## Advised Theses

- Luke Robins, "Coherence Effects in Nonlinear Thomson Scattering from Electrons Born of the Same Atom" (Senior Thesis, 2024).
- Aaron Peatross, "Stability of Photophoretic Trapping of Microscopic particles in a Laser Beam" (Senior Thesis, 2023).
- Joshua Newey, "Space-Time-Resolved Simulation of Photon Vacuum Polarization and Bhabha Scattering" (Senior Thesis, 2022). Full Text PDF
- Ryan Scott, "Space-Time Resolving Quantum Electrodynamic States of Two Charges" (Senior Thesis, 2022). Full Text PDF
- Kristen Funk, "Quantization of SU(3) Yang-Mills Theory" (Senior Thesis, 2021).
- Christoph Alexander Schulzke, "Angular Dependence of Nonlinear Thomson Scattering From Electrons in a High Intensity Laser Focus" (Masters Thesis, 2020). Full Text PDF
- Mahonri Romero Carranza, "Nonlinear Thomson Scattering: Minimum Useful Focal Spot Size as a Function of Laser Pulse Duration" (Senior Thesis, 2020).
- Brittni Tasha Pratt, "Polarization of Nonlinear Thomson Scattering from a High-Intensity Laser Focus" (Masters Thesis, 2020). Full Text PDF
- Daniel Hodge, "Intensity Dependence of Radiation Scattered by Electrons in a Laser Focus" (Senior Thesis, 2020).
- Hyrum Richardson, "Linear and Nonlinear Properties of Pancharatnam's Phase in Polarization Optics\" (Senior Thesis, 2017). Full Text PDF
- Matthew Ashby, "Measurement of Scattered Radiation from Free Electrons in an Intense Laser Focus" (Senior Thesis, 2016).
- James Fletcher, "Time Delayed Double Pulse Variation of Radiation Scattering From Free Electrons Inside an Intense Laser Focus" (Senior Thesis, 2015).
- Zak Jones, "Single Pixel Camera" (Senior Thesis, 2015).
- COLIN Mann, "Use of Correlated Photon Pairs in Absolute Efficiency Measurement of Single Photon Source" (Senior Thesis, 2014).
- Matthew Groesbeck, "Control System for Experiment Probing Potential Time-Variance in Nuclear Beta Decay Rates" (Senior Thesis, 2013).
- Caleb Coburn, "Characterizing Single Electron Radiation in an Intense Laser Field" (Senior Thesis, 2013). Full Text PDF
- Eric Flint Cunningham, "Photoemission by Large Electron Wave Packets Emitted Out the Side of a Relativistic Laser Focus" (Masters Thesis, 2011). Full Text PDF
- Patrick van Langen, "Two-Source Two-Slit Spatial Interferometer" (Senior Thesis, 2011).
- John P. Corson, "Time-Frequency Description of Precursor Fields" (Senior Thesis, 2009).
- Dustin Shipp, "Numerical Model Of Non-Collinear Parametric Down-Conversion" (Senior Thesis, 2008). Full Text PDF
- Lee Johnson, "Observation of Two-Photon Quantum Interference Using Entangled Photons" (Capstone, 2007). Full Text PDF
- David A Niemi, "Coupling Down Converted Light Into Single Mode Fibers" (Masters Thesis, 2007). Full Text PDF
- Tyler Weeks, "Absolute Soft X-Ray Calibration Of Laser Produced Plasmas Using A Focusing Crystal Von Hamos Spectrometer" (Capstone, 2005). Full Text PDF

## Theses, Captstones, and Dissertations

To calibrate the efficiency of our detection channel, we use parametric downconversion to generate correlated photon pairs. By sending UV laser light into a non-linear crystal, some light is downconverted into lower energy pairs. These pairs are correlated, so by sending one pair member through the detection channel and the other pair member directly into a single photon counter, we can compare the two signals and find absolute efficiency. This work was supported by the National Science Foundation (Grant No. PHY-0970065).

We describe the motivation for a research project measuring decay rates of various beta decay-type isotopes. Recent publications have suggested that nuclear decay rates show an unexpected slight annual oscillation. The unknown factor causing this fluctuation is hypothesized to be the variable flux of solar neutrinos through the earth. Our experiment is designed to test these claims by tracking the counts of ten beta-decay samples over a period of up to ten years. The samples will be measured by multiple radiation detectors under strict environmental controls. The central LabView control program is also described in depth.

We report the intensity measurement of a high intensity pulsed laser focus and the efficiency characterization of an optical signal collection system. We seek experimental confirmation that large free electron wave packets radiate like point particles. Our experiment requires intensities on the order of 1018 W/cm2 to produce red-shifted signal photons. The red shift is important in discriminating against a large background. We use time-of-flight spectroscopy to measure the charge to mass ratio of laser induced multiply ionized argon and compare the highest achieved charge state with known strong-field ionization intensities. We also use parametric down conversion to make an absolute efficiency measurement of our detection system. These measurements are necessary to ensure our apparatus is capable of producing the intensity dependent signal that we seek and allow us to calculate the total radiated signal. We measure a pulse intensity of at least 1:571018 W/cm2. The collection efficiency is 22:71%. This work was supported by the National Science Foundation (Grant No. PHY-0970065).

There are at least two common models for calculating the photoemission of accelerated electrons. The ‘extended-charge-distribution’ method uses the quantum probability current (multiplied by the electron charge) as a source current for Maxwell’s equations. The ‘point-like-emitter’ method treats the electron like a point particle instead of like a diffuse body of charge. Our goal is to differentiate between these two viewpoints empirically. To do this, we consider a large electron wave packet in a high-intensity laser field, in which case the two viewpoints predict measurable photoemission rates that differ by orders of magnitude. Under the treatment of the ‘extended-charge-distribution’ model, the strength of the radiated field is significantly limited by interferences between different portions of the oscillating charge density. Alternatively, no suppression of photoemission occurs under the ‘point-like-emitter’ model because the electron is depicted as having no spatial extent. We designed an experiment to characterize the photoemission rates of electrons accelerated in a relativistic laser focus. Free electron wave packets are produced through ionization by an intense laser pulse at the center of a large vacuum chamber. These quantum wave packets can become comparable in size to the laser wavelength through natural spreading and interactions with the sharp ponderomotive gradients of the laser focus. Electron radiation emitted out the side of the focus is collected by one-to-one imaging into a 105-micron gold-jacketed fiber, which carries the light to a single photon detector located outside the chamber. The electron radiation is red-shifted due to mild relativistic acceleration, and we use this signature to spectrally filter the outgoing light to discriminate against background. In addition, the temporal resolution of the electronics allows distinction between light that travels directly from the focus into the collection system and laser light that may scatter from the chamber wall.

We investigate the utility of a spatial interferometer based on fiber optics for future applications in quantum interference. The interferometer is constructed by having two separate fibers with one end free and the other end bundled with the other. This allows for the free ends to be moved freely to capture the source and the other end to be close together and effectively form a two slit. The interferometer is tested by making two coherent sources with a beam splitter and then coupling the sources into the fiber optics much like a Michelson interferometer. It was found that the interferometer did provide the desired interference pattern with good visibility. However, the fringes would frequently and randomly move which limits some of the possible uses. It is believed that these problems arise from small movements in the fibers caused by vibrations from the ground and surrounding area. Despite the limitations caused by the moving fringes it would still be possible to use the apparatus for spatial quantum interference. In addition, this setup could also have uses in endoscopes and microscopes.

We investigate the phenomenon of precursor fields within the framework of joint time-frequency distributions. Our approach utilizes the Spectrogram, the Wigner Distribution, and the Choi-Williams Distribution. We model pulse propagation and precursor evolution for single-resonance and double-resonance Lorentz media using each distribution. None of the three distributions gives a completely intuitive picture for all scenarios. The Choi-Williams Distribution resolves features only after the precursor components temporally separate. The Spectrogram distinguishes signal components well, but poorly resolves their chirp and does not match the group delay. The Wigner Distribution aptly resolves chirp, but clouds time-frequency plots with non-physical interference terms. We discuss the advantages and limitations of time-frequency analysis.

We used a numerical model to study spontaneous parametric down-conversion, a process in which a single photon splits into two "daughter" photons. The model predicts the location of daughter photons based on phase matching conditions. The user can vary parameters such as crystal type, pump and signal photon wavelength, and geometries of the system. Varying these parameters allows properties of down-conversion to be tested and optimized. We experimentally confirmed several features included in the model for Type I down-conversion in a BBO crystal. We found that the diameter of the down- conversion ring is well modeled by our numerical approach. We experimentally measured the total down-conversion output over all angles at a single wave- length to remain roughly constant as the size of the ring varied. Our model does not predict this well due to its incompleteness.

We constructed a two particle interferometer. Using the finished interferometer, we were able to observe two-photon interference using entangled photon pairs produced through parametric down conversion. This phenomenon cannot be explained classically, but demonstrates purely quantum effects, explainable using quantum theory.

We investigate the influence of the pump and collection mode parameters on the collection efficiency of Type I down converted photons into single mode fibers. For best single and coincidence counting rates, we find that the mode sizes should be close to the same size and that the mode waists should be located near the down-conversion crystal. Larger collection waists give higher collection efficiencies, but lower singles counts.

Absolute x-ray calibration of laser-produced plasmas was performed using a focusing crystal von Hamos spectrometer. The plasmas were created by an Nd-YAG laser on massive solid targets (Mg, Cu, Zn, Sn, Mo, Ta, Ti, Steel). A Cylindrical mica crystal and a CCD linear array detector were used in the spectrometer. Both the mica crystal and CCD linear array were absolutely calibrated in the spectral range of λ=7 – 15 Å. The spectrometer was used for absolute spectral measurements and the determination of the plasma parameters. The unique target design allowed for multiple instruments to observe the plasma simultaneously which improved analysis. The high spectrometer efficiency allowed for the monitoring of absolute x-ray spectra, x-ray yield and plasmaparameters in each laser shot. This spectrometer is promising for absolute spectral measurements and for monitoring laser-plasma sources intended for proximity print lithography.

Free electrons in an intense laser field scatter harmonic radiation when driven relativistically. In our experiments, free electrons are donated from helium or argon atoms randomly distributed throughout the laser focus. The atoms become ionized early during the laser pulse. The relative positions of multiple electrons born from a particular atom are correlated, which can affect their scattered light. Simulations approximating the free electrons as dipole emitters show the strength of this coherence effect is not strongly dependent on the density of electrons. We hope to see this coherence effect experimentally, but we must eliminate prepulses from our laser to a contrast of at least 10,000:1. Otherwise, the prepulses will ionize the electrons prematurely, disrupting any chance for coherence between electrons. I describe a new method of pulse cleaning that exploits the mirage effect in light to deflect the main pulse and filter out pre-pulses. We see evidence of pulse deflection, but the distortion of the pulse is too high to be experimentally viable.

When light heats an object, surrounding air molecules can bounce off the object with increased speed, imparting momentum to the object. This can cause light-weight objects, and in particular microscopic particles, to move in a process called photophoresis. Microscopic particles can be caught and suspended in a laser focus by this mechanism. We investigate what leads to stable trapping. It has been hypothesized that because of spherical aberration, light is preferentially absorbed on the downstream side of a particle (i.e. the ‘shady’ side), preventing the particle from escaping the focus. We recorded stable trapping locations for particles caught in a focused 532 nm Gaussian laser beam wherein we introduced spherical aberration. We compared these trapping locations with diffraction patterns in the beam and found that exact particle positions upstream of the focus are inconsistent. We compared these results to the energy transport velocity in the beam. We also focused a counter-propagating beam onto trapped particles and observed that it had a smaller effect on trapping location than anticipated.

Space-Time-Resolved Simulation of Photon Vacuum Polarization and Bhabha Scattering (by Joshua Newey)

We create a limited particle content model in one spatial dimension to study the interaction between single particle photon states, and electron-positron pair states. We use this model to simulate the phenomena of vacuum polarization in a propagating photon, and Bhabha Scattering. This approach supplements the S-matrix approach to Quantum Field Theory, which provides an effective approach for predicting the results of scattering experiments but gives little physical insight into the dynamics of the field during interactions. We find divergences arise in attempting to calculate the eigenvalues of particles states with interaction in out limited content model. This leads to areas requiring further study of further study, namely, how to implement renormalization within space-time-resolved frameworks.

The degree to which predictions made by Quantum Field Theory (QFT) agree with experiment make it one of the most accurate physical theories ever constructed. Quantum Electrodynamics (QED) is the branch of QFT that deals with charged particles and their interactions. Generally, one approaches problems in QED using scattering theory, and while this one-time "snapshot" of the input and output states is useful in many applications, it does not tell the whole story of the interaction. In this thesis, a non-perturbative approach of finding space-time resolved dynamics of a system of two spin-up electrons is shown. The techniques applied as well as some of the resulting equations can easily be extended to states with electrons, positrons, or photons of any spin.

Yang-Mills theory is a non-abelian gauge theory based on a special unitary group that seeks to describe the behavior of various elementary particles. The behavior of gluons in the absence of quarks is described when the underlying Lie group is the special unitary group of degree 3 (SU(3)). Additionally, SU(3) Yang-Mills theory is foundational to quantum chromodynamics (QCD). Experiment and computer simulation suggest that a mass-gap should exist in the solution of quantum Yang-Mills equations, but this property is not understood from an analytical perspective. We present a simple method for quantizing SU(3) Yang-Mills theory based on methods used in the quantization of the electromagnetic field. However, we conclude that this method is insufficient for further study of gluon self-interaction or the mass-gap as the resulting Hamiltonian is extraordinarily complicated.

The theory of nonlinear Thomson scattering is presented. A model for the scattered light is developed. The orthogonal polarizations of the second harmonic of the scattered light are examined. The predictions of the model are compared to measurements by our group in collaboration with the Extreme Light Laboratory at the University of Nebraska-Lincoln (UNL). The veracity of the theory and model are confirmed by comparison to the experimental data.

We investigate nonlinear Thomson scattering from electrons driven relativistically in an intense laser focus. At low intensities, the magnetic field is negligible and does influence the electron fractior. At high-intensity ( 1:51018 W/cm2), the magnetic field contributes markedly to the Lorentz force, resulting in characteristic relativistic movement. Strongly driven electrons emit harmonic light in all directions from the focus. We investigate nonlinear Thomson scattering using a focused 800 nm Ti:sapphire laser with 40 fs pulses that fire at 10 Hz. For the first time, Thomson scattering is recorded via single-photon counting using an avalanche photodiode and photomultiplier tube, We also make the first polarized-resolved observations of harmonics emitted out the side of the laser focus. The minimal useful focal spot size is computed theoretically through mathematical models. Furthermore, data taken by our research group in collaboration with a group at the University of Nebraska-Lincoln is compared to theoretical modeling.

Thomson scattering from free electrons in a high-intensity laser focus has been widely studied analytically, but not many measurements of this scattering have been made. We measure polarization-resolved nonlinear Thomson scattering from electrons in a high-intensity laser focus using a parabolic mirror. The weak scattering signal is distinguished from background noise using single-photon detectors and nanosecond time-resolution to distinguish a prompt scattering signal from noise photons. The azimuthal and longitudinal components of the fundamental, second, and third harmonics were measured. Our measurements reasonably match theoretical results, but also show some asymmetry in the emission patterns.

According to the Lorentz force, when high-intensity light is incident on a free electron, the electric and magnetic field of the laser influences the electron’s trajectory and what radiation it produces. As laser intensity increases, electrons reach relativistic speeds as they oscillate in the laser field. Particularly, in our lab we used a high-intensity pulsed laser with the intensity 10^18 W/cm^2 to allow us to study Thomson scattering in this relativistic regime. When a free electron is moving at this speed, it radiates light at harmonics of the incident laser wavelength. Specifically and most importantly, with the added dimension of polarization, we measured the fundamental, second, and third harmonic emissions from electrons in a high-intensity laser focus. Consequently, we obtained graphs depicting each harmonic’s own unique angular distribution of light. Furthermore, I investigate how varying the laser intensity alters the angular distribution of light emitted by radiating electrons for the azimuthal and longitudinal polarizations. Also, I compare the ratio of light distribution between the azimuthal and longitudinal polarizations as intensity increases. Ultimately, we gathered this information to analyze the electron dynamics in the high-intensity laser focus and to understand the details of the vector-field distributions in this focus.

Pancharatnam's phase is the additional phase beyond the dynamical phase of electromagnetic radiation that arises due to polarization evolution, and although it is a fundamental property of polarization, the linear and nonlinear properties it exhibits are not well understood or discussed. A computer simulation extendable to any polarization circuit was developed that makes Pancharatnam's phase more intuitive and understandable. Two types of interferometers were tested, a symmetric Sagnac interferometer and a Mach-Zehnder interferometer, to measure the linearity and nonlinearity of Pancharatnam's phase. The simulation and experimental results were compared and shown to match closely. The linearity of Pancharatnam's phase can be predicted and measured, and our model is accurate to the physical phenomenon and useful for interferometry applications.