First, we investigate the Bouguer-Lambert-Beer (BLB) law as applied to the transmission of ultrashort pulses through water in the linear absorption regime. We present a linear theory for propagation of ultrashort laser pulses, and related experimental results are in excellent agreement with this theory. Thus we conclude that recent claims of the BLB law violations are inconsistent with the experimental data obtained by our group. Second, we study the dynamics of ultrashort pulses in a Lorentz medium and in water via the saddle point method. It shows that the saddle point method is a more efficient and faster method than the direct integration method to study one-dimensional pulse propagation over macroscopic distances (that is, distance comparable to the wavelength) in a general dielectric medium. Comments are also made about the exponential attenuation of the generalized Sommerfeld and Brillouin precursors. By applying the saddle point method, we also determined that the pulse duration estimated by the group velocity dispersion (GVD) approximation is within 2% of the value computed with the actual refractive index for a propagation distance of 6 m in water.

<p>All-optical devices have attracted many research interests due to their ultimately low heat dissipation compared to conventional devices based on electric-optical conversion. With recent advances in nonlinear optics, it is now possible to design the optical properties of a medium via all-optical nonlinear effects in a table-top device or even on a chip.</p><p>In this thesis, I realize all-optical control of the optical group velocity using the nonlinear process of stimulated Brillouin scattering (SBS) in optical fibers. The SBS-based techniques generally require very low pump power and offer a wide transparent window and a large tunable range. Moreover, my invention of the arbitrary SBS resonance tailoring technique enables engineering of the optical properties to optimize desired function performance,</p><p>which has made the SBS techniques particularly widely adapted for</p><p>various applications.</p><p>I demonstrate theoretically and experimentally how the all-optical</p><p>control of group velocity is achieved using SBS in optical fibers.</p><p>Particularly, I demonstrate that the frequency dependence of the</p><p>wavevector experienced by the signal beam can be tailored using</p><p>multi-line and broadband pump beams in the SBS process. Based on the theoretical framework, I engineer the spectral profile</p><p> to achieve two different application goals: a uniform low group velocity (slow light) within a broadband spectrum, and a group velocity with a linear dependence on the frequency detuning (group velocity dispersion or GVD).</p><p>In the broadband SBS slow light experiment, I develop a novel noise current modulation method that arbitrarily tailors the spectrum of a diode laser. Applying this method, I obtain a 5-GHz broadband SBS gain with optimized flat-topped profile, in comparison to the ~40 MHz natural linewidth of the SBS resonance. Based on the broadband SBS resonance, I build a 5-GHz optical buffer and use this optical buffer to delay a return-to-zero data sequence of rate 2.5 GHz (pulse width 200 ps). The fast noise modulation method significantly stabilizes the SBS gain and improves the signal fidelity. I obtain a tunable delay up to one pulse-width with a peak signal-to-noise ratio of 7. I also find that SBS slow light performance can be improved by avoiding competing nonlinear effects. A gain-bandwidth product of 344 dB.GHz is obtained in our system with a highly-nonlinear optical fiber.</p><p>Besides the slow light applications, I realize that group velocity dispersion is also optically controlled via the SBS process. In the very recent GVD experiment, I use a dual-line SBS resonance and obtain a tunable GVD parameter of 7.5 ns$^2$/m, which is 10$^9$ times larger than the value found in a single-mode fiber. The large GVD system is used to disperse an optical pulse with a pulse width of 28 ns, which is beyond the capability for current dispersion techniques working in the picosecond and sub picosecond region. The SBS-based all-optical control of GVD is also widely tunable and can</p><p>be applied to any wavelength within the transparent window of the</p><p>optical fiber. I expect many future extensions following this work</p><p>on the SBS-based all-optical GVD control using the readily developed SBS tailoring techniques.</p><p>Finally, I extend the basic theory of backwards SBS to describe the forward SBS observed in a highly nonlinear fiber, where asymmetric forward SBS resonances are observed at the gigahertz range. An especially large gain coefficient of 34.7 W$^{-1}$ is observed at the resonance frequency of 933.8 MHz. This is due to good overlap between the optical wave and the high order guided radial acoustic wave. The interplay from the competing process known as the Kerr effect is also accounted for in the theory.</p> / Dissertation

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[pt] Neste trabalho é apresentado um estudo sobre a determinação matemática dos valores da dispersão cromática total, do zero de dispersão distribuído e efeitos não lineares em fibras ópticas de dispersão deslocada (DS). Uma metodologia para caracterização das dispersões cromáticas e para os zeros de dispersão local das fibras estudadas é elaborada com a utilização do modelo de fibra degrau equivalente e de aproximações entre as fibras ópticas dos enlaces trabalhados. A relação entre o diâmetro do campo modal e o zero de dispersão cromática distribuído segundo A. Rossaro [6] é discutida e comprovada através da realização de uma série de medidas práticas para a determinação dos efeitos não lineares das fibras de dispersão deslocada dos enlaces da Petrobrás. O objetivo deste trabalho é analisar estes efeitos prejudiciais a transmissão de sinais ópticos de alta velocidade apresentados nos cabos submarinos da Petrobrás entre o Porto de Imbetiba e as plataformas de Pargo I e Pampo I na Bacia de Campos, analisando os resultados obtidos e caracterizando as possibilidades de upgrade destes enlaces. / [en] This work presents a study on the mathematical determination of the total chromatic dispersion, zero dispersion wavelength and nonlinear optical effects in dispersion shifted (DS) fiber optic system. A methodology to determine the chromatic dispersion and zero dispersion wavelength is proposed using the equivalent step index model and the similarity of the total chromatic dispersion measured in fibers of the links under study. The relationship between the mode field diameter and the zero dispersion wavelength according to A. Rossaro [6] is discussed and proven with a series of practical measurements for the determination of the nonlinear effects of the dispersion shifted optical fibers of Petrobras links Imbetiba - Pargo and Imbetiba - Pampo of the Campos Basin. / [es] En este trabajo se presenta un estudio sobre la determinación matemática de los valores de dispersión cromática total, del cero de dispersión distribuido y los efectos no lineales en fibras ópticas de dispersión desplazada (DS). Se elabora una metodología para la caracterización de las dispersiones cromáticas y para los ceros de dispersión local de las fibras estudiadas; utililizando el modelo de fibra escalón equivalente y de aproximaciones entre las fibras ópticas de los enlace. Se discute la relación entre el diámetro del campo modal y el cero de dispersión cromática distribuido según A. Rosaro [6] se comprueba a través de la realización de una serie de medidas prácticas para la determinación de los efectos no lineales de las fibras de dispersión desplazada de los enlaces de la Petrobrás. EL objetivo de este trabajo es analizar los efectos perjudiciales a la transmisión de señales ópticos de alta velocidad que se presentan en los cables submarinos de la Petrobrás entre el Puerto de Imbetiba y las plataformas de Pargo I y Pampo I en la Bacia de Campos, analizando los resultados obtenidos y caracterizando las posibilidades de upgrade de estos enlaces.