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IEEE Journal of Quantum Electronics

Optimum noise performance of optical amplifiers

H. A. Haus

Published Jun 1, 2001• 16 citations
Publisher

Abstract

The concept of noise figure F and noise measure M applicable to radio frequency and microwave amplifiers is reviewed and extended to cover optical amplifiers. Two noise figures are defined in the optical regime: one gives the ASE output, while the other gives the ratio of signal-to-noise ratios at the input and output. In the quantum regime, the lower limit on these optimum values is set by a generalization of Heisenberg's uncertainty relation. A Raman back-pumped fiber link with post-amplification with an erbium-doped fiber amplifier is used to illustrate the use of noise measure.

DOI
10.1109/3.922780

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The concept of noise figure F and noise measure M applicable to radio frequency and microwave amplifiers is reviewed and extended to cover optical amplifiers. Two noise figures are defined in the optical regime: one gives the ASE output, while the other gives the ratio of signal-to-noise ratios at the input and output. In the quantum regime, the lower limit on these optimum values is set by a generalization of Heisenberg's uncertainty relation. A Raman back-pumped fiber link with post-amplification with an erbium-doped fiber amplifier is used to illustrate the use of noise measure.
This article presents an application of a recently published probablistic model for traveling wave optical amplification. Both optical signal and amplified spontaneous emission (ASE) noise are modeled as bunches of photons traveling along the amplifying region with size varying according to simple random rules. The results of the theory enable one to obtain a complete and accurate characterization of the signal and noise counting at the amplifier output. On the basis of the above statistics, we find a realistic evaluation of the limits imposed by both quantum and ASE noise on the performances of a receiver including an optical amplifier at a preamplifier stage.
Noise is one of the basic characteristics of optical amplifiers. Whereas there are various noise sources, the intrinsic one is quantum noise that originates from Heisenberg’s uncertainty principle. This chapter describes quantum noise in optical amplifiers, including population-inversion–based amplifiers such as an Erbium-doped fiber amplifier and a semiconductor optical amplifier, and optical parametric amplifiers. A full quantum mechanical treatment is developed based on Heisenberg equation of motion for quantum mechanical operators. The results provide the quantum mechanical basis for a classical picture of amplifier noise widely used in the optical communication field.
Introduction In previous chapters we studied wave propagation in fiber OPAs from a classical standpoint, i.e. starting from Maxwell's equations. That approach provides only a partial view of the rich nature of the electromagnetic field, namely its wave nature. However, a complete description of the electromagnetic field requires quantum mechanics. This quantum description of the electromagnetic field (called quantum electrodynamics, or QED) predicts fluctuations in measurable quantities due to the Heisenberg uncertainty principle and sets ultimate limits on the performance of devices such as optical amplifiers. A remarkable result of this theory is that the statistics and thus the noise performance of a system are affected by the quantum statistics of the source and by the physical measurement that is made. Thus a different analysis is needed depending on whether homodyne, heterodyne, or direct detection (where the field simply impinges on a photodiode) is used. Direct detection reveals the particle nature of the electromagnetic field. More specifically, energy arrives in discrete units, called photons, each of which may create an electron–hole pair in a semiconductor photodetector. In particular, the number of photons in an optical pulse can be thought of as a random variable having a mean and a variance. By deriving the mean and variance of the photocurrent that would be present if one performed direct detection of ideal laser light at the input of an optical amplifier and then a similar measurement at its exit, one can quantify the degradation of the signal-to-noise ratio (SNR) caused by the amplifier.
Using the semiclassical approach the gain and the noise powers, associated to signal and, generated in optical Raman amplifiers, are estimated for forward and backward configurations. Because it combines a corpuscular approach to a phase-amplitude description of the optical field and of the associated noise, this classical formalism allows to identify, to distinguish and to evaluate the respective noise contributions linked, first, to incident fields, such as input zero-point fluctuations, and relative intensity noise associated to the pump, and to the amplifier itself due to the electron momentum fluctuations at the optical frequency. The contribution of Rayleigh backscattering and pump depletion effects are taken into account. For both configurations, the effects of gain and pump power distribution on noise generation are underlined. The determination of the origin and of the amount of intensity noise at the output constitutes a first step toward the amplification of signal with reduced noise amount in Raman amplifiers.
The problem of output moments, photon statistics, and signal-to-noise ratio in fiber Raman amplification is considered using a master equation approach, including absorption in the signal and pump modes. In the parametric approximation for the pump, results are obtained for the output moments which can be cast in a general form derived by Loudon and Shepherd [23] for phase-insensitive quantum amplifiers and attenuators. Beyond the parametric approximation, it is shown that the output moments of the signal may be obtained through iteration from lower order moments in an approximation where signal-pump correlation is ignored. Comparison with other work is discussed.
In this paper we evaluate experimentally measured signal-to-noise ratio performance of different types of optical amplifiers [V. Josse, M. Sabuncu, N. Cerf, et al., Phys. Rev. Lett. 96 163602 (2006); Z.Y. Ou, S.F. Pereira and H.J. Kimble, Phys. Rev. Lett. 70 3239 (1993)]. We pay particular attention to the low gain regime where the quantum limit of the amplifier varies with gain. Independent of the amplifier type the noise performance is remarkably close to the quantum limit. Low gain optical amplifiers are of interest for quantum communication.