Nonlinear optics is the study of interactions of materials with intense light beams made possible by the invention of laser. Arguably the most trivial but technologically most important nonlinear optical effect is the intensity-dependent nonlinear refraction: an intense light beam can temporarily and reversibly change the refractive index of a material. However, the changes to the refractive index of a material due to the presence of a strong laser beam are very weak---maximum on the order of $10^{-3}$---and tend to be a small fraction of the linear refractive index. It must be noted that at optical frequencies vacuum has a refractive index of 1 and glass has a refractive index of 1.5. Thus, one of the foundational assumptions of nonlinear optics is that the nonlinear optical changes to material properties are always a small perturbation to the linear response. In the 58-year history of nonlinear optics, one of the overarching themes of research has been to find ways to increase the efficiency of nonlinear interactions. This thesis is a collection of six manuscripts motivated by our experimental finding that at least in a certain class of materials the above long-standing view of nonlinear optics does not necessarily hold true. We have found that in a material with low refractive index, known as an epsilon-near-zero material or ENZ material, the nonlinear changes to the refractive index can be a few times larger than the linear refractive index, i.e. the nonlinear response becomes the dominant response of the material in the presence of an intense optical beam. We believe that the results presented in this thesis collectively make a convincing case that ENZ materials are a promising platform for nonlinear nano-optics.

Laser filamentation is a highly complex and dynamic nonlinear process that is sensitive to many physical parameters. The basic properties that define a filament consist of (i) a narrow, high intensity core that persists for distances much greater than the Rayleigh distance, (ii) a low density plasma channel existing within the filament core, and (iii) a supercontinuum generated over the course of filamentation. However, there remain many questions pertaining to how these basic properties are affected by changes in the conditions in which the filaments are formed; that is the premise of the work presented in this dissertation. To examine the effects of anomalous dispersion and of different multi-photon ionization regimes, filaments were formed in solids with different laser wavelengths. The results provided a better understanding of supercontinuum generation in the anomalous dispersion regime, and of how multi-photon ionization can affect the formation of filaments. Three different experiments were carried out on filamentation in air. The first was an investigation into the effects of geometrical focusing. A simplified theoretical model was derived to determine the transition of filamentation in the linear-focusing and nonlinear- focusing regimes. The second examined the effects of polarization on supercontinuum generation, where a polarization-dependent anomalous spectral broadening phenomenon due to molecular effects was identified. The third involved the characterization of filaments in the ultraviolet. The combination of physical mechanisms responsible for filamentation in the ultraviolet was found to be different from that in the near infrared.

No / We measured the wavefront aberrations of the eyes of five subjects with a Shack-Hartmann sensor sampling at 21.2 Hz and decomposed the measurements into Zernike aberration terms up to and including the fifth radial order. Coherence function analysis was used to determine the common frequency components between the aberrations within subjects. We found the results to be highly subject dependent. The coherence values were typically <0.4. Possible reasons for this are discussed. Coherence function analysis is a useful tool that can be used in future investigations to determine correlations between the aberration dynamics of the eye and other physiological mechanisms.

<p>The Daniel K Inouye Solar Telescope (DKIST), when completed in 2019 will be the largest solar telescope built to date. DKIST will have a suite of first light polarimetric instrumentation requiring broadband polarization modulation and calibration optical elements. Compound crystalline retarders meet the design requirements for efficient modulators and achromatic calibration retarders. These retarders are the only possible large diameter optic that can survive the high flux, 5 arc minute field, and ultraviolet intense environment of a large aperture solar telescope at Gregorian focus. </p><p> This dissertation presents work performed for the project. First, I measured birefringence of the candidate materials necessary to complete designs. Then, I modeled the polarization effects with three-dimensional ray-tracing codes as a function of angle of incidence and field of view. Through this analysis I learned that due to the incident converging F/13 beam on the calibration retarders, the previously assumed linear retarder model fails to account for effects above the project polarization specifications. I discuss modeling strategies such as Mueller matrix decompositions and simplifications of those strategies while still meeting fit error requirements. Finally, I present characterization techniques and how these were applied to prototype components. </p>

I have measured the refractive index of zinc selenide for wavelengths between 8 and 12 mum and temperatures from 85 to 300 K. Each measurement was made by finding the deviation angle of a beam perpendicularly incident on a right triangle prism. The resulting data curves are fitted to polynomials for the temperature dependence and to three different dispersion formulae for the wavelength dependence. I achieved accuracies in the refractive index of ±0.0008 and my results agree well with most previously available data. Refinements to the previously established experimental procedure and error analysis are also presented.

Over the past decade, circular grating surface emitting DBR lasers (CGSELs) have progressed from theory to reality. These devices possess several properties that make them attractive options for such applications as optical interconnects and laser arrays. These advantages include low divergence angles, circular beam profiles, and high power output. In this dissertation, the addition of new functionality to these lasers including wavelength tunability, focusing, beam steering and beam shaping is investigated. The theory governing device operation is presented. Pertinent discussions include the coupled mode equations, grating coupling, focusing and changes to the effective index of refraction resulting from current injection through a transparent electrode on the grating. The development and refinement of the device fabrication process is detailed. Key milestones in the grating writing process included achieving first order gratings (Λ = 0.15 μm), creating chirped period gratings for focusing and optimizing the linewidth and uniformity of the grating for high power devices. Of equal importance in obtaining high efficiency devices was the reactive ion etch process. Two different etch recipes were developed: one for mesa-definition and a shallower grating-defining etch. Significant evaluation of the electrical and optical properties of the transparent electrode, Indium Tin Oxide, was performed. Incorporating ITO into the fabrication process required optimization of deposition, patterning, etching and annealing. Device performance, efficiency and functionality improved with each generation. Consequentially, over 225 mW of output power for a injection current of 600 mA, or a slope efficiency of 0.43 mW/mA, was produced by the final generation of high power CGSELs. Focusing was demonstrated by the creation of individual devices with different focal lengths. Coarse mode selection was obtained by removing radial segments of the circular grating thereby eliminating both feedback coupling and surface outcoupling. Dynamic functionality such as beam steering and wavelength tuning was also realized for devices with ITO. Over 1° of beam steering was achieved for an ITO injection current of 35 mA. Similarly, over 1 nm of tuning, or 0.5 nm of continuous tuning, was accomplished. In conclusion, possibilities for improvements in device performance and future work are suggested.

published_or_final_version / Physics / Master / Master of Philosophy

The use of segmented mirrors in astronomy and adaptive optics is increasing as the ability to measure and control the position of the individual segments to a fraction of the wavelength of light becomes possible. A novel technique is presented in which the relative piston error of adjacent segments is measured using inductive edge-sensors. This technique alleviates the need to have an absolute piston sensor for each of the segment. Modelling of the performance of such a mirror for the case of correcting atmospheric turbulence is presented. This modelling shows that an edge-matched segmented mirror can correct the piston errors in the wavefront even though it does not sense them directly. In addition to this modelling, an experiment. which demonstrates the utility of this technology for adaptive secondary mirrors is described. The results of this experiment, which demonstrates for the first time that an edge-matched mirror can correct for atmospheric piston errors, are presented.

The objective of imaging spectrometry is to collect three-dimensional data about object space. Two of the three dimensions are spatial. The third dimension is spectral. Current techniques rely on some form of scanning, causing instruments to include moving components and/or to be capable of imaging only static or slowly changing scenes. An interpretation of the problem in terms of computed tomography leads to a system design which can fulfill the objective of imaging spectrometry without scanning. The imaging spectrometer assumes the frame-rate and integration-time properties of its imaging array. The raw data collected by such an instrument must be processed to yield temporally coincident spectral images of the scene. The computed tomography imaging spectrometer is therefore an example of indirect imaging. The three-dimensional frequency-space viewpoint and the associated central slice theorem form the theoretical basis for an understanding of this technique and its limitations. As described here, computed tomography imaging spectrometry belongs to the class of limited-view-angle problems. The spectrometer is treated as a discrete-to-discrete mapping and described accordingly by the linear imaging equation g = Hf + n. The M-element vector g represents the data collected by the spectrometer. The purpose of the instrument and the subsequent processing is the acquisition of the object cube f. In the discrete-to-discrete model, f is approximated as a vector of N independent elements. The vector n represents measurement-computing noise. The M-by-N matrix H embodies the imaging properties of the instrument. We have developed and implemented an experimental method of characterizing H. Such an approach yields a description of the imaging spectrometer which is more accurate than techniques that model the instrument and compute H. Inversion of the imaging equation to find an estimate of f has been best performed by the Expectation-Maximization algorithm. This approach is based on a Poisson likelihood law and therefore the assumption of quantum noise dominating the measurements g.

Absolute radiometric calibrations of Landsat 5 Thematic Mapper satellite are improved with the inclusion of a method to invert optical depth measurements to obtain an aerosol particle size distribution and a non-lambertian surface reflectance model. Also, a program is developed to improve speed and standardization of the entire calibration procedure. The inverted size distributions can predict radiances varying from the previous jungian distributions by as much as 5 percent, though the reduction in the estimated error is less than one percent. An empirical model for the surface reflection of White Sands using a two-degree polynomial fit as a function of scattering angle was employed. The model reduced estimated errors in radiance predictions by up to one percent. Satellite calibrations dating from October, 1984 are reprocessed using the improved methods and a linear estimation of satellite counts per unit radiance versus time since launch is determined.