Photonic crystals can be thought of as 'optical analogues' to electronic semiconductors, and have been widely studied for their periodically-varying indexes of refraction. This allows for controlling the propagation of photons inside the crystals, similar to the way electrons are excited in a semiconductor crystal. The superprism phenomenon is the extremely large angular dispersion experienced by a light beam when entering a photonic crystal. This arises from the anisotropy of the photonic band structure which can be present even in systems without a complete photonic band gap. Here, we describe theoretical and experimental investigation of the superprism effect in three-dimensional macroporous polymer photonic crystals formed from colloidal crystal templates. We explore the extreme sensitivity of the propagation direction to various input parameters, including the input angle, the light frequency, and the composition of the photonic lattice. Such effects can be exploited for sensing and filtering applications.

Oblique-incidence, fiber-optic reflectometry is a simple and accurate method for measuring the absorption and reduced scattering coefficients, $\mu\sb{a}$ and $\mu\sb{s}\sp\prime ,$ of semi-infinite turbid media. Obliquely incident light produces a spatial distribution of diffuse reflectance that is not centered about the point of light entry. The shift in the center of diffuse reflectance is related to the medium's diffusion coefficient, D. We developed a fiber-optic probe to deliver light obliquely and sample the profile of diffuse reflectance. From a relative profile, we measure D, deduce the effective attenuation coefficient, $\mu\sb{eff},$ then calculate $\mu\sb{a}$ and $\mu\sb{s}\sp\prime .$ This method was verified with Monte Carlo simulations and tested on tissue phantoms. Measurements at 632.8 nm were accurate to within 5% for D and $\mu\sb{eff},$ resulting in 10% and 5% accuracy for $\mu\sb{a}$ and $\mu\sb{s}\sp\prime .$ In addition, $\mu\sb{a}$ and $\mu\sb{s}\sp\prime$ spectra were deduced from wavelength-resolved measurements of the diffuse reflectance from a white light source.

A new widely tunable mid-infrared (IR) source based on difference-frequency generation (DFG) in Gallium Selenide (GaSe) for use in high-resolution spectroscopy and trace gas detection is described. The characteristics of type-I phasematching in GaSe are studied. Preliminary results on the improvement of the dispersion relations for GaSe are presented. Spectroscopic feasibility experiments are reported that involve the spectroscopy of ethylene $\rm (C\sb2H\sb4)$ at low pressures near 950 $\rm cm\sp{-1}.$ Two near-IR Ti:Sapphire lasers served as convenient pump sources, which can be eventually replaced by two high power near-IR diode lasers. Design issues (including optimum elliptical focusing conditions), potential improvements and new directions are also discussed.

Real-time, compact, laser absorption-based sensors for trace gas detection have been developed. Difference-frequency generation in a periodically poled lithium niobate (PPLN) crystal pumped by two compact lasers, a near-infrared diode laser and a monolithic ring Nd:YAG laser, is used as a mid-infrared laser source. Detection of carbon monoxide (CO) and formaldehyde $\rm (H\sb2CO)$ in ppm to sub-ppm level has been performed, based on a direct absorption spectroscopy. The portable sensor designed for monitoring the CO concentration in ambient air was built and operated in the laboratory, in the open air, and a test chamber located at the NASA Johnson Space Center.

The chemistry, optical properties, and femtosecond electron dynamics of gold nanoshells are described. The gold nanoshells consist of Au-coated Au$\sb2$S nanoparticles prepared via aqueous phase chemistry using HAuCl$\sb4$ and Na$\sb2$S. During the course of the reaction, the plasmon-related absorption peak first shifts from $\sim$650 nm out to $\sim$900 nm, then shifts back to $\sim$650 nm. It is shown, using generalized Mie scattering theory, that this plasmon peak shift is determined by the relative thickness of the Au shell and the Au$\sb2$S core diameter. This understanding of the optical properties of these nanoparticles is used to elucidate the nanoparticle growth kinetics. The dynamics of the electrons in the Au shell are studied with femtosecond pump-probe spectroscopy using a cavity-dumped Ti:sapphire laser. The induced change in the transmission of the gold nanoshell films studied has a lifetime of $\sim$1.6 ps. The origin of the measured signal is shown to be due to the creation of a hot electron distribution that returns to equilibrium via electron-dissipative interactions with the nanoparticle core and the embedding medium.

A new type of confocal Raman microscope called a Fourier transform confocal Raman microscope (FT-CRM) was designed, built and characterized with respect to its spatio-spectral imaging properties. Several different applications of the FT-CRM are presented that take advantage of its unique spectral and spatial imaging characteristics. The instrument combines focused illumination with spatially-filtered detection in a confocal optical configuration to collect photons scattered from a diffraction-limited volume in the sample (typically ${<}5 times10 sp{-18} m sp3)$ and reject photons from outside that region. The molecular vibrational information encoded in the inelastic, or Raman, spectral component of light scattered from the confocal volume is measured with a visible light Fourier transform Raman spectrometer. By scanning the sample relative to the confocal volume, a volumetric Raman spectrochemical image of the sample can be constructed. / Raman scattering is an inherently inefficient process; hence an optimal radius pinhole must be found that balances the FT-CRM optical throughput against the microscope spatial resolution and image contrast. Detailed experimental measurements mapped out the FT-CRM spatial response (axial and lateral), optical throughput and image signal-to-background and signal-to-noise ratios as a function of pinhole radius. Excellent agreement was found between these measurements and the predictions of a theoretical microscope model also developed as part of this thesis. Several applications of the FT-CRM included volumetric compositional imaging of three-dimensional chemically inhomogeneous materials such as cellulose and polyester fibers in water or two immiscible optically-similar liquids, water and trichloroehthylene, in a porous quartz sandstone matrix. The potential of the FT-CRM for non-invasive spectrochemical detection and imaging through a turbid tissue-like medium was demonstrated and a new spectral estimator, Fast Orthogonal Search, was evaluated to replace the discrete Fourier transform to improve the microscope performance.

The problem of geometrical distortion in MR images is addressed in the context of the applicability of stereotactic techniques. For this purpose, the distortion of phantom images is measured at various readout bandwidths and the spatial linearity is evaluated in view of the use of a stereotactic frame. The presence of a contribution to the overall distortion of non-linear magnetic gradients is shown from the data, although the distortion observed seems to be mostly attributable to the main field inhomogeneity. The specific problems of distortion of the fiducial markers due to bulk magnetic susceptibility effects is addressed. The occurrence of such effects is characterized with the help of imaging, and the role of the phenomenon on proper target localization is demonstrated. In addition, a method of bypassing the detrimental aspect of these effects is presented. / Various distortion correction approaches are discussed, and their benefits and drawbacks are evaluated. In the light of this discussion, a recently reported correction method is then presented. This method allows the calculation of an image free from geometrical and intensity distortion from the combined effect of main field inhomogeneity, susceptibility effects and chemical shift.

<p> The Mott metal-insulator transition (MIT) in transition-metal complex oxides results from strong electron-electron interactions and is accompanied by a rich spectrum of phenomena, including magnetic, charge, and orbital ordering, superconductivity, structural distortions, polarons, and very high-density 2-dimensional interface electron liquids. Recent advances in oxide heteroepitaxy allow interface control as a promising new approach to tuning the exotic properties of materials near the quantum critical point, with potential application to technologies including phase-change electronics, high power transistors, and sensors. The dynamical conductivity of oxide heterostructures is measured using a combination of terahertz time-domain spectroscopy, Fourier transform infrared spectroscopy, and dc magnetotransport. The rare-earth nickelates <i> R</i>NiO₃ (<i>R</i> = La, Nd...) exhibit a temperature and bandwidth controlled MIT in bulk. Measurements of the Drude response in epitaxial thin films provide quantification of the strain-dependent mass enhancement in the metallic phase due to strong correlations. Reduction of LaNiO₃ film thickness leads to additional mass renormalization attributed to structural distortions at the heteroepitaxial interface, and an MIT is observed depending on the interfacing materials in coherent perovskite heterostructures. The rare-earth titanates <i>R</i>TiO₃ exhibit a bandwidth and band filling controlled Mott MIT. Furthermore, the heterointerface between Mott insulating GdTiO₃ and band insulating SrTiO₃ exhibits a 2-dimensional itinerant electron liquid, with extremely high sheet densities of 3 &times; 10¹⁴ cm^-2. The dynamical conductivity of the interface electrons is analyzed in terms of subband-dependent electron mobility and the established large polaron dynamics in bulk SrTiO₃. Additional confinement of the electron liquids is achieved by decreasing the SrTiO₃ layer thickness, with attendant increase in the dynamical mass. Taking the confinement to its extreme limit, a single (GdO)⁺ plane in Mott insulating GdTiO₃ is replaced with a (SrO)⁰ plane. This is equivalent to "delta-doping" the Mott insulator with an extremely high density sheet of holes. The transport and absorption in the resulting two-dimensional insulator are consistent with a simple model of small polaron hopping. A comparison is made to similar features in the conductivity of randomly doped Sr_1-xGd_xTiO₃ films.</p>

<p> The rapidly evolving global information infrastructure requires ever faster data transfer within computer networks and stations. Integrated chip scale photonics can pave the way to accelerated signal manipulation and boost bandwidth capacity of optical interconnects in a compact and ergonomic arrangement. A key building block for integrated photonic circuits is an on-chip laser. In this dissertation we explore ways to reduce the physical footprint of semiconductor lasers and make them suitable for high density integration on silicon, a standard material platform for today's integrated circuits. We demonstrated the first room temperature metalo-dielectric nanolaser, sub-wavelength in all three dimensions. Next, we demonstrated a nanolaser on silicon, showing the feasibility of its integration with this platform. We also designed and realized an ultracompact feedback laser with edge-emitting structure, amenable for in-plane coupling with a standard silicon waveguide. Finally, we discuss the challenges and propose solutions for improvement of the device performance and practicality.</p>

<p> Six spatial parameters, (<i>x, y, z</i>) for translation, and pitch, roll, and yaw for rotation, are used to describe the 3-dimensional position and orientation of a rigid body&mdash;the 6 degrees of freedom (DOF). The ability to measure these parameters is required in a diverse range of applications including machine tool metrology, robot calibration, motion control, motion analysis, and reconstructive surgery. However, there are limitations associated with the currently available measurement systems. Shortcomings include some of the following: short dynamic range, limited accuracy, line of sight restrictions, and capital cost. The objective of this dissertation was to develop a new metrology system that overcomes line of sight restrictions, reduces system costs, allows large dynamic range and has the potential to provide high measurement accuracy. </p><p> The new metrology system proposed in this dissertation is based on a combination of photogrammetry and optical pattern projection. This system has the potential to enable real-time measurement of a small lightweight module's location. The module generates an optical pattern that is observable on the surrounding walls, and photogrammetry is used to measure the absolute coordinates of features in the projected optical pattern with respect to a defined global coordinate system. By combining these absolute coordinates with the known angular information of the optical projection beams, a minimization algorithm can be used to extract the absolute coordinates and angular orientation of the module itself. The feasibility of the proposed metrology system was first proved through preliminary experimental tests. By using a module with a 7&times;7 dot matrix pattern, experimental agreement of 1 to 5 parts in 10³ was obtained by translating the module over 0.9 m and by rotating it through 60&deg;. The proposed metrology system was modeled through numerical simulations and factors affecting the uncertainty of the measurement were investigated. The simulation results demonstrate that optimum design of the projected pattern gives a lower associated measurement uncertainty than is possible by direct photogrammetric measurement with traditional tie points alone. Based on the simulation results, a few improvements have been made to the proposed metrology systems. These improvements include using a module with larger full view angle and larger number of dots, performing angle calibration for the module, using a virtual camera approach to determine the module location and employing multiple coordinates system for large range rotation measurement. With the new proposed virtual camera approach, experimental agreement at the level of 3 parts in 10⁴ was observed for the one dimension translation test. The virtual camera approach is faster than the algorithm and an additional minimization analysis is no longer needed. In addition, the virtual camera approach offers an additional benefit that it is no longer necessary to identify all dots in the pattern and so is more amenable to use in realistic and usually complicated environments. A preliminary rotation test over 120&deg; was conducted by tying three coordinate systems together. It was observed that the absolute values of the angle differences between the measured angle and the encoder reading are smaller than 0.23&deg; for all measurements. It is found that this proposed metrology system has the ability to measure larger angle range (up to 360&deg;) by using multiple coordinate systems. The uncertainty analysis of the proposed system was performed through Monte Carlo simulation and it was demonstrated that the experimental results are consistent with the analysis. </p>