High Harmonic Generation (HHG) enables the production of bursts of coherent soft x-rays with attosecond pulse duration. This process arrises from the nonlinear interaction between intense infrared laser pulses and an ionizing gas medium. Soft x-ray photons are used for spectroscopy of inner-shell electron correlation and exchange processes, and the availability of attosecond pulse durations will enable these processes to be resolved on their natural time scales. The maximum or cutoff photon energy in HHG increases with both the intensity as well as the wavelength of the driving laser. It is highly desirable to increase the harmonic cutoff as this will allow for the generation of shorter attosecond pulses, as well as HHG spectroscopy of increasingly energetic electronic transitions. While the harmonic cutoff increases with laser wavelength, there is a corresponding decrease in harmonic yield. The first part of this thesis describes the experimental measurement of the wavelength scaling of HHG efficiency, which we report as lambda^(-6.3) in xenon, and lambda^(-6.5) in krypton. To increase the HHG cutoff, we have developed a 1.8 um source, with stable carrier envelope phase and a pulse duration of <2 optical cycles. The 1.8 um wavelength allowed for a significant increase in the harmonic cutoff compared to equivalent 800 nm sources, while still maintaing reasonable harmonic yield. By focusing this source into neon we have produced 400 eV harmonics that extend into the x-ray water window. In addition to providing a source of photons for a secondary target, the HHG spectrum caries the signature of the electronic structure of the generating medium. In krypton we observed a Cooper minimum at 85 eV, showing that photoionization cross sections can be measured with HHG. Measurements in xenon lead to the first clear observation of electron correlation effects during HHG, which manifest as a broad peak in the HHG spectrum centred at 100 eV. This thesis also describes several improvements to the HHG experiment including the development of an ionization detector for measuring laser intensity, as well as an investigation into the role of laser mode quality on HHG phase matching and efficiency.

The linear and nonlinear optical response of plasmon hybridized systems is the subject of study of this thesis. Plasmonic silver nanoprisms are able to confine light to a sub-wavelength volume, which provides local field enhancement. This confined field is promising for achieving an enhanced nonlinear optical response. For many of plasmon nanoparticles, however, the plasmonic resonance is not at the near-infrared wavelengths of a Ti:Sapphire laser, the most common source used for ultra-fast measurements. To achieve resonance at these wavelengths, a tuning mechanism is required. The plasmon hybridization between silver nanoprisms and a thin gold film provides this tuning mechanism, which allows for enhanced optical second harmonic generation. Overlapping the plasmon resonance of the system with excitation source, by varying the spacer layer between the nanoprisms and the gold film, enhances the second harmonic counts by approximately three orders of magnitude. The finite-difference time-domain calculations agree to within a factor of two with the experimental findings in terms of the predicted enhancement factor. This plasmon hybridization approach is promising for future applications, including enhanced multi-photon lithography and nonlinear sensing using metal nanoparticles. / Graduate

This Thesis is concerned with the prediction, synthesis, characterization and testing of inorganic materials for Second Harmonic Generation (SHG). Chapter One describes the fundamentals of non-linear optics, and poses the problems, and some of their solutions which confront the synthetic chemist and the theoretical prediction of the second order hyperpolarizability constant β using CNDOVSB calculations. Chapter Two describes the design, implementation and calibration of an apparatus for measurements of the second harmonic generating efficiency of solids based on the Kurtz powder technique, and a solvatochromic method for the determination of β. Novel compounds with potential chirality due to atropisomerism, asymmetric octahedral structures, and asymmetric tetrahedral symmetry of metal centers are discussed in Chapters Three to Five. Chapter Three surveys the use of pentane-2,4-dionato- ligands and their coordination compounds as possible NLO active materials. The single crystal X-ray structures of bis(triphenylphosphine)(4-nitrobenzoylacetonato)palladium(II) tetrafluoroborate and tris(triphenylphosphine)[3-(2,4-dinitrophenyl)-pentane-2,4-dionato]palladium(II) tetrafluoroborate were determined. Chapter Four describes the syntheses, characterization and SHG properties of trans-β-ionylidenecyanoacetic acid (2-cyano-3-methyl-5-(2,6,6-trimethyl-l-cyclohexen-1- yl)-2,4-pentadienoic acid) and some of its metal and non-metal salts. Chapter Five describes the synthesis, characterization and second harmonic generation properties of some platinum(II) and palladium(II) complexes of β- ionylidenecyanoacetic acid. Chapter Six describes the use of conventional asymmetric carbon centers to introduce chirality into centrosymmetric compounds. The chiral compound (L)-N-[2-cyano- 3-methyl-5-(2,6,6-trimethyl-1 -cyclohexene-1 -yl)-2,4-pentadiene-1 -one]-L-proline and some of its salts were synthesized from β-ionylidenecyanoaeetic acid and tested for SHG.

Thesis (Ph. D. in Physics)--Vanderbilt University, Aug. 2008. / Title from title screen. Includes bibliographical references.

Thesis (Ph. D.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 280-300).

Thesis (Ph. D. in Physics)--Vanderbilt University, Dec. 2006. / Title from title screen. Includes bibliographical references.

With more atoms in a system, coupling between quantum states complicates the system dynamics. We shine intense laser pulses on three systems with increasing complexity: a molecule, a dimer, and a solid. For single molecules, a 400 nm photon excites NO_2 and initiates a dissociation process. We probe the dynamics using a strong laser pulse to ionize the molecule, and detect the resulting electrons and ions. The evolution of the NO-O molecular bond was directly measured in our experiment. For dimers, a laser pulse removes three electrons from (CO)_2. The dimer breaks up into C^+, O^+ and CO^+. Compared to a monomer, CO^{2+} in the dimer has a new prompt dissociation pathway that produces fragments with higher kinetic energy. Calculation shows that the Coulomb field of the neighboring CO^+ modifies the electronic state of the dimer, giving rise to a prompt channel. Coupling between different charge state configurations results in a new dimer electronic state, which leads to dissociation with higher kinetic energy. For solids, coupling among many atoms creates bands and a bandgap that plays the role of the ionization potential and reduces the threshold for electron-hole pair generation. Thus, solids are a good medium for high-order harmonic generation at the high repetition rates needed for frequency combs. We generate up to the 7th harmonic in silicon and zinc oxide with femtosecond pulses from a thulium fiber laser.

We present the results of a numerical simulation tool for modeling the second-harmonic generation (SHG) interaction experienced by a diffracting beam. This code is used to study the simultaneous frequency and spatial profile conversion of a truncated Bessel beam that closely resembles a higher-order mode (HOM) of an optical fiber. SHG with Bessel beams has been investigated in the past and was determined have limited value because it is less efficient than SHG with a Gaussian beam in the undepleted pump regime. This thesis considers, for the first time to the best of our knowledge, whether most of the power from a Bessel-like beam could be converted into a second-harmonic beam (full depletion), as is the case with a Gaussian beam. We study this problem because using HOMs for fiber lasers and amplifiers allows reduced optical intensities, which mitigates nonlinearities, and is one possible way to increase the available output powers of fiber laser systems. The chief disadvantage of using HOM fiber amplifiers is the spatial profile of the output, but this can be transformed as part of the SHG interaction, most notably to a quasi-Gaussian profile when the phase mismatch meets the noncollinear criteria. We predict, based on numerical simulation, that noncollinear SHG (NC-SHG) can simultaneously perform highly efficient (90%) wavelength conversion from 1064 nm to 532 nm, as well as concurrent mode transformation from a truncated Bessel beam to a Gaussian-like beam (94% overlap with a Gaussian) at modest input powers (250 W, peak power or continuous-wave operation). These simulated results reveal two attractive features – the feasibility of efficiently converting HOMs of fibers into Gaussian-like beams, and the ability to simultaneously perform frequency conversion. Combining the high powers that are possible with HOM fiber amplifiers with access to non-traditional wavelengths may offer significant advantages over the state of the art for many important applications, including underwater communications, laser guide stars, and theater projectors.

This thesis focuses on the development of high harmonic generation (HHG) by using polarisation controlled quasi-phase matching QPM as well as related topics. A new class of QPM techniques called polarisation-controlled QPM is introduced where linear or circlar birefringence enables the modulation of the driving field's polarisation state called polarisation-beating QPM (PBQPM) for linear birefringence and optical rotation QPM (ORQPM) for circular birefringence respectively. PBQPM uses a linear birefringence to modulate periodically the driving pulse between linear and circular/elliptical polarisation states. Because elliptical or circular polarisation of the driving pulse suppresses harmonic generation, by appropriately matching the beat length of the driving field's polarisation state to the coherence length of the harmonic generation, QPM can be achieved. In the second technique, ORQPM, propagation of the driving radiation in a system exhibiting circular birefringence causes its plane of polarisation to rotate; by appropriately matching the period of rotation to the coherence length, it is possible to avoid destructive interference of the generated radiation. Not only does ORQPM have similar enhancements as true-phase matching, it is also the first proposed QPM source for circularly polarised high harmonics. The importance of phase modulation in QPM, especially relating to modebeating in hollow-core waveguides where harmonics is being generated are also explored theoretically. Based on this, a novel technique for analyzing random phase matching using a continuous phase-diffusion treatment has been developed; theoretical analytical models are shown to produce excellent agreement with simulations. It is further shown that random phase matching may be responsible for additional broadening of the high harmonic spectrum, especially at higher harmonic orders. Because mode and polarisation control is central to polarisation-controlled QPM, four waveguide mode decomposition techniques from single shot CCD data have been developed. The extraction of phase and coupling coefficients are demonstrated experimentally. A novel analytical general solution for the phase introduced by a phase-only spatial light modulator to generate a given far-field phase and amplitude was developed. The solution was demonstrated experimentally and shown to enable excellent control of the far-field amplitude and phase. Finally, circular and linear birefringent waveguides were explored. Analytic solutions to rectangular birefringent hollow-core waveguides were developed and some initial demonstration experiments were performed.

High Harmonic Generation (HHG) enables the production of bursts of coherent soft x-rays with attosecond pulse duration. This process arrises from the nonlinear interaction between intense infrared laser pulses and an ionizing gas medium. Soft x-ray photons are used for spectroscopy of inner-shell electron correlation and exchange processes, and the availability of attosecond pulse durations will enable these processes to be resolved on their natural time scales. The maximum or cutoff photon energy in HHG increases with both the intensity as well as the wavelength of the driving laser. It is highly desirable to increase the harmonic cutoff as this will allow for the generation of shorter attosecond pulses, as well as HHG spectroscopy of increasingly energetic electronic transitions. While the harmonic cutoff increases with laser wavelength, there is a corresponding decrease in harmonic yield. The first part of this thesis describes the experimental measurement of the wavelength scaling of HHG efficiency, which we report as lambda^(-6.3) in xenon, and lambda^(-6.5) in krypton. To increase the HHG cutoff, we have developed a 1.8 um source, with stable carrier envelope phase and a pulse duration of <2 optical cycles. The 1.8 um wavelength allowed for a significant increase in the harmonic cutoff compared to equivalent 800 nm sources, while still maintaing reasonable harmonic yield. By focusing this source into neon we have produced 400 eV harmonics that extend into the x-ray water window. In addition to providing a source of photons for a secondary target, the HHG spectrum caries the signature of the electronic structure of the generating medium. In krypton we observed a Cooper minimum at 85 eV, showing that photoionization cross sections can be measured with HHG. Measurements in xenon lead to the first clear observation of electron correlation effects during HHG, which manifest as a broad peak in the HHG spectrum centred at 100 eV. This thesis also describes several improvements to the HHG experiment including the development of an ionization detector for measuring laser intensity, as well as an investigation into the role of laser mode quality on HHG phase matching and efficiency.