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The goal of this dissertation has been to develop techniques in order to use Brillouin spectroscopy as a tool for studying the elastic properties of thin films on a scale of ≃100 Å. In order to develop that capability we have built a tandem multi-pass Fabry-Perot interferometer, and that interferometer was used to study the elastic properties of Langmuir-Blodgett films. These films were chosen because they can be deposited one molecular layer at a time. As a result of these investigations we have measured the density and elastic constants of the Langmuir-Blodgett film cadmium arachidate. Samples of cadmium arachidate were prepared on molybdenum and BK-7 glass substrates. Data were accumulated for a range of thicknesses and for different scattering geometries. These data will be used to argue that guided acoustic waves were observed in a highly anisotropic film. The observed guided acoustic waves will be identified as a Rayleigh wave and a tight band of Sezawa modes. No Love modes were detected in these experiments; however, evidence for reorientational modes typical of anisotropic liquids was detected. The dispersion of the Rayleigh wave as a function of thickness together with thick film scattering data were used to estimate the elastic constants in cadmium arachidate. In particular the shear elastic constant c₄₄ was found to be a small value: c₄₄ < 4.0x10⁸ N/m². The remaining elastic constants were estimated, assuming hexagonal film symmetry, to be c₆₆ < 4.5x10⁹ N/m², C₁₁ ≃ 1.1x10¹⁰ N/m², c₃₃ ≃ 2.1x10¹⁰ N/m², c₁₃ ≃ 1.0x10¹⁰ N/m², and c₁₂ > 3.x10¹⁰ N/m². It is interesting to note that the acoustical behavior of cadmium arachidate is quite similar to the smectic phase liquid crystals (c₄₄ = 0).

Solutions to the dispersion relation for waves propagating parallel to the static magnetic field in a plasma of arbitrary β are obtained. (β is the ratio of thermal to magnetic pressure.) Resonant scattering by these waves is evaluated. It is found that the magnetostatic approximation, used extensively in the past, breaks down for particles with pitch angles near 90°, and one must consider the more complicated process of particle scattering in electromagnetic turbulence. Many aspects of particle propagation in a finite temperature plasma can be discussed without assuming magnetostatic turbulence. This is accomplished by using a graphical method to obtain the solutions of the resonance condition. Results show that in a high β plasma, wave damping causes a gap, or hole, in μ-space where the resonant particle scattering rate is severely depressed. It is found that only high energy (γ ≥10⁵) electrons can be trapped within a typical supernova remnant. When the notion of electromagnetic resonance is applied to particle propagation in the interplanetary β ≤ 1) plasma, it is found that significant modifications to the conventional scattering picture must be made. It is found that a resonance gap exists which is similar to the one in a high β plasma. For electrons, this gap provides a natural explanation for scatter-free events. Theory predicts that these events should occur for kinetic energies T ≤ 300 keV while observations indicate that the majority have T ≤ 500 keV. For protons and energetic electrons, the scattering mean free path is critically dependent on the non-resonant scattering rate for particles within the gap. This fact provides a way to resolve the well known discrepancy between the theoretical and observational values for the mean free path, λ.

A rigorous analysis based upon the extinction theorem is presented to study anomalous resonance effects from single- and multilayer-overcoated, low-efficiency diffraction gratings. Anomalously high diffraction efficiency at resonance results from the coupling of the incident beam into guided waves that can be propagated within the composite structure. Both the traditional characteristic matrix technique and a recursive or R-matrix propagation technique are presented. The R-matrix propagation algorithm was found to be stable numerically, and computational results agree favorably with both experimental and other theoretical work. Numerical results are presented in order to investigate the influence of certain parameters (i.e., groove depth and shape and the number of high- and low-index overlayers) on the diffraction efficiency at resonance. In this analysis, a wavelength of 0.6328 μm and grating period of 0.7 μm were chosen so that only a -1 diffracted order other than the specular is reflected from the gratings. Perfect transfer of the grating relief to the film boundaries does not occur in all instances; it depends on the grating and film characteristics together with the conditions during deposition. Investigated in this work is the effect of nonreplication of the grating profile at film interfaces on anomalous diffraction; a transition from trapezoidal profile at the grating substrate to a rounded relief at the top surface of the multilayer structure is assumed. For the cases studied, it was found that nonreplication has the effect of reducing the strength of the resonance outcoupling. Finally, experimental results on anomalous resonance effects for multilayer-coated gratings are presented. Good agreement with computational results was attained.

Measurements of the differential cross-section for elastic scattering of positive and negative kaons off of a proton target are given in this dissertation. The beam momenta were 100 GeV/c and 200 GeV/c. The range of t, the four momentum transfer squared, measured was 0.4 < -t < 3.0. The experiment was performed at Fermilab. The data is consistent with previous experiments. Because of the much greater statistical accuracy of this experiment, it is now clear that the apparent equality of the pion and kaon cross-sections at larger t was due to poor statistical accuracy. The experimental results are not predicted by any theory. Furthermore, the difference between the pion and kaon differential cross-sections is not explained by geometrical scaling, as it was in the past.

The amount of information (types of solutions, accuracy and moments of the solution) about tropospheric rural aerosol size distribution that can in theory be obtained from backscattered measurements, without using any additional information about the anticipated solution, has been discussed. In practice, additional assumptions (constraints) must be used to solve for aerosol size distribution. The inferred solution reflects those assumptions and is therefore not objective. The quality of the solution depends on the applicability of the constraints to the given problem. A library of pseudo-empirical functions is used to form a set of orthogonal basis functions. It is assumed that any unknown aerosol size distribution may be constructed from a linear sum of these basis functions. The problem then becomes one of solving for the unknown coefficients of the basis functions. A solution with a smoothing constraint and a positivity constraint has been developed. Results of the method, when backscattered radiation is used as measurements, are presented. Discussion on the limitations of the method and the effects upon the solution of the different assumptions that are used is given. Some possible uses of the solution are considered.

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