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IEEE photonics journal

Fast Light and the Speed of Information Transfer in the Presence of Detector Noise

M.Z. Feng, Wayne V. Sorin, R.S. Tucker

Published Sep 1, 2009• 7 citations
Publisher

Abstract

The phenomenon of fast-light pulse propagation has seen renewed interest in recent years, but its relationship to thespeed of information transferis still being debated. In this paper, we define thespeed of information transferas the propagation speed of a point of constant signal-to-noise ratio (SNR) on the leading edge of a signal pulse. We use standard telecommunication analysis to include the effects of noise so that the bit-error rate (BER) can be calculated as a function of a variable decision time. We introduce the concept of a time-dependent Q-factor so that pulse arrival times can be compared at equivalent BERs. We show that when receiver noise is included in a gain-assisted fast-light system, the measuredspeed of information transfercan exceed the speed of light for an equivalent pulse travelling through a vacuum.

DOI
10.1109/jphot.2009.2031684

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The phenomenon of fast-light pulse propagation has seen renewed interest in recent years, but its relationship to thespeed of information transferis still being debated. In this paper, we define thespeed of information transferas the propagation speed of a point of constant signal-to-noise ratio (SNR) on the leading edge of a signal pulse. We use standard telecommunication analysis to include the effects of noise so that the bit-error rate (BER) can be calculated as a function of a variable decision time. We introduce the concept of a time-dependent Q-factor so that pulse arrival times can be compared at equivalent BERs. We show that when receiver noise is included in a gain-assisted fast-light system, the measuredspeed of information transfercan exceed the speed of light for an equivalent pulse travelling through a vacuum.
We study the physical mechanism and the information velocity of fast light based on the time-domain propagator governing light propagation in a dispersive system. We show that the output pulse can be regarded as the superposition of multiple ``copies'' of the input pulse, each traveling at a well-defined signal velocity no greater than the speed of light in vacuum, and the interference between the front edges of these copies generates the peak of the output pulse. The information velocity is defined as the ratio of the propagation distance to the mini-mum time required to complete any given information transfer process, directly reflecting how fast the signal of interest, i.e., the part of the pulse that carries the information of interest, propagates. With the peak of the output pulse representing the information, as is typical in slow- and fast-light applications, we find that the information velocity is significantly smaller than the speed of a discontinuity in the pulse, which was traditionally proposed to be the signal velocity of fast light. The analysis can also be applied to slow-light propagation.
The velocity of detectable information (signal velocity) in a medium capable of supporting abnormal (superluminal or negative) group velocities is calculated. This is carried out by tracking the time instant at which the signal-to-noise ratio (SNR) at the detector output reaches a predetermined threshold while considering the total classical and quantum noise of the channel in addition to the detector noise. Furthermore, the method of steepest descent is incorporated to systematically study various forms of pulse reshaping associated with superluminal propagation and its effect on SNR. By studying the behavior of SNR as a function of both space and time, the present analysis predicts the existence of a cutoff distance beyond which signal velocity of a superluminal pulse is delayed as compared to a companion pulse traveling the same distance in vacuum. Finally, the interplay between the relative strength of the medium-generated noise and the detector noise and its effect on signal velocity is discussed.
Contemporary observational and theoretical studies on the temporal nature of microscopic measurements renewed the discussion about the fundamental constants, leading to the possibility of light speed variation and superluminal pulse propagation. Gain assisted experiments using anomalous dispersion near an absorption line in atomic gas, a "fast - light" medium, seem to lead to a wave group velocity vG exceeding c, the vacuum speed of light; moreover, definition of the information velocity vi sets the question of interpretation of the three speeds: one view is that vi = vG, but this violates Causality; another view is that vi = c in all situations, but this limits, a priori, the transport of information. Another view is that vi, vG and c are distinct. This contribution follows the last possibility. A draft discussion on space-time is given.
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.
Summary form only given. It is well known that the group velocity v/sub g/ of a light pulse can exceed c in an anomalously dispersive medium. As discussed many years ago by Sommerfeld and Brillouin, a group velocity greater than c does not violate causality because it is not the velocity of information transmission. They noted that the "frontal velocity," the velocity at which an infinitely sharp step-function-like disturbance of the light intensity propagates, can serve as a velocity of information transfer. We suggest here an operational definition of the signal velocity and apply it to the recently observed superluminal propagation of a light pulse in a gain medium.