We investigate theoretically nonlinear Thomson scattering by multiple electrons ionized from individual atoms during a short high-intensity laser pulse. The emitted light is influenced by the distance that the electrons move apart from each other during the passage of the pulse, owing to coherence effects. We examine trajectories of electrons born from the same atom via successive ionizations as the laser pulse ramps up. While the overall trajectory of an individual electron is influenced by the ponderomotive force, we find that the separation between electrons arises mostly from stronger and differing initial drift velocities associated with the moment of ionization in the laser field. In the case of helium, we find that the separation between its two ionized electrons becomes appreciable (compared to emitted wavelengths) primarily along the dimension of laser linear polarization. This distorts the angular emission patterns of nonlinear Thomson scattering in comparison with emission from individual free electrons. Radiation scattered perpendicular to the laser polarization tends to add constructively, while radiation scattered along the direction of linear laser polarization tends to add incoherently. This effect becomes more pronounced for atoms with higher numbers of ionized electrons. The effect influences primarily the lower harmonic orders.

The individual polarization components of nonlinear Thomson scattering arise from the separate dimensions of electron figure-8 motion caused by a linearly polarized laser field. We present the first measurements of nonlinear Thomson scattering in both emission hemispheres. In the electron average rest frame, the shape of the electron figure-8 path is symmetric about the laser polarization dimension. However, the periodic electron velocity is intrinsically asymmetric. The full scattering emission pattern reveals this asymmetry and the direction that electrons move around the figure-8 path.

We present first measurements of nonlinear Thomson scattering over the entire emission sphere. Inherent asymmetry in electron relativistic figure-8 motion gives different emission patterns in ‘northern’ and ‘southern’ hemispheres (with laser propagating along poles).

Measurements of first and second harmonic radiation from nonlinear Thom- son scattered light as a function of laser polarization ellipticity are reported. Polarization-resolved patterns were observed and connected to the underlying electron motion, confirming half-century old theoretical predictions.

We report experimental results from a study of nonlinear Thomson scattering of elliptically polarized light. Polarization-resolved radiation patterns of the scattered light are measured as a function of the elliptical polarization state of the incident laser light. The relativistic electron trajectory in intense elliptically polarized fields leads to the formation of unique radiated polarization states, which are observed by our measurements and predicted by a theoretical model. The polarization of Thomson scattered light depends strongly on the intensity of the incident light due to nonlinearity. The results are relevant to high-field electrodynamics and to research and development of light sources with novel capabilities.

Photophoresis can trap opaque microscopic particles in a focused laser beam surrounded by a gas such as air. The particle is heated by the laser, and in turn, interactions with the ambient gas provide a stabilizing force that holds the particle in a specific region of the beam. The particles can stay trapped while the beam ismoved side to side up to 2 m/s, enabling three-dimensional images to be traced out in a display application. Structure in the laser beam is associated with the trapping phenomenon, but the fundamental mechanism for stability of the trap remains mysterious. Particles prefer regions of the beam with diffraction features such as those that arise from spherical aberration. Nevertheless, the ability of near-unidirectional light, albeit light that undergoes focusing and exhibits structure, to provide a restoring force to trapped particles in the direction opposite to beam propagation needs to be explained. Through repeated trials of capturing particles in a well characterized beam, we map out the preferred locations for particle capture and correlate them with diffraction features of the beam. The specific beam locations that host trapped particles, when compared with neighboring regions that do not, can offer insight into the stability mechanism. We analyze the Poynting vector in the vicinity of trapped particles. The flow of light energy can provide important clues into the trapping mechanism.

We measure polarization-resolved fundamental, second, and third harmonic nonlinear Thomson scattering out the side of a laser focus with 1018 W/cm2. The separate measured polarization components are each associated with a distinct dimension of predicted electron figure-8 motion. Taken together, the measured angular emission patterns for the two polarizations unambiguously confirm the figure-8 motion. Electrons are donated from lowdensity helium (10−3 to 1 Torr) ionized early during the laser pulse. Time-resolved single-photon detection is used to distinguish signal from noise.

Lasers are ubiquitous in modern society. They transmit the vast bulk of all information on the internet through fiber optics, are commonly used for medical tasks from dentistry to surgery, play crucial roles in everyday technologies like printing and manufacturing, and are common in almost all disciplines of scientific inquiry. The collimated beam serves as a reference to reveal the phase of the focused beam through interference. Getting a basic understanding of how to manipulate and control them is an essential task for most experimental disciplines. A wave plate is made from a birefringent crystal wherein the index of refraction that light experiences depends on the orientation of its polarization. Wave plates have the appearance of thin windows and do not absorb light. Rather, a wave plate introduces a relative phase delay between field components oriented along the slow axis and the fast axis. These two axes are associated with higher and lower refractive indices, respectively.

We measure fundamental, second, and third harmonics of nonlinear Thomson scattering emitted by free electrons out the side of a laser focus with 10 18 W/cm 2 . The redshifted photons show distinct spatial patterns when resolved by polarization.

We report measurements of polarization-resolved nonlinear Thomson scattering made using single-photon detection techniques in a regime of low density electrons. This low density allows the study of electron dynamics in a high-intensity focus.

Isotopic Separation and Spectroscopy of Ytterbium-173(3/2) using Laser Cooling Quinton Dayle McKnight Department of Physics and Astronomy, BYU Bachelor of Science A multi-laser approach is used in which we correct errors in the atomic spectroscopy that seriously compromised previous measurements by another group [Phys. Rev. A 76, 062505 (2007)]. We report precision measurements of the 173Yb 6s6p 1Po 1 (F ′ = 3/2,7/2) transition frequencies. We use a frequency comb to determine the laser frequency. Our work completes a set of isotopeand hyperfine-shift measurements reported in [1], published by our group. The frequency shift between the 6s6p 1Po 1 (F ′ = 3 2 , 7 2) levels is 86.29± 0.77 MHz. The uncertainty is dominated by quantum interference effects in the excitation and decay pathways. Appendix A is a summary of notes made on an overheating problem encountered in our laboratory, and a copy of both papers on which I was primary author while completing my undergraduate work included at the end of the thesis.

Since the introduction of optical trap displays in 2018, there has been significant interest in further developing this technology. In an effort to channel interest in the most productive directions, this work seeks to illuminate those areas that, in the authors' opinion, are most critical to the ultimate success of optical trap displays as a platform for aerial 3D imaging. These areas include trapping, scanning, scaling, robustness, safety, and occlusion.

Photophoresis can stably hold opaque microscopic particles in a laser focus surrounded by room air with strength sufficient to enable centimeter-scale patterns to be drawn by sweeping the laser beam. The resulting images rely on visual persistence as laser light scatters from the particle, which is rapidly swept through the 3-D pattern. Control can be maintained while moving the particle with air speeds up to 2 m/s. A desire to greatly increase the sweep speed motivates a re-examination of the fundamentals of photophoresis-based laser-particle traps. Most explanations offered are qualitative, with differing opinions as to whether, for example, asymmetric heating or asymmetric thermal accommodation is primarily at work. Which particles become trapped in the beam is typically based on self-selection, as a variety of particles with possible differing shapes and sizes are offered to the laser focus for capture. Characteristics that make some particles preferred over others are especially relevant. There is broad consensus that structure in the laser focus greatly aids in stable photophoretic trapping. An interesting question is how smooth can a beam be and still capture and hold particles. Even in a structured focus (i.e. with aberrations and local intensity minima and maxima), questions remain as to exactly how a particle becomes stably trapped in certain beam locations. A zoomed-in look at trapped particles reveals oscillations or orbits with excursions over tens of microns and accelerations up to 10 gs. We trapped particles in zero-gravity as well as 2-g environments with no noticeable difference in stability.

We report nearly continuous beta-decay-rate measurements of Na-22, Cl-36, Co-60, Sr-90, and Cs-137 over a period of 2.7 years using four Geiger-Müller tubes. We carefully control the ambient pressure and temperature for the detectors, sources, and electronics in order to minimize environmentally-dependent systematic drifts in the measurement chains. We show that the amplitudes of an annual oscillation in the decay rates are consistent with zero to within 0.004%.

Free-space volumetric displays, or displays that create luminous image points in space, are the technology that most closely resembles the three-dimensional displays of popular fiction. Such displays are capable of producing images in 'thin air' that are visible from almost any direction and are not subject to clipping. Clipping restricts the utility of all three-dimensional displays that modulate light at a two-dimensional surface with an edge boundary; these include holographic displays, nanophotonic arrays, plasmonic displays, lenticular or lenslet displays and all technologies in which the light scattering surface and the image point are physically separate. Here we present a free-space volumetric display based on photophoretic optical trapping that produces full-colour graphics in free space with ten-micrometre image points using persistence of vision. This display works by first isolating a cellulose particle in a photophoretic trap created by spherical and astigmatic aberrations. The trap and particle are then scanned through a display volume while being illuminated with red, green and blue light. The result is a three-dimensional image in free space with a large colour gamut, fine detail and low apparent speckle. This platform, named the Optical Trap Display, is capable of producing image geometries that are currently unobtainable with holographic and light-field technologies, such as long-throw projections, tall sandtables and 'wrap-around' displays.

We assess several widely used vector models of a Gaussian laser beam in the context of more accurate vector diffraction integration. For the analysis, we present a streamlined derivation of the vector fields of a uniformly polarized beam reflected from an ideal parabolic mirror, both inside and outside of the resulting focus. This exact solution to Maxwell's equations, first developed in 1920 by V. S. Ignatovsky, is highly relevant to high-intensity laser experiments since the boundary conditions at a focusing optic dictate the form of the focus in a manner analogous to a physical experiment. In contrast, many models simply assume a field profile near the focus and develop the surrounding vector fields consistent with Maxwell's equations. In comparing the Ignatovsky result with popular closed-form analytic vector models of a Gaussian beam, we find that the relatively simple model developed by Erikson and Singh in 1994 provides good agreement in the paraxial limit. Models involving a Lax expansion introduce a divergences outside of the focus while providing little if any improvement in the focal region. Extremely tight focusing produces a somewhat complicated structure in the focus, and requires the Ignatovsky model for accurate representation.