This thesis reports on a new design of photonic crystal waveguides (PCWs) to achieve large guiding bandwidth, linear dispersion, single-mode behavior, good coupling efficiency to dielectric waveguides, and small loss. The design is based on using the linear dispersion region of one PCW in the photonic bandgap (PBG) of another PCW. While perturbing the period can result in a PCW with linear dispersion and large guiding bandwidth, it introduces an odd mode at those frequencies, as well. By using another perturbation scheme, it is shown that single-mode behavior can also be achieved. The linear dispersion of these waveguides and their operation at lower frequencies of the PBG, where the density of states of radiation modes is smaller, gives rise to very small loss coefficients as verified experimentally. Full characterization of a waveguide requires the measurement of not only the transmission coefficient, but also the dispersion and spectral phase. We have developed a real-time characterization technique based on spectral interferometry with femtosecond laser pulses at optical communication wavelengths to measure the spectral phase of waveguides. This haracterization technique can be used to study fast dynamics in timevarying structures and makes the alignment easy.

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.

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The purpose of this work is to study the initial value problem for coherent pulse propagation (SIT) for zero area pulses. We employ the machinery of the newly developed mathematical technique of the inverse scattering method (ISM) to deduce general rules by which one can predict the kind of output pulses for a given input pulse impinging on a resonant attenuator. This study is relevant since the area theorem cannot provide unambiguous information about zero area pulses. Thus in effect we introduce an equivalent and more general formulation to the theorem in terms of the reflection coefficient, r(ν), of the ISM. The poles of r(ν) correspond to the steady state solitary pulses called solitons. We show that the threshold for soliton generation, including breathers, is for an absolute initial area of about π, a result consistent with the predictions of the area theorem. We solve an example of an input zero area profile. We also show that if the input pulse has an odd profile with respect to time, only breathers can be expected as solitons. We demonstrate that the conservation equations are of limited use when applied to zero area pulses. They give satisfactory results only in a limited region. We compare the predictions of the conservation equations to the predictions of the ISM, and come to the conclusion that for zero area pulses, the ISM is the only known satisfactory approach.

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This thesis deals with several theoretical aspects of the interaction of an intense femtosecond laser pulse with a plasma. A mechanism for the enhancement of the collisional absorption of light at high intensities is described, involving the direct excitation of collective modes of the plasma, and the importance of this mechanism for a solid-density laser-produced plasma is studied under a range of conditions. An intensity-dependent collision rate is used in a numerical calculation of the reflectivity of a steep-gradient plasma, such as might be produced by an intense femtosecond laser pulse, and the conditions required to maximize absorption at high intensities are determined. The relative contributions of field-induced ionization and collisional ionization in laser-produced plasmas are studied, and it is shown that the behaviour of a gaseous plasma is almost solely governed by the field-induced process. A model is developed to simulate the propagation of an intense femtosecond laser pulse through an initially neutral gas, and this model is used to make predictions about spectral modifications to the laser pulse. Under certain conditions the spectrum is significantly broadened and suffers an overall blue shift. Quantitative fitting of theoretical spectra to experimental results in the literature is attempted, but is complicated by associated defocusing effects in the plasma. Field-induced ionization can produce a gaseous plasma which is significantly colder, for the same degree of ionization, than a plasma produced by collisional ionization. One possible application for a cold highly-ionized plasma is in a recombination x-ray laser, and the propagation model allows the calculation of the plasma temperature, which is a crucial parameter in assessing the feasibility of such schemes.

Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2005. / You, Li, Committee Member ; Buck, John A., Committee Member ; Kvam, Paul, Committee Member ; Kennedy, Brian, Committee Member ; Trebino, Rick, Committee Chair. Vita. Includses bibliographical references.