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IEEE Journal of Selected Topics in Quantum Electronics

Information Efficiencies of Parametric Devices

Colin J. McKinstrie, Nikola Alić

Published May 20, 2011• 8 citations
Publisher

Abstract

In this paper, studies are made of the information efficiencies of optical amplifiers, attenuators, and frequency convertors. Attenuators always reduce the amount of information carried by a signal. In contrast, parametric amplifiers and frequency convertors redistribute information between the signal and idler sidebands, but preserve the total information. Homodyne detection of the sideband quadratures degrades their signal-to-noise ratios. Detection always reduces the back-to-back and converted information capacities by moderate amounts, which do not depend on how the input information is encoded. The effects of detection on the amplified information capacity can be small or large, depending on how the input information is encoded. For (standard) two-sideband amplifiers, it is best to encode correlated information in both sidebands.

DOI
10.1109/jstqe.2011.2135334

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In this paper, studies are made of the information efficiencies of optical amplifiers, attenuators, and frequency convertors. Attenuators always reduce the amount of information carried by a signal. In contrast, parametric amplifiers and frequency convertors redistribute information between the signal and idler sidebands, but preserve the total information. Homodyne detection of the sideband quadratures degrades their signal-to-noise ratios. Detection always reduces the back-to-back and converted information capacities by moderate amounts, which do not depend on how the input information is encoded. The effects of detection on the amplified information capacity can be small or large, depending on how the input information is encoded. For (standard) two-sideband amplifiers, it is best to encode correlated information in both sidebands.
In a previous paper [Opt. Express 13, 4986 (2005)], formulas were derived for the field-quadrature and photon-number variances produced by multiple-mode parametric processes. In this paper, formulas are derived for the quadrature and number correlations. The number formulas are used to analyze the properties of basic devices, such as two-mode amplifiers, attenuators and frequency convertors, and composite systems made from these devices, such as cascaded parametric amplifiers and communication links. Amplifiers generate idlers that are correlated with the amplified signals, or correlate pre-existing pairs of modes, whereas attenuators decorrelate pre-existing modes. Both types of device modify the signal-to-noise ratios (SNRs) of the modes on which they act. Amplifiers decrease or increase the mode SNRs, depending on whether they are operated in phase-insensitive (PI) or phase-sensitive (PS) manners, respectively, whereas attenuators always decrease these SNRs. Two-mode PS links are sequences of transmission fibers (attenuators) followed by two-mode PS amplifiers. Not only do these PS links have noise figures that are 6-dB lower than those of the corresponding PI links, they also produce idlers that are (almost) completely correlated with the signals. By detecting the signals and idlers, one can eliminate the effects of electronic noise in the detectors.
Optical communication links are usually made with erbium-doped fiber amplifiers, which amplify the signal waves in a phase-insensitive (PI) manner. They can also be made with parametric fiber amplifiers, in which the signal waves interact with idler waves. If information is transmitted using only the signals, parametric amplifiers are PI and their noise figures are comparable to those of erbium amplifiers. However, transmitting correlated information in the signals and idlers, or copying the signals prior to transmission, allows parametric amplifiers to be phase-sensitive (PS), which lowers their noise figures. The information capacities of two-mode PS links exceed those of the corresponding PI links by 2 b/s-Hz.
In a parametric amplifier (PA) driven by two pump waves the signal sideband is coupled to three idler sidebands, all of which are frequency-converted (FC) images of the signal, and two of which are phaseconjugated (PC) images of the signal. If such a device is to be useful, the signal must be amplified, and the PC and FC idlers must be produced, with minimal noise. In this paper the quantum noise properties of two-sideband (TS) parametric devices are reviewed and the properties of many-sideband devices are determined. These results are applied to the study of two-pump PAs, which are based on the aforementioned four-sideband (FS) interaction. As a general guideline, the more sidebands that interact, the higher are the noise levels. However, if the pump frequencies are tuned to maximize the frequency bandwidth of the FS interaction, the signal and idler noise-figures are only slightly higher than the noise figures associated with the limiting TS interactions.
Recently, there has been some controversy concerning the role of signal-to-noise ratio (SNR) calculations in conjunction with optical amplifiers and phase-shift keying. Analysis has shown that the large-signal SNR at the output of an optical parametric amplifier (OPA) or optical parametric oscillator (OPO) can exceed the shot-noise limit when an injected signal beam is used to elicit small-signal gain saturation. Although no small-signal SNR gain is obtained in this way, the large-signal SNR improvement does translate into a communication performance improvement if binary phase-shift keying is applied to the resulting output beam. Analysis has also shown that the large-signal, shot-noise limited SNR can be exceeded when a binary phase-shift keyed coherent-state beam is applied to a preamplify-feedforward-homodyne receiver. In this case, however, there is no communication performance improvement. Indeed, the preamplify-feed-forward-homodyne receiver requires twice as many signal photons, on average, to equal the error probability of ordinary homodyne detection. In this talk we will show that there is no contradiction between these two examples.
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.