This dissertation investigates the modeling, design, fabrication and testing of the input and output coupling properties of waveguide grating couplers. It is motivated by the application of waveguide gratings to integrated optics. The coupling in both normal incidence and oblique incidence are described, but more attention is paid to the normal incident case. The perturbation transmission line theory is chosen as a theoretical model to design grating couplers in this work. The fundamental coupling parameters were carefully measured by many experiments. The comparison of experimental results to theoretical results is also discussed in this dissertation. For the case of normal incidence, the emphasis is on the optimization of the input coupling efficiency. The maximum input coupling efficiency carried out from our experiment was 75% by means of blazed grating in dielectric waveguide at a wavelength 0.6328 $\mu$m, which is very close to the maximum theoretical value of 80%. This coupling efficiency is significantly larger than that having been reported (40-50%). To achieve this goal, some parameters, such as, output coupling efficiency (branching ratio) and coupling distance (leakage factor), have been measured to test the theoretical model. The effect of the angular divergence and the wavelength dispersion of the incident beam on the input coupling efficiency is taken into account, which was modeled by coupled mode equation and tested by experiment. In addition, the design and fabrication procedure is also discussed in detail. In the case of oblique incidence the emphasis is on the output coupling only, i.e. the coupling from guided wave to radiated wave. In this part of the work the important features of the radiated wave-mode coupling efficiency and mode-conversion efficiencies, the phase difference between TE and TM components and the polarization state--were revealed and compared with the theory. These parameters were measured using one shallow rectangular grating and one deep blazed grating. These measurements were compared with the theoretical model.

Apertures are usually placed in optical systems to reduce unwanted light, which generally comes from sources other than the intended object. However, even though geometrical rays may be blocked from the detector plane, diffraction of the unwanted radiation will produce an increase in measured irradiance. Therefore, the goal of this dissertation is to model this diffractive scatter in a system of one or two circular apertures and confirm or reject the model through comparison of theoretical and experimental results. The model is based on the Geometric Theory of Diffraction, which uses coefficients of diffraction to predict the complex amplitude of an electromagnetic field following a diffracting aperture. A near field sampling theorem is derived and applied to both one and two aperture calculations. In addition, because this theory relies on root finding techniques to determine points of diffraction, a modification is made to the one-dimensional bisection method for use as a global root-finding technique for the case of two apertures. Comparison of theoretical and experimental data confirms the validity of the model for both cases. However, because diffraction from the second aperture is so weak, results from one aperture are shown to correctly model diffraction for the two aperture case as well. Furthermore, because theoretical results for both one and two aperture cases are quite close, but agreement between theory and experiment is better for the two aperture case, the role of the second aperture is determined to be that of blocking reflective scatter from the rim of the first aperture.

An interactive computer program .has been developed to compute accurate values of lightning-caused changes in the cloud electric field (ΔE). The ΔE' s for individual discharges in eight Florida thunderstorms have been analyzed using a nonlinear, least-squares minimization procedure and point charge (Q) and point dipole (P) models of the change in cloud charge. The results indicate that the temporal and spatial behavior of the Q- and P- model parameters are similar to those reported previously by Koshak and Krider [1989]. In all storms, the high altitude P-vectors tend to point downward toward a narrow altitude band of Q-solutions that is centered at about 8 km; low altitude P-vectors tend to point upward toward the Q-region: and the P-vectors that are at the same altitude as the Q-solutions tend to be horizontal. Because there are inherent limitations in the above least-squares analysis method and models, a new, fundamentally different approach for analyzing lightning field changes has been developed. This method finds an optimum volume charge distribution on a grid of finite dimensions and resolution. with this linear approach, we now have the ability to describe complex field change patterns subject to a variety of external constraints. We also have a framework in which a standard eigenanalysis can be used to access the general information content of data and the effects of measurement errors. Tests of the linear method with simulated lightning sources show that a centroid of the lightning charge distribution can be retrieved to within the grid resolution (2 km) when a Landweber iterative algorithm is used. Tests on three natural lightning events show that there is good agreement with previous Q- and P- model solutions and a resonable result for one event that could not be described with either a Q- or a Pmodel.

This dissertation considers both a lossless and a dissipative micromaser in which a monoenergetic beam of two-level atoms in a coherent superposition of their upper and lower states is injected inside a single mode, high-Q cavity. In the lossless case, we find that under appropriate conditions a field initially in a mixed state will evolve to previously unknown pure states, which we call the tangent and cotangent states. In various limits, these states exhibit interesting properties such as sub-Poissonian photon statistics and squeezing, and most importantly they acquire the characteristics of "macroscopic" quantum superpositions. When dissipation of the cavity mode is incorporated into the model, we find that although the field no longer evolves to a pure state, the mixed steady-state field may still retain the properties of a macroscopic superposition under experimentally realizable damping rates. We then evaluate the experimental conditions necessary for the preparation and detection of such macroscopic superpositions.

The thickness and refractive index of thin films determines their performance. Thickness variation due to the deposition process is well understood and correctable. Variation in the refractive index due to the deposition process is a considerably more complex problem. In this work two important members of the class of high index refractory materials: Tantalum pentoxide and Titania are investigated. These materials are known to produce very high quality films. Ion plating of tantalum results in the extremely high quality films, but ion plating of titania results in films with absorption that is too high and the process is now no longer used. Ion assisted deposition of titania, however, results in high quality films. The variation in refractive index due to the columnar microstructure of these materials has been eliminated but the subtler aspects of the thin films behavior is more difficult to improve. It is this aspect that I have investigated. In particular what improvements can be made by post deposition annealing of ion plated and ion assisted deposition of Tantalum pentoxide, and can the ion bombardment of Titania result in films with increased birefringence. If this anisotropy can be increased a number of interesting polarizing elements can be produced. These investigations were performed in distinct methods. The absorption of these films required the design and construction of a specialized highly sensitive waveguide apparatus. The investigation of anisotropy involved examining the evolution of form birefringence in situ by polarimetry. A further parameter of interest, although not as yet widely studied in thin films as the effects are small and difficult to observe is material nonlinearity. In the future the design of dynamic filters or coatings for powerful laser systems will require a good means of determining this kind of behavior in thin films. To this end we have designed our absorption instrument to be able to determine changes in refractive index due to a strong external pump beam. These effects are described in chapter three as an indication of future trends in this area.

A new model for computing radiative transfer in a spherically symmetric atmosphere has been developed which uses a Gauss-Sidel iteration similar to Herman(1963). To account for inhomogeneities in the horizontal intensity field, the current work introduces a conical boundary on which solutions are found. This boundary is used in an interpolation scheme to obtain the intensity at the center of the cone. The model includes absorption and aerosols but neglects polarization and refraction. Checks of the model were performed. Results for a high sun and small optical depth compared to flat atmosphere results were consistent with geometric arguments. The results where the radius of the planet was increased by a factor of 100 agree with flat atmosphere results to better than 1%. Flux is conserved to better than 3%, and boundary solutions are accurate to better than 3% for nontangent paths, and 12% for tangent paths. A 10% biased boundary solution caused less than a 1% change in the final solution. The model also agreed favorably with models developed by Asous (1982), Marchuk et al. (1980) and Adams and Kattawar (1978). From the results of tests the model is concluded to be accurate to 3%, and in most earth-atmosphere situations accurate to 1%. This accuracy is on the order of, or better than, previous techniques and more computationally efficient than Monte Carlo simulations. The current model is more versatile and accurate than techniques that strive for computational efficiency. The model was used to examine the atmospheric limb problem and results from this work indicate that ozone and stratospheric dust layers may be detected from limb measurements.

Optical component alignment and testing using reverse optimization has been investigated for different measurement methods and optical systems. The methods discussed were ray aberration measurement and wavefront aberration measurement. The methods were applied to real and simulated optical systems and compared. A testbed was designed to measure ray aberrations by means of physical raytracing of a three-mirror telescope in order to align the telescope by means of ray aberration measurement and reverse optimization, a technique of computer aided alignment. Ray aberration measurements were used to align the three-mirror telescope. Experimental results and improvements to the technique are discussed. Wavefront aberration methods are described and compared to ray aberration measurements. The wavefront aberration method was more easily used with systems with low nominal aberrations and when figure testing is desired. The ray aberration technique is most useful with systems of large aberration when capture range may be a problem and when component figure is well known. The method of reverse optimization is shown to work for wavefront aberration measurements in computer simulations using a Cassegrainian telescope, Cooke triplet and afocal two-Petzval telescope. Component figure errors and misalignments were determined simultaneously with sufficient spatial sampling of the wavefront aberrations. Surface parameters and component alignments were used as optimization variables. The effects of gaussian noise on the wavefront data were simulated for misalignment of the two-Petzval design. Results showed that noise can be compensated by the use of large numbers of optimization targets. Wavefront aberration measurements and reverse optimization were used to align a laboratory two-Petzval system to verify the results of the simulations.

The light scattering problem of a sphere on or near a plane surface is solved using an extension of Mie theory. The approach taken is to solve the boundary conditions at the sphere and at the surface simultaneously and develop the scattering amplitude and Mueller scattering matrices. This is performed by projecting the fields in the half space region not including the sphere multiplied by an appropriate Fresnel reflection coefficient onto the half space region including the sphere. An assumption is made that the scattered fields from the sphere, reflecting off the surface and interacting with the sphere, are incident on the surface at near-normal incidence. The exact solution is asymptotically approached when either the sphere is a large distance from the surface or the conductivity of the medium behind the surface approaches infinity. The solution is greatly simplified in the asymptotic limit when the sphere is small compared with the wavelength. Comparisons are made between the experimental Mueller matrices of a contaminated surface and matrices predicted using this simplified system. Comparisons are also made between experimental BRDFs and those predicted using the sphere-surface scattering theory.

The nonlinear optical properties of bulk and quantum well semiconductor waveguides were measured as well as their time response near half the band gap. Experiments were performed on different semiconductors including the following bulk semiconductors GaAs, AlGaAs, InGaAlAs, and on GaAs/AlGaAs quantum well samples, to measure the two and three photon absorption, the free carrier cross section, and the nonlinear index of refraction. Also all-optical switching was demonstrated in a nonlinear directional coupler, and for the first time in a nonlinear X-switch. The switching exhibited high throughput, and the switching time is shorter than the 400 femtosecond pulses used in the experiment. A three photon figure of merit including the influence of nonlinear index, waveguide parameters, and three photon absorption was developed for a nonlinear directional coupler. This new figure of merit as well as the other figures of merit developed for all-optical switching are shown to be satisfied in AlGaAs when used below half the band gap.

This dissertation investigates imaging phenomena by lenses of high relative numerical aperture (NA) in the first layer of a homogeneous thin film stack. The imaging is described by a high NA model that combines elements of vector imaging theory with traditional thin-film optics. Various examples are studied with an emphasis on analyzing the polarization effects of the illumination. Experiments are shown that verify aspects of the model. A brief review of the development of high NA imaging theory is given. The use of the Debye approximation dominates most of the previous work. Investigation of imaging in thin films has been limited to the area of micro-photolithography, where verification studies are done in photoresist. High NA imaging in films is described in terms of matrix formalism. The image is based on the Debye approach in which the vector field is characterized as a plane wave decomposition for each Cartesian component of the electric field, E. This is used to describe propagation from object to entrance pupil, from entrance pupil to exit pupil, and from exit pupil to thin-film stack. If the first film of the stack is located at or near focus, the amplitude and phase of each plane wave, weighted by factors due to polarization, aberration and object diffraction, are used as input into thin-film equations to calculate the local field volume. The image distribution within the film is described by the absorbed electric energy distribution, which is proportional to |E|². The overall effect of the film is shown to significantly reduce vector effects and asymmetries in the image. This is mainly due to the reduction of NA in the film by refraction. The image of a tri-bar object with an extreme NA of 0.95 is simulated. The differences between two orthogonal polarizations are shown to be small. This is attributed to the large contribution due to the central zone of the pupil. The behavior is shown to be similar to three-beam interference. Modification of this simulation with a annular pupil results in image behavior that is very similar to two-beam interference with increased image differences between two polarizations. Two-beam and three-beam interference is shown to be derived from the general imaging equation, resulting in concise analytic vector equations. Experimental verification in photoresist film is shown using a cross-sectioning technique that highlights the image distribution. Structural artifacts within the simulated image are identified in experimental scanning electron microscope photographs. Large differences are seen between S and P polarized illumination.