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Journal of Optics

Noise properties of propagation through slow- and fast-light media

Robert W. Boyd, Zhimin Shi, Peter W. Milonni

Published Sep 24, 2010• 16 citations
Publisher

Abstract

We consider the fundamental noise properties of propagation through slow- and fast-light optical media based on gain or loss processes. For purely quantum mechanical reasons, any gain or loss process will add noise to a transmitted light field. We derive a relation between the noise figure describing the decreased signal-to-noise ratio of the transmitted laser pulse and the fractional delay or advancement of the pulse. We apply these results explicitly to the situation of operation on the line center of a gain or loss line. We find that for an ideal gain medium the noise figure never exceeds a factor of two. For a loss medium, there is no limit as to how large the noise figure can become. The increased noise in this case is the result of the random loss of photons from the optical field.

DOI
10.1088/2040-8978/12/10/104007

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We consider the fundamental noise properties of propagation through slow- and fast-light optical media based on gain or loss processes. For purely quantum mechanical reasons, any gain or loss process will add noise to a transmitted light field. We derive a relation between the noise figure describing the decreased signal-to-noise ratio of the transmitted laser pulse and the fractional delay or advancement of the pulse. We apply these results explicitly to the situation of operation on the line center of a gain or loss line. We find that for an ideal gain medium the noise figure never exceeds a factor of two. For a loss medium, there is no limit as to how large the noise figure can become. The increased noise in this case is the result of the random loss of photons from the optical field.
We present an analysis of the propagation of light pulses through materials possessing extreme values of the group velocity. We begin with an analysis of the behaviour that occurs upon propagation through materials possessing simple Lorentzian gain or absorption lines or materials possessing sharp dips in gain or absorption features. We also describe how more complicated lineshapes can be used to tailor the dispersion of a slow-light system. We furthermore present an analysis of fundamental limitations to how many pulse widths a pulse of light can be delayed or advanced. We show how these mechanisms lead to different limits for slow and fast propagation media.
It is noted that the fiber propagation loss is a random process along the length of propagation. The stochastic nature of the loss process induces a random fluctuation to the energy of the optical signals, which, as an extra source of noise, could become comparable to the amplified-spontaneous-emission noise of optical amplifiers. The optical noise in random loss/gain has a quantum origin, as a manifestation of the corpuscular nature of electromagnetic radiation. This paper adopts the Schrodinger representation, and uses a density matrix in the basis of photon number states to describe the optical signals and their interaction with the environment of loss/gain media. When the environmental degrees of freedom are traced out, a reduced density matrix is obtained in the diagonal form, which describes the total energy of the optical signal evolving along the propagation distance. Such formulism provides an intuitive interpretation of the quantum-optical noise as the result of a classical Markov process in the space of the photon number states. The formulism would be more convenient for practical engineers, and should be sufficient for fiber-optic systems with direct intensity detection, because the quantity of concern is indeed the number of photons contained in a signal pulse. Even better, the model admits analytical solutions to the photon-number distribution of the optical signals.
Fast or slow light propagation means that the group velocity of a quasi-monochromatic light pulse propagating in a resonant medium can be significantly faster or slower than the light speed in a vacuum. Since the end of the last century and the beginning of this century, studies on this subject have attracted a great deal of interest. Remarkable progress has been achieved, based on various nonlinear optical interactions in resonant media. The fundamental research on this subject can enrich our understanding of special relativity and causality in physics. On the other hand, those mechanisms and techniques developed for fast and slow light propagation have provided the potential for many future applications, such as optical buffers and variable delay lines for optical networks, optical computing, optical telecommunications, optical data storage, and signal processing.
We analytically study the linear propagation of arbitrarily shaped light pulses through an absorbing medium with a narrow transparency window or through a resonant amplifying medium. We point out that, under certain general conditions, the pulse acquires a nearly Gaussian shape, irrespective of its initial shape and of the spectral profile of the line. We explicitly derive in this case the pulse parameters, including its skewness, responsible for a deviation of the delay of the pulse maximum from the group delay. We illustrate our general results by analyzing the slow-light experiments having demonstrated the largest fractional pulse delays.
Slow & fast light with null amplification or loss of a light signal is experimentally demonstrated. This novel method for producing zero-gain slow & fast light takes advantage of the great flexibility of stimulated Brillouin scattering in optical fibers to generate synthesized gain spectra. Generation of optical delays and advancements with minor amplitude change is realized through the superposition of gain and loss profiles showing very different spectral widths, resulting in a synthesized spectral profile identical to an ideal electromagnetically-induced transparency.