Initial data to vacuum Einstein equations with asymptotic expansion

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1998.Includes bibliographical references (leaf 92).by Sang Hoon Chin.Ph.D

Governing the speed of a light signal in optical fibers:Brillouin slow and fast light

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

Enhancing the light-matter interaction using slow light: towards the concept of dense light

A couple of experiments are here presented to clarify the impact of slow light on light-matter interaction. The experiments are designed, so that the process generating slow light and the probed light-matter interaction only present a marginal cross-effect. The impact of slow light on simple molecular absorption could be separately evaluated under either material or structural slow light propagation in the same medium and led to an entirely different response

Movable dynamic grating-based optical delay line in polarization maintaining fibers

A new type of all optical delay line is realized in fibers. A local dynamic grating reflector can be generated everywhere in the fiber, demonstrating >1 us delay for 650 ps pulses

Structural slow light can enhance Beer-Lambert absorption

We experimentally demonstrate that structural slow light can enhance Beer-Lambert absorption. A 4-fold reduction of the group velocity induced by mere cavity effects has caused an increase of molecular absorption by 130%

Optical pulse differentiation based on a resonant slow & fast light system

We experimentally demonstrate that temporal differentiation of optical pulses can be realized in a slow & fast light system based on a resonance. The waveform of a 13 ns Gaussian pulse was experimentally first-order differentiated

Ultra Wide Range Tunable Delay Line Using Dynamic Grating Reflectors in Optical Fibers

We experimentally demonstrate a novel technique to realize a tunable delay line based on dynamic Brillouin gratings in a high birefringence fiber. A 8ns pulse signal is continuously delayed up to 184ns with minor distortion

Progress in Brillouin Slow Light and Its Impact in Fiber Sensing

This paper reviews the major advances in Brillouin slow light devices along the last two years. We also focus on the positive and negative implications of this effect in the development of fiber sensors

All-optical calculus based on dynamic Brillouin grating reflectors in optical fibers

We experimentally demonstrate that all-optical signal calculus can be realized based on dynamic Brillouin gratings in optical fibers. Temporal integration and first-order differentiation were performed for optical pulse with various waveforms

La lumière lente et rapide: une future pièce maîtresse pour la photonique

Nous présentons une technique permettant de réaliser un contrôle extensif et très souple de la vitesse de groupe de signaux se propageant dans une fibre optique. Ce contrôle, directement piloté par une source lumineuse, est effectué par le truchement de gains ou de pertes générés dans la fibre par diffusion Brillouin stimulée. Nos résultats montrent que des vitesses de groupe inférieures à 71'000 km/s d’une part, dépassant la vitesse de la lumière dans le vide d’autre part, et même des vitesses négatives, ont pu être obtenues à l’aide d’un simple montage tenant sur une table optique