of spatially inhomogeneous laser amplifiers is presented. Based on the Green’s function method, the amplifier output is related to the input and the amplified spontaneous emission noise. By using the correlation properties of spatially distributed spontaneous emission, the amplifier noise variance is obtained in a rigorous way. Compared with the density operator method, this approach can easily take into account the influence of spatially inhomogeneous amplifier structures, such as in the case of erbium-doped fiber amplifiers and distributed-feedback semiconductor amplifiers. The results show that the canonical expression of noise variance is valid for any type of amplifier if one defines an effective gain and noise power density, which can be accurately calculated by this approach.
Adopting a new classical approach, the additive noise power generated in optical amplifiers is calculated in terms of power spectral density. The classical formalism used combines a coruscular approach to a phase-amplitude description of the optical field. The noise contributions of the input field fluctuations, including zero-point fluctuations, and of the electron momentum fluctuations at optical frequency linked to the amplifier itself, are clearly identified. The excess of noise associated to coupling or built-in losses is determinated. The well-known result of the Amplified Spontaneous Emission (ASE) is obtained for the laser amplifiers. This description is applied to linear phase-insensitive amplifiers and to inhomogeneous, nonlinear phase-insensitive Raman amplifier, pointing out the effects of gain compression and gain distribution. This new approach makes possible the treatment of the squeezed-state of light and the quadrature reduced noise amplifications.
Characteristics of noise in erbium doped fiber amplifier (EDFA) are theoretically analyzed and experimentally verified. Four discreet energy models are used for erbium ion transition. Spatially varying photon number for traveling optical field was defined in a spatially divided segment with finite length, whose length is decided by property of the spontaneous emission. Quantitative evaluation of the Langevin noise sources becomes possible by this model. The amplified spontaneous emission was included in terms of discrete longitudinal mode, which is defined for whole length of the EDFA. It was found that the relative intensity noise (RIN) in the EDFA hardly changes with noise frequency in the region higher than several kHz. The phase noise in EDFA also hardly changes with the noise frequency. The frequency noise of the signal light in the EDFA increases proportional to squared value of the noise frequency. The amount of RIN and the phase noise decrease in higher input optical power. Good correspondence between theoretical and experimental results was obtained.
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.
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.
Intensity fluctuation characteristics of amplified-spontaneous emission are found using intensity rate equations and the noise-amplifier approximation for saturation coupling between two and four competing modes. The existence of more than one mode leads to the retention of relatively large fluctuations in each mode even as the amplifier gain is saturated, an operating regime which by contrast has been shown to reduce significantly the fluctuations when only a single beam is present. The noise-amplifier approximation is found to be an adequate approximation of the effects of the spontaneous emission distributed along the length of a laser amplifier. The intensity fluctuations in all cases approach limiting distributions functions as the amplifier becomes heavily saturated. Characteristics of these limiting distributions are found for one, two, and four beams; for combinations of beams copropagating and counterpropagating; in the presence and absence of loss; for differences in gain; and for saturation of the sources due to high intensities.