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Optics Express

Physical limits to broadening compensation in a linear slow light system

Miguel González‐Herráez, Luc Thévenaz A

Published Mar 10, 2009• 18 citations
Publisher

Abstract

The dispersion experienced by a signal in a slow light system leads to a significant pulse broadening and sets a limit to the maximum delay actually achievable by the system. To overcome this limitation, a substantial research effort is currently being carried out, and successful strategies to reduce distortion in linear slow light systems have already been demonstrated. Recent theoretical and experimental works have even claimed the achievement of zero-broadening of pulses in these systems. In this work we obtain some physical limits to broadening compensation in linear slow light systems based on simple Fourier analysis. We show that gain and dispersion broadening can never compensate in such a system. Additionally, it is simply proven that all the linear slow light systems that introduce a low-pass filtering of the signal (a reduction in the signal root-mean- square spectral width), will always cause pulse broadening. These demonstrations are done using a rigorous shape-independent definition of pulse width (the root-mean-square temporal width) and arguments borrowed from time-frequency analysis.

DOI
10.1364/oe.17.004732

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Dynamic control of the speed of a light signal, based on stimulated Brillouin scattering in optical fibers, was theoretically studied and also experimentally demonstrated as the core object of this thesis. To date, slow light based on stimulated Brillouin scattering has shown the unmatched flexibility to offer an efficient timing tool for the development of all-optical future router. Nevertheless, the seeming perfect Brillouin slow light suffered from three major obstacles: naturally narrow signal bandwidth, strong change of signal amplitude, and significant signal distortion. The essential contribution of this work has been mostly dedicated to resolve all those impairments so as to make Brillouin slow light a completely operating all-optical delay line for practical applications. Actually, high capability of tailoring the spectral distribution of the effective Brillouin resonance makes possible to resolve partially or completely all those problems. 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As a result, the Brillouin gain led to effectively a spectral hole in the center of the broadband absorption and opened a transparent window while the sharp change in the refractive index was preserve. This way it makes possible to realize zero-gain Brillouin slow light. This configuration was also exploited to produce Brillouin fast light with a total absence of signal loss, simply by swapping the spectral position of the two pumps. At last, a signal was continuously delayed through a Brillouin fiber delay line without any distortion. Due to the strong induced dispersion, pulse broadening is a major difficulty in all slow light systems and it is impossible to compensate such broadening using a linear system. Therefore, a conventional Brillouin slow light system was combined with a nonlinear optical fiber loop mirror that gives a nonlinear quadratic transmission. Using this configuration, the inevitable pulse broadening was completely compensated at the output of the loop and a signal was delayed up to one symbol without any distortion. Brillouin slow light systems were further studied in the spectral domain. For a given Brillouin resonance the spectrum of a light pulse was optimized to better match the Brillouin bandwidth. When the time envelope of a pulse was properly shaped, it was clearly observed that the spectral width of the pulse became minimized while preserving the pulse duration. This way the maximum time delay through Brillouin slow light could be enhanced for a fixed pulse width. Brillouin fast light was even realized in total absence of any pump source, which is a plain requirement for the generation of Brillouin slow or fast light. This self-generated delay line, key contribution of this thesis, relies on both spontaneous and stimulated Brillouin scattering in optical fibers. In this implementation, a light signal was strongly boosted above the so-called Brillouin threshold, so that most power of the signal was transferred to a backward propagating wave, namely the generation of amplified spontaneous Stokes wave. Since the center frequency of the intense Stokes wave is below the signal frequency by exactly Brillouin shift of the fiber used, this wave led to a Brillouin loss band centered at the signal frequency. Consequently, the signal experienced fast light propagation and the propagation velocity of the signal was self-controlled, simply by varying the signal input power. This technique has many practical advantages such as its high simplicity of the configuration and an invariant signal power in the output of this delay line. Additionally, this system self-adapts the signal bandwidth as the spectrum of the amplified Stokes wave matches the spectral distribution of the signal. An alternative method to generate all-optical delay line was proposed instead of slow light. This scheme makes use of the combination of wavelength conversion and group velocity dispersion. This type of delay line was mainly aimed at improving the storage capability of delaying element. The wavelength of a signal was simply and efficiently converted at a desired wavelength using cross gain modulation in semiconductor optical amplifiers. Then the converted signal was delivered to a high dispersive medium and arrived at the end of the medium with relative time delay due to the group velocity dispersion. A fractional delay of 140 was continuously produced through this delay line for a signal with a duration of 100 ps, preserving signal bandwidth and wavelength. The effect of slow light on linear interactions between light and matter was experimentally investigated to clarify the current scientific argument regarding slow light-enhanced Beer-Lambert absorption. It was predicted that real slowing of the light group velocity could enhance the molecular linear absorptions so as to improve the sensitivity of this type of sensing. However, the experimental results unambiguously show that material slow light (slow light in traveling wave media) does not enhance the Beer-Lambert absorption.

•Jan 1, 2009•0 citations
The dispersion experienced by a signal in a slow light system leads to a significant pulse broadening and sets a limit to the maximum delay actually achievable by the system. To overcome this limitation, a substantial research effort is currently being carried out, and successful strategies to reduce distortion in linear slow light systems have already been demonstrated. Recent theoretical and experimental works have even claimed the achievement of zero-broadening of pulses in these systems. In this work we obtain some physical limits to broadening compensation in linear slow light systems based on simple Fourier analysis. We show that gain and dispersion broadening can never compensate in such a system. Additionally, it is simply proven that all the linear slow light systems that introduce a low-pass filtering of the signal (a reduction in the signal root-mean- square spectral width), will always cause pulse broadening. These demonstrations are done using a rigorous shape-independent definition of pulse width (the root-mean-square temporal width) and arguments borrowed from time-frequency analysis.
We study analytically pulse distortion in linear slow light systems, and provide some useful limits on these devices. Additionally, we also show that the contributions of phase and amplitude broadening can be de-coupled and quantified. It is observed that phase broadening is generally smaller than amplitude broadening in conventional slow light media (lorentzian gain profile) except for very large fractional delays, where it becomes larger. Upon these expressions, we may envisage new strategies to minimize the distortion in the delaying of pulses, depending on the specific application and the required fractional delay. To overcome the residual distortion, we show that nonlinear systems can lead to a resharpening of the pulses and a re-generation of the filtered frequencies.
We show a simple method to reduce the distortions in SBS based slow light systems. The distortion reduction is simply based on a broadening and adaptation of the gain bandwidth. However, a broadened gain reduces the achievable fractional delay which cannot be compensated by higher pump powers. Here we will show that this compensation can be done by additional loss spectra. With the presented method low distortions for high fractional pulse delays are possible. We show the theory and experimental verifications of our method. For Gaussian pulses with a fractional delay of 1 Bit we achieved a distortion reduction of around 23%.
We derive an analytical expression for the broadening of a Gaussian input pulse in an arbitrary linear slow light medium. The expression consists of two terms, one corresponding to amplitude broadening (low-pass filtering of the pulse bandwidth) and another corresponding to phase broadening (phase dispersion around the resonance). It is shown that for a Lorentzian gain profile, the amplitude broadening is dominant at small fractional delays. However, for large fractional delays, phase broadening is inevitably dominate.
The manipulation of the velocity of optical pulses in fibers by so-called slow-light systems seems to be very promising for future all-optical networks, but actual approaches suffer from an inevitable pulse broadening due to the delay process. In this article two different methods for the achievement of zero-broadening in Brillouin based slow-light systems are compared in theory and experiment. While one system works in the saturated regime of a Brillouin amplifier the other works in its linear regime. Both approaches fully avoid the system inherent broadening of conventional slow-light delays and can therefore extend such systems to increase their efficiency significantly. (6 pages)
Dynamic control of the speed of a light signal, based on stimulated Brillouin scattering in optical fibers, was theoretically studied and also experimentally demonstrated as the core object of this thesis. To date, slow light based on stimulated Brillouin scattering has shown the unmatched flexibility to offer an efficient timing tool for the development of all-optical future router. Nevertheless, the seeming perfect Brillouin slow light suffered from three major obstacles: naturally narrow signal bandwidth, strong change of signal amplitude, and significant signal distortion. The essential contribution of this work has been mostly dedicated to resolve all those impairments so as to make Brillouin slow light a completely operating all-optical delay line for practical applications. Actually, high capability of tailoring the spectral distribution of the effective Brillouin resonance makes possible to resolve partially or completely all those problems. First of all, a broadband spectral window was passively obtained in between two Brillouin gain/loss resonances by simply appending two segments of fibers showing different Brillouin frequency shifts. The global Brillouin gain of the concatenated fibers manifests a gain/loss doublet resonance showing a broad window in between gain/loss peaks. In practice, this configuration has a crucial advantage that it removes the need of the pump modulation, generally used to create a polychromatic pump source. Therefore, a broadband Brillouin slow and fast light was simple realized with a reduced distortion. Secondly, the signal amplification or attenuation associated to the signal delay was completely compensated by superposing Brillouin gain and loss resonances with identical depth but different width. As a result, the Brillouin gain led to effectively a spectral hole in the center of the broadband absorption and opened a transparent window while the sharp change in the refractive index was preserve. This way it makes possible to realize zero-gain Brillouin slow light. This configuration was also exploited to produce Brillouin fast light with a total absence of signal loss, simply by swapping the spectral position of the two pumps. At last, a signal was continuously delayed through a Brillouin fiber delay line without any distortion. Due to the strong induced dispersion, pulse broadening is a major difficulty in all slow light systems and it is impossible to compensate such broadening using a linear system. Therefore, a conventional Brillouin slow light system was combined with a nonlinear optical fiber loop mirror that gives a nonlinear quadratic transmission. Using this configuration, the inevitable pulse broadening was completely compensated at the output of the loop and a signal was delayed up to one symbol without any distortion. Brillouin slow light systems were further studied in the spectral domain. For a given Brillouin resonance the spectrum of a light pulse was optimized to better match the Brillouin bandwidth. When the time envelope of a pulse was properly shaped, it was clearly observed that the spectral width of the pulse became minimized while preserving the pulse duration. This way the maximum time delay through Brillouin slow light could be enhanced for a fixed pulse width. Brillouin fast light was even realized in total absence of any pump source, which is a plain requirement for the generation of Brillouin slow or fast light. This self-generated delay line, key contribution of this thesis, relies on both spontaneous and stimulated Brillouin scattering in optical fibers. In this implementation, a light signal was strongly boosted above the so-called Brillouin threshold, so that most power of the signal was transferred to a backward propagating wave, namely the generation of amplified spontaneous Stokes wave. Since the center frequency of the intense Stokes wave is below the signal frequency by exactly Brillouin shift of the fiber used, this wave led to a Brillouin loss band centered at the signal frequency. Consequently, the signal experienced fast light propagation and the propagation velocity of the signal was self-controlled, simply by varying the signal input power. This technique has many practical advantages such as its high simplicity of the configuration and an invariant signal power in the output of this delay line. Additionally, this system self-adapts the signal bandwidth as the spectrum of the amplified Stokes wave matches the spectral distribution of the signal. An alternative method to generate all-optical delay line was proposed instead of slow light. This scheme makes use of the combination of wavelength conversion and group velocity dispersion. This type of delay line was mainly aimed at improving the storage capability of delaying element. The wavelength of a signal was simply and efficiently converted at a desired wavelength using cross gain modulation in semiconductor optical amplifiers. Then the converted signal was delivered to a high dispersive medium and arrived at the end of the medium with relative time delay due to the group velocity dispersion. A fractional delay of 140 was continuously produced through this delay line for a signal with a duration of 100 ps, preserving signal bandwidth and wavelength. The effect of slow light on linear interactions between light and matter was experimentally investigated to clarify the current scientific argument regarding slow light-enhanced Beer-Lambert absorption. It was predicted that real slowing of the light group velocity could enhance the molecular linear absorptions so as to improve the sensitivity of this type of sensing. However, the experimental results unambiguously show that material slow light (slow light in traveling wave media) does not enhance the Beer-Lambert absorption.