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IEEE Journal of Quantum Electronics

Theory of noise accumulation in linear optical-amplifier chains

R. Loudon

Published Jul 1, 1985• 81 citations
Publisher

Abstract

The noise properties of the two main kinds of linear optical amplifier, phase-insensitive and phase-sensitive, are reviewed, with particular emphasis on their minimum-noise limits. An optical communications link is considered, in which identical sections of attenuating fiber alternate with identical linear amplifiers. The limits on the overall signal-to-noise ratios of such chains are derived. More attention is paid to the signal-to-noise ratio appropriate to phase-sensitive detection, but some results for direct detection are also given.

DOI
10.1109/jqe.1985.1072735

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The noise properties of the two main kinds of linear optical amplifier, phase-insensitive and phase-sensitive, are reviewed, with particular emphasis on their minimum-noise limits. An optical communications link is considered, in which identical sections of attenuating fiber alternate with identical linear amplifiers. The limits on the overall signal-to-noise ratios of such chains are derived. More attention is paid to the signal-to-noise ratio appropriate to phase-sensitive detection, but some results for direct detection are also given.
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We analyze the noise characteristics of an optical transmission system repeated by two-mode phase-sensitive optical parametric amplifiers. In such a system, the non-degenerated signal and idler waves co-propagate through the link, interacting with each other in the optical parametric amplifiers. For the first time, we derive a closed-form expression for the accumulated noise using the quantum-mechanical Langevin-equation approach. The derived noise formula allows calculating the noise figure of the optical-amplifier chain under the influence of the internal loss of the amplifiers and the transmission loss of the link, thereby theoretically demonstrating its low-noise characteristics.
We analyze the noise characteristics of an optical transmission system repeated by two-mode phase-sensitive optical parametric amplifiers. In such a system, the non-degenerated signal and idler waves co-propagate through the link, interacting with each other in the optical parametric amplifiers. For the first time, we derive a closed-form expression for the accumulated noise using the quantum-mechanical Langevin-equation approach. The derived noise formula allows calculating the noise figure of the optical-amplifier chain under the influence of the internal loss of the amplifiers and the transmission loss of the link, thereby theoretically demonstrating its low-noise characteristics.
The input-output relations for linear amplifiers and attenuators that have two input and two output channels are used to derive inequalities that relate their gain profiles and output noise spectra. The results generalize earlier derivations, which mainly focus their attention on single-channel devices, to the two-ended amplifiers and attenuators often used in practical communications systems. The present inequalities are satisfied by the results of previous calculations for specific model systems. It is shown that; in contrast to single-channel devices, a two-ended system can act as an amplifier for some input signals and an attenuator for others, even when all the signal frequencies are the same. The output from the two-channel amplifier has a minimum noise determined by the sum of the gains for both input channels, even when only one input channel is used and the other is in its vacuum state. The conditions on device construction needed to achieve equal gains for signals that arrive at the two ends of the device are determined. The present results reduce to those of single-channel theory in special cases where the two output channels are each separately fed by only one of the two input channels.
The properties of a linear optical amplifier or attenuator in which the input light is coupled to a collection of non-saturable atoms are considered. The photon-number factorial moments and probability distribution of the amplifier output are derived for arbitrary input statistics. Relations are obtained between the output and input variances in photon number, phase-angle cosine, and electric-field magnitude. The effects of amplification and attenuation on signal-to-noise ratio are obtained for both direct and homodyne detection. Particular attention is paid to the extents to which the non-classical properties of photon antibunching and squeezing are preserved by amplification and attenuation. It is found that both properties can at best survive only twofold intensity amplification.