Indiana University-Purdue University Indianapolis (IUPUI) / More than a decade ago, it was shown that non-Hermitian Hamiltonians with combined parity (P) and time-reversal (T ) symmetry exhibit real eigenvalues over a range of parameters. Since then, the field of PT symmetry has seen rapid progress on both the theoretical and experimental fronts. These effective Hamiltonians are excellent candidates for describing open quantum systems with balanced gain and loss. Nature seems to be replete with examples of PT -symmetric systems; in fact, recent experimental investigations have observed the effects of PT symmetry breaking in systems as diverse as coupled mechanical pendula, coupled optical waveguides, and coupled electrical circuits. Recently, PT -symmetric Hamiltonians for tight-binding lattice models have been extensively investigated. Lattice models, in general, have been widely used in physics due to their analytical and numerical tractability. Perhaps one of the best systems for experimentally observing the effects of PT symmetry breaking in a one-dimensional lattice with tunable hopping is an array of evanescently-coupled optical waveguides. The tunneling between adjacent waveguides is tuned by adjusting the width of the barrier between them, and the imaginary part of the local refractive index provides the loss or gain in the respective waveguide. Calculating the time evolution of a wave packet on a lattice is relatively straightforward in the tight-binding model, allowing us to make predictions about the behavior of light propagating down an array of PT -symmetric waveguides. In this thesis, I investigate the the strength of the PT -symmetric phase (the region over which the eigenvalues are purely real) in lattices with a variety of PT - symmetric potentials. In Chapter 1, I begin with a brief review of the postulates of quantum mechanics, followed by an outline of the fundamental principles of PT - symmetric systems. Chapter 2 focuses on one-dimensional uniform lattices with a pair of PT -symmetric impurities in the case of open boundary conditions. I find that the PT phase is algebraically fragile except in the case of closest impurities, where the PT phase remains nonzero. In Chapter 3, I examine the case of periodic boundary conditions in uniform lattices, finding that the PT phase is not only nonzero, but also independent of the impurity spacing on the lattice. In addition, I explore the time evolution of a single-particle wave packet initially localized at a site. I find that in the case of periodic boundary conditions, the wave packet undergoes a preferential clockwise or counterclockwise motion around the ring. This behavior is quantified by a discrete momentum operator which assumes a maximum value at the PT -symmetry- breaking threshold. In Chapter 4, I investigate nonuniform lattices where the parity-symmetric hop- ping between neighboring sites can be tuned. I find that the PT phase remains strong in the case of closest impurities and fragile elsewhere. Chapter 5 explores the effects of the competition between localized and extended PT potentials on a lattice. I show that when the short-range impurities are maximally separated on the lattice, the PT phase is strengthened by adding short-range loss in the broad-loss region. Consequently, I predict that a broken PT symmetry can be restored by increasing the strength of the short-range impurities. Lastly, Chapter 6 summarizes my salient results and discusses areas which can be further developed in future research.

Lasers find a wide range of applications in many areas including photo-biology, photo-chemistry, materials processing, imaging and telecommunications. However, the practical use of such sources is often limited by the bulky nature of existing systems. By fabricating channel waveguides in solid-state laser-gain materials more compact laser systems can be designed and fabricated, providing user-friendly sources. Other advantages inherent in the use of waveguide gain media include the maintenance of high intensities over extended interaction lengths, reducing laser thresholds. This thesis presents the development of Yb:tungstate lasers operating around 1μm in waveguide geometries. An Yb:KY(WO₄)₂ planar waveguide laser grown by liquid phase epitaxy is demonstrated with output powers up to 190 mW and 76 % slope efficiency. This is similar to the performance from bulk lasers but in a very compact design. Excellent thresholds of only 40 mW absorbed pump power are realised. The propagation loss is found to be less than 0.1 dBcm⁻¹ and Q-switched operation is also demonstrated. Channel waveguides are fabricated in Yb:KGd(WO₄)₂ and Yb:KY(WO₄)₂ using ultrafast laser inscription. Several of these waveguides lase in compact monolithic cavities. A maximum output power of 18.6 mW is observed, with a propagation loss of ~2 dBcm⁻¹. By using a variety of writing conditions the optimum writing pulse energy is identified. Micro-spectroscopy experiments are performed to enable a fuller understanding of the induced crystal modification. Observations include frequency shifts of Raman lines which are attributed to densification of WO₂W bonds in the crystal. Yb:tungstate lasers can generate ultrashort pulses and some preliminary work is done to investigate the use of quantum dot devices as saturable absorbers. These are shown to have reduced saturation fluence compared to quantum well devices, making them particularly suitable for future integration with Yb:tungstate waveguides for the creation of ultrafast, compact and high repetition rate lasers.

Approved for public release, distribution is unlimited / In this thesis, the ocean was modeled as a waveguide with an ideal pressure - release surface, and an ideal rigid bottom. The ocean waveguide was then treated as a linear, time - invariant, space - variant (TISV) filter or communication channel. The filter is time - invariant because no motion was modeled and because the properties of the ocean were assumed to be constant. The filter is space - variant because of the presence of the two boundaries, that is, the ocean surface and ocean bottom. This thesis investigates the ocean as a linear TISV filter by evaluating 1) the complex frequency response, 2) the impulse response, and 3) the transfer function of the ocean with respect to depth. It is shown that the TISV impulse response of the ocean contains information that can be used to help localize a target in range and whether the target is above or below the receiver. Computer simulation results were obtained by evaluating the three filter functions for several different test cases. / Ensign, United States Navy