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International Journal of Modern Physics B

SQUEEZING AND FIBER-OPTIC COMMUNICATIONS

Michael Vasilyev, Nikolai M. Stelmakh

Published May 20, 2006• 3 citations
Publisher

Abstract

We review the relations between squeezing and optical communication advances and introduce the field of distributed phase-sensitive amplification, where we expect this cross-fertilization to happen next. We consider the quantum noise properties of phase-sensitive amplifiers in lossy fiber in the case of arbitrary parametric gain distribution along the fiber length. Three most important cases of gain followed by loss, loss followed by gain, and ideally distributed gain, are discussed in detail. We show that ideally distributed phase-sensitive amplifier maximizes the signal-to-noise ratio for a fixed non-linear phase shift in the fiber span, and is promising for both classical and quantum communications.

DOI
10.1142/s021797920603411x

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The equivalence between squeezing of the loss and phase-dependent amplification of the signal in an optical transmission line is shown. The properties of the radiation at the end of a lossy line, where N phase sensitive linear amplifiers have been inserted, are analyzed and discussed. In the large N limit a logarithmic dependence of the noise on the loss, which reduces the degradation of the signal-to-noise ratio, is obtained. It is also shown that by considering a χ(2) waveguide the same result can be achieved.
Optical parametric amplifiers (PAs) utilize highly efficient nonlinear effects in an optical fiber and they have the ability to operate in phase-sensitive mode. The inclusion of PAs in optical systems can give an ultimate limit for lumped amplified links in terms of achievable signal to noise ratio. The drawback is the complexity stemming from the requirement of phase matching a number of waves at each amplifier, phase lock, and the extra spectrum consumed by idler waves. In this chapter, the theories of a parametric amplifier, including the quantum-optical equations, are given. The properties of the gain saturation and the noise figure are presented. Practical amplifier systems and their applications in phase-sensitive amplification, all-optical signal regeneration, and squeeze state generation are outlined.
We present a semi-classical approach for predicting the quantum noise properties of fiber optical parametric amplifiers. The unavoidable contributors of noise, vacuum fluctuations, loss-induced noise, and spontaneous Raman scattering, are included in the analysis of both phase-insensitive and phase-sensitive amplifiers. We show that the model agrees with earlier fully quantum approaches in the linear gain regime, whereas in the saturated gain regime, in which the classical equations are valid, we predict that the amplifier increases the signal-to-noise ratio by generating an amplitude-squeezed state of light. Also, in the same process, we analyze the quantum noise properties of the pump, which is difficult using standard quantum approaches, and we discover that the pump displays complicated dynamics in both the linear and the nonlinear gain regimes.
Abstract Phase-sensitive amplification of squeezed states is a technique to mitigate high detection loss, which is especially attractive at 2 µm wavelengths. We derived an analytical model proving that amplified squeezed states can mitigate phase noise significantly. Our model discloses two practical parameters: the effective measurable squeezing and the effective detection efficiency of amplified squeezed states. A realistic case study includes the dynamics of the gain-dependent impedance matching conditions of the amplifier. Our results recommend operating the optical parametric amplifier at high gains because of the signal-to-noise ratio’s robustness to phase noise. Amplified squeezed states are relevant in proposed gravitational wave detectors and interesting for applications in quantum systems degraded by the output coupling loss in optical waveguides.
Recent theoretical work predicts that the quantum-limited noise figure of a x(3)-based fiber-optical parametric amplifier operating as a phase-insensitive in-line amplifier or as a wavelength converter exceeds the standard 3-dB limit at high gain. The degradation of the noise figure is caused by the excess noise added by the unavoidable Raman gain and loss occurring at the signal and the converted wavelengths. We present detailed experimental evidence in support of this theory through measurements of the gain and noise-figure spectra for phase-insensitive parametric amplification and wavelength conversion in a continuous-wave amplifier made from 4.4 km of dispersion-shifted fiber. The theory is also extended to include the effect of distributed linear loss on the noise figure of such a long-length parametric amplifier and wavelength converter.
Optical parametric amplifiers rely on second-order susceptibility (three-wave mixing) or third-order susceptibility (four-wave mixing) in a nonlinear process where the energy of incoming photons is not changed (elastic scattering). In the latter case, two pump photons are converted to a signal and to an idler photon. Under certain conditions, related to the phase evolution of the waves involved, this conversion can be very efficient, resulting in large amplification of an input signal. As the nonlinear process can be very fast, all-optical applications aside from pure amplification are also possible. If the amplifier is implemented in an optical input-phase-sensitive manner, it is possible to amplify a signal wave without excess noise, i.e., with a noise figure of 0 dB. In this paper, we will provide the fundamental concepts and theory of such amplifiers, with a focus on their implementation in highly nonlinear optical fibers relying on four-wave mixing. We will discuss the distinctions between phase-insensitive and phase-sensitive operation and include several experimental results to illustrate their capability. Different applications of parametric amplifiers are also discussed, including their use in optical communication links.