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Journal of the Optical Society of America B

Information theoretic framework for the analysis of a slow-light delay device

Mark Allen Neifeld, Myungjun Lee

Published Sep 5, 2008• 11 citations
Publisher

Abstract

We present a framework for the information theoretic analysis of slow-light devices. We employ a model in which the device input is a binary-valued data sequence and the device output is considered within a window of finite duration. We use the mutual information between these two quantities to measure information content. This approach enables the information theoretic definitions of delay and throughput. We use our new framework to analyze a delay device based on stimulated Brillouin scattering (SBS) and find good agreement with previous SBS delay bounds.

DOI
10.1364/josab.25.000c31

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 9, 2006•5 citations
We present a framework for the information theoretic analysis of slow-light devices. We employ a model in which the device input is a binary-valued data sequence and the device output is considered within a window of finite duration. We use the mutual information between these two quantities to measure information content. This approach enables the information theoretic definitions of delay and throughput. We use our new framework to analyze a delay device based on stimulated Brillouin scattering (SBS) and find good agreement with previous SBS delay bounds.
We use an information-theoretic method developed by Neifeld and Lee [J. Opt. Soc. Am. A 25, C31 (2008)] to analyze the performance of a slow-light system. Slow-light is realized in this system via stimulated Brillouin scattering in a 2 km-long, room-temperature, highly nonlinear fiber pumped by a laser whose spectrum is tailored and broadened to 5 GHz. We compute the information throughput (IT), which quantifies the fraction of information transferred from the source to the receiver and the information delay (ID), which quantifies the delay of a data stream at which the information transfer is largest, for a range of experimental parameters. We also measure the eye-opening (EO) and signal-to-noise ratio (SNR) of the transmitted data stream and find that they scale in a similar fashion to the information-theoretic method. Our experimental findings are compared to a model of the slow-light system that accounts for all pertinent noise sources in the system as well as data-pulse distortion due to the filtering effect of the SBS process. The agreement between our observations and the predictions of our model is very good. Furthermore, we compare measurements of the IT for an optimal flattop gain profile and for a Gaussian-shaped gain profile. For a given pump-beam power, we find that the optimal profile gives a 36% larger ID and somewhat higher IT compared to the Gaussian profile. Specifically, the optimal (Gaussian) profile produces a fractional slow-light ID of 0.94 (0.69) and an IT of 0.86 (0.86) at a pump-beam power of 450 mW and a data rate of 2.5 Gbps. Thus, the optimal profile better utilizes the available pump-beam power, which is often a valuable resource in a system design.
Over the past few years, researchers have directed a significant amount of effort towards realizing tunable all-optical devices using nonlinear optical methods. It is now possible to exercise dynamic control of the group velocity of light traveling through a wide variety of material systems. The slow and fast light refer to situations in which the group velocity íg of an optical pulse through a dispersive material can be made to be smaller and larger, respectively, than the phase velocity vp = c/n. This ability could overcome the remaining challenge in current optical networks of storing and manipulating an optical signal directly in optical domain so as to avoid a bottleneck due to optical-to-electrical (O/E) and electrical-to-optical (E/O) conversions. The overall purpose of the dissertation is to study novel slow-light systems that provide controlled generation of large pulse delays relative to the pulse width with minimal pulse shape distortion by optimally design resonance profiles of such systems. The system design studies utilize several measures of performance such as the fractional delay, power throughput, and signal distortion under the limited system resource constraints. To this end, powerful data fidelity metrics are required to quantify the performance of tunable delay devices. Here, a new framework for measuring an information velocity and throughput is described and implemented using Shannon mutual information concepts. This new technique is used to investigate trends, trade-offs, and limits in slow light devices, which are physically sensible and in good agreement with analyses obtained using a conventional eye-opening(EO) metric. Using these information-theoretic and/or conventional metrics, we present the quantifying performance of gain-based stimulated Brillouin scattering (SBS) system in optical fibers as well as optical passive devices such as Fabry-Perot, fiber Bragg gratings, and ring resonators. It is shown that combining the SBS gain medium with these passive devices can compensate their respective disadvantages and thus increase delay performance without using additional resource of SBS pump power. The results show the possibility of achieving a fractional delay up to 10 at a signal bandwidth up to tens of GHz.
Slow light technology will play a key role in future all-optical communication. The slow-light technology based on stimulated Brillouin scattering has become a research highlight because of its additional advantages, such as compatibility of the devices with existing telecommunication systems, room-temperature operation, and tunable at arbitrary wavelengths. According to the propagation of a cw pulse through a Brillouin fiber amplifier, whose frequency is near the Stokes resonance, via three-wave coupling equations, both pump depletion and fiber losses taken into consideration, the principle of how slow-light effect based on stimulated Brillouin scattering produced and the mathematical expression of time delay are strictly deduced. A delay of 8 ns is obtained when the input Stokes pulse is 200ns and the SBS (stimulated Brillouin scattering) gain G is ~18 in our designed experiment of SBS slow-light system. Then the extent of transformation from pump waves to Stokes waves is measured using MATLAB numerical simulation according to the experiment dates, based on the relation between output pump light power and input pump light power and also the relation between output Stokes light power and input pump light power. And the relation between the input light power and propagation distance is discussed as well. Finally the relation between slow light pulse delay and SBS gain is also obtained.
Slow light due to stimulated Brillouin scattering in fibers is a promising technique to realize all-optical data storage and synchronization. For delaying high-speed data, we demonstrate an approach to solve the problem of narrowband Brillouin gain by phase-modulating the Brillouin pump. The bit rate of the phase-modulating signal determines the Brillouin gain bandwidth. A 1.25-Gb/s nonreturn-to-zero pseudorandom binary sequence data is delayed by 520 ps with a phase-modulated pump operating at 2.5-Gb/s bit rate. We have also observed the pattern-dependent delay and distortion of the data caused by the filtering characteristics of Brillouin amplification, and we have suppressed the distortion by detuning the carrier of the signal away from the Brillouin gain peak
Slow-light components will degrade the data bits in an optical communication system due to narrow-band amplitude and phase responses. A bit-pattern dependence is produced in the output data stream. These effects are observed in simulation as well as in an experiment based on slow light induced by stimulated Brillouin scattering (SBS) in an optical fiber. We define figure of merit involving pulse delay and data degradation to optimize slow-light components. It is demonstrated experimentally and numerically that the pattern dependence can be reduced by detuning the slow-light devices.