Femtosecond laser filamentation in gaseous media is a new source of broadband, ultrashort radiation that has the potential for application to many fields of research. In this dissertation filamentation is studied with a view to understanding the underlying physics governing the formation and propagation dynamics of filamentation, as well as to developing a method for vibrational spectroscopy based on the filament-induced impulsive vibrational excitation of molecules in the filamentation region. In pursuit of a better understanding of the underlying physical processes driving filamentation, the development of a new method for characterizing high intensity ultrashort laser pulses is presented, wherein two laser beams generate a transient grating in a noble gas, causing the pulse undergoing filamentation to diffract from the grating. Measuring the spectrum as a function of time delay between the filament and probe beams generates a spectrogram that can be inverted to recover the spectral and temporal phase and amplitude of the filamentary pulse. This technique enables measurement of the filamentary pulse in its native environment, offering a window into the pulse dynamics as a function of propagation distance. The intrinsic pulse shortening observed during filamentation leads to the impulsive excitation of molecular vibrations, which can be used to understand the dynamics of filamentation as well. Combined measurements of the longitudinally-resolved filament Raman spectrum, power spectrum, and fluorescence intensity confirm the propagation dynamics inferred from pulse measurements and show that filamentation provides a viable route to impulsive vibrational spectroscopy at remote distances from the laser source. The technique is applied to thermometry in air and in flames, and an analytical expression is derived to describe the short-time dynamics of the rovibrational wave-packet dispersion experienced by diatomic molecules in the wave of the filament. It is found that no energy is initially partitioned into the distribution of rovibrational states during the filamentation process. Filament-assisted impulsive stimulated Raman spectroscopy of more complex systems is also performed, showing that filament-assisted vibrational measurements can be used as an analytical tool for gas phase measurements and has potential for use as a method for standoff detection. Finally, a study of the nonlinear optical mechanisms driving the filamentation process is conducted using spectrally-resolved pump-probe measurements of the transient birefringence of air. Comparison to two proposed theories shows that a newly described effect, ionization grating-induced birefringence, is largely responsible for saturation and sign inversion of the birefringence at 400 nm and 800 nm, while the magnitude of contributions described by a competing theory that relies on negative terms in the power series expansion of the bound electron response remain undetermined. / Chemistry

The central objective of this dissertation is developing new methods for calculating higher-order nonlinear optical responses of atoms, molecules, and ions, and discussing the relevant physical mechanisms that give rise to harmonic generation, Kerr effect, and higher-order Kerr effect. The applications of nonlinear optical properties in development of predictive models for femtosecond laser filamentation dynamics, photoemission spectroscopy, imaging, and design of new molecular systems have motivated the theoretical investigations in advancing methods for calculating nonlinear optical properties and finding the optimum conditions for controlling the nonlinearities. The time-dependent nonlinear refractive index coefficient 4 n is investigated for argon and generalized for all noble gas atoms helium, neon, krypton, and xenon in the wavelengths ranging from 250 nm to 2000 nm, using ab initio methods. The secondorder polynomial fitting of DC-Kerr, electric-field-induced second-harmonic generation (ESHG), and static second-order hyperpolarizability have been performed, using an auxiliary electric field approach to obtain the corresponding fourth-order optical properties. An expression on the basis of static, DC-Kerr, DFWM fourth-order hyperpolarizability is derived, which allows the calculations of the DSWM coefficients with considerably reduced error. The results of the calculations suggest that filament stabilization is most likely to be induced by the generation of free electrons. Applications of these calculations resolve the HOKE controversy and are important for the development of predictive models for femtosecond laser filamentation dynamics. In a series of proof-of-concept studies, the approach was employed for calculating dynamic linear and nonlinear hyperpolarizability of the radical cations. In this regard, the polarizability and second-order hyperpolarizability of nitrogen radical cation were investigated, using density functional theory (DFT) and multi-configurational self-consistent field (MCSCF) methods. The open-shell electronic system of nitrogen radical cation provides negative second-order optical nonlinearity, suggesting that the hyperpolarizability coefficient for nitrogen radical cation, in the non-resonant regime is mainly composed of combinations of virtual one-photon transitions rather than two-photon transitions. The calculations of second-order optical properties for nitrogen radical cation as a function of bond length have been investigated to study the effect of internuclear bond distance on optical process. The variation of nonlinear responses versus bond length shows the potential application in finding optimum conditions for higher values of nonlinear coefficients. Furthermore, the computation of dynamic second-order hyperpolarizabilities for multiply ionized noble gases have been studied in the wavelength ranging from 100 nm to the red of the first multi-photon resonance all the way toward the static regime, using the MCSCF method. The results indicate that the second-order hyperpolarizability coefficients decrease when the electrons are removed from the systems. As the atoms reach higher ionization states, the second-order hyperpolarizability responses as a function of wavelength, become less dispersive. The second-order hyperpolarizability coefficients for each ionized species have also been investigated in terms of quantum state symmetries; the results suggest that the sign of the optical responses for each ionized atom depends on the spin of the quantum states defined for the ionized species. The calculations are of value for predictive models of high-harmonic generation in multiply ionized plasma at X-ray photon energies. This research also focuses on investigating possible mechanisms for photodissociation of polyatomic molecules (acetophenone and the substituted derivatives) ionized through strong field infrared laser pulses. In this regard, quantum mechanical methods are combined with pump-probe spectroscopy to understand and control the dissociation dynamics in strong field regime. The applications of quantum mechanical models in interpreting time-resolved wavepacket dynamics and achieving coherent control has stimulated the interest to explore the PESs and investigate the role of conical intersections in wavepacket dynamics in strong field regime. The electronic ground and excited states for acetophenone radical cation and the substituted derivatives have been investigated to probe the resonance features observed in measurements at 1370 nm with laser intensity of 1013 W cm-2. The ten lowest lying ionic potential energy surfaces (PESs) of the acetophenone radical cation were explored, and the three-state conical intersection was mapped onto the PES, using MCSCF model to propose a photo-dissociation mechanism for acetophenone undergoing tunnel ionization and elucidate the potential dissociation pathways for formation of benzoyl fragment ion, as well as phenyl, acylium, and butadienyl small fragment ions. Similar calculations are presented for propiophenone radical cation which support the existence of a one-photon transition from the ground ionic to a bright dissociative D2 state, where motion of the acetyl group from a planar to nonplanar structure within the pulse duration enables the otherwise forbidden transition. The wavepacket dynamics in acetophenone molecular ion is modeled using the classical wavepacket trajectory calculations, to propose the mechanism wherein the 790 nm probe pulse excites a wavepacket on the ground surface D0 to the excited D2 surface at a delay of 325 fs. The innovations of this research are used to design control strategies for selective bond-breaking in acetophenone radical cation, as well as design control schemes for other molecules. / Chemistry

In this thesis, detailed studies are presented into self-assembled, noncentrosymmetric, optically active films. Second harmonic generation (SHG) is used to measure the second order nonlinear optical susceptibility (?(2)) of ionically self-assembled monolayer (ISAM) thin films. Conventional ISAM films are fabricated by alternately immersing a substrate into oppositely-charged polyelectrolyte solutions. The polyelectrolytes bind electrostatically to the oppositely-charged substrate, and thus reverse the charge of the substrate. The charge reversal limits the amount of adsorbed material and primes the substrate for the next layer. During the deposition of the nonlinear optical (NLO) active layer, the chromophores are attracted to the oppositely-charged surface, which results in net orientation of the chromophores. Some of the net orientation is lost during the deposition of the next NLO-inactive layer as this layer orients some of the chromophores away from the substrate. A disadvantage of the polymer ISAM deposition method is that although there is a net orientation toward the substrate, a large number of chromophores are randomly or oppositely oriented. This reduces the nonlinear optical response. To overcome this problem, two alternative methods with a better net orientation are discussed: hybrid covalent / ionic deposition and multivalent monomer deposition. In both deposition methods, the NLO-active material is a monomer instead of a polymer. In hybrid covalent / ionic deposition, the NLO-inactive polymer is deposited using electrostatic attraction while the NLO-active monomer is deposited covalently. This forces alignment of the chromophores. The multivalent method uses chromophores with multiple charges on one side of the molecule and one charge (same sign) on the other. The difference in electrostatic attraction causes a preferential orientation of the chromophores during deposition. Attempts have been made to further improve the net orientation by complexation of the monomers with cyclodextrins (cone shaped organic molecules), so far with only limited success. The SHG response of NLO-active layers near the glass and air interfaces is much stronger than the SHG response of layers in the bulk of the film for all deposition methods and NLO-active materials investigated in this thesis. For larger number of bilayers (the bulk regime), the square root of the SHG signal increases linearly with the number of bilayers as expected for a uniform chromophore orientation. We isolated the interface effects through use of buffer layers of NLO-inactive polymers. The glass interface effect extends roughly one bilayer deep for all investigated materials. The air interface effect is different for polymers and monomers. For monomers, this effect extends only one bilayer deep, while it extends multiple layers deep for polymers. Using glass cells to contain the polyelectrolyte solutions, we were able to measure the SHG signal in situ, which proved to be a powerful tool to monitor the deposition rate as a function of chosen parameters. All depositions were rapid, on the order of one minute or less. Provided that a minimum concentration is met, the deposition rate and final SHG values are independent of concentration. Bulk layers deposit at the same rate as layers near the interface. For polymer NLO-active layers a secondary, slower growth of SHG is observed that is presumably due to reorganization of the adsorbed polymer layer. This secondary growth is not observed in the deposition of NLO-active monomers. / Ph. D.

Detailed studies are presented of thin films that self-assemble into the noncentrosymmetric structure required for second order nonlinear optical responses. Second harmonic generation is used as a probe of the second-order nonlinear optical susceptibility (c(2)) of ionic self-assembled monolayer (ISAM) films. Films produced from the ISAM technique are shown to possess significant c(2), with values presently comparable to quartz (c(2)=1.53*10⁹ esu). These films show exceptional stability over time, with negligible decrease in c(2) after 26 months. ISAM films self-assemble from polyelectrolyte solutions due to coulombic interactions between a charged substrate and the charged polymer in solution. This process is self-limiting since charge overcompensation at the surface restricts further deposition as like charges accumulate at the surface. We have found that this 'kinetically hindered equilibrium' occurs quickly for the samples studied, after approximately 45 seconds immersion. Non-centrosymmetry is obtained during deposition as chromophores orient towards the substrate as a strong, localized collection of opposite charge. This net orientation is partially diminished as some amount of chromophore extends in the opposite direction at the film/solution interface. Second harmonic measurements suggest that chromophores at the outermost interface collapse against the film surface when dried, resulting in a larger c(2) than other 'capped' layers. Any polymer which is not located at the interfaces is thought to possess random orientation, and therefore does not contribute to c(2). We have investigated how ionic strength and solution pH affect the structure of ISAM films. These parameters serve to control the electrostatic screening in solution. Low salt concentrations result in low or no electrostatic screening. As a result, charges on a polymer strongly feel one another's presence, and decrease the net electrostatic energy by maximizing their distance from each other. This results in a rod-like conformation, which when adsorbed onto the film surface produces thin layers. Large salt concentrations serve to screen the electrostatic interaction. Because charges do not experience the strong repulsion from their neighbors, the polymer backbone is more likely to loop and coil. If the polymer is weakly soluble (pH near the solubility edge), the polymer will loop about itself and other polymer chains in order to reduce the number of polymer/water contacts. Increased screening results in adsorption of thicker films. We show that this also results in a marginal increase in film density, likely due to an increase in polymer interpenetration of adjacent layers. We can associate an increase in chromophore population at the interface with this increase in density. The reduction in screening also is shown to decrease the chromophore orientation angle, presumably by decreasing the repulsion between charges located on the chromophore ends. The improved orientation leads to an increased non-centrosymmetry in the layer. c(2) is decreased, however, as film thickness (and therefore the population of randomly oriented chromophore between interfaces) increases faster than the improvements to non-centrosymmetry at the interface. We have investigated the thermal stability of ISAM films at elevated temperatures, and have found that these films do not exhibit a permanent decay of c(2) with increased temperature as do poled guest-host polymers. A temperature-dependent decrease is observed for temperatures up to 250°C. This decrease is completely reversible (for films heated to 150C), with c(2) recovering its initial value upon cooling in spite of a glass transition temperature measured as Tg=140°C The decrease in c(2) is thought to be due to a combination of effects. Predominant decrease is thought to be due to disassociation of ionic bonds, which serve to provide noncentrosymmetry in films. A slower, smaller decay due to decrease in moisture content of the films at high temperature is also thought to be present. / Ph. D.

The spatiotemporal dynamics of a photorefractive phase-conjugate resonator (PPCR) is studied both experimentally and analytically. The resonator is a confocal cavity bounded by a dielectric mirror and a phase-conjugate mirror in a four wave mixing geometry. The effect of the Bragg mismatch, which is caused by the misalignment of the pump fields, is experimentally shown to break the cylindrical symmetry of the system and to increase the speed of the dynamics. By studying the first non stationary state at a cavity Fresnel number of F=2.0, the effect of the transverse component of the mismatch is shown to add a transverse phase to the wavefront of the phase-conjugate field, leading to the periodic nucleation of a pair of phase defects. A model of this state is developed in terms of the competition of a few transverse patterns. The model is experimentally verified using a holographic optical correlator designed to identify the modes presumed by the model. The dynamics are also studied using a Karhunen-Loeve decomposition in which the eigenvectors of the covariance matrix are calculated. The covariance matrix is obtained from the transverse intensity fluctuations of the cavity field and the eigenvectors are interpreted as the active cavity modes of the resonator. The results of the application of this experimental method to the F=2.0 state match those obtained by the correlator. This demonstrates its validity as a useful tool for studying the system. Application of the decomposition to states at higher F reveal that aperiodic and periodic states can have very similar active mode structures. An analytical model of the PPCR is then developed using a plane wave decomposition of the cavity field and the n1aterial variables contained in Kukhtarev's equations. Numerical simulations using the model demonstrate its accuracy. In addition, the different effects of the longitudinal and transverse components of the Bragg mismatch on the dynamics and defect nucleation are revealed. The relevant assumptions involved in the development of the model are discussed in detail. / Ph. D.

Theoretical studies of nonlinear optical effects in nematic liquid crystals including degenerate four-wave mixing are presented. The optically induced Freedericksz transition which is essential for these effects is also described. Experimental investigations are performed using a homeotropically aligned MBBA thin film. Good agreement is obtained between the theoretical predictions and the experiments. Some potential applications of phase conjugation obtained by the backward degenerate four wave-mixing process in the field of adaptive optics and image processing are demonstrated. / Ph. D.

In the past two decades, integrated photonics and nonlinear optics have flourished alongside one another. New developments in materials science and fabrication technologies have delivered lower loss photonic platforms and commercial foundries can produce high quality photonic devices in large quantites. These advances in photonics have allowed for new applications of nonlinear optics for quantum technologies, optical sensing and spectroscopy, and optical frequency combs. The challenge remains to integrate the lasers needed for these nonlinear photonic devices onto the same photonic platform and fully realize the size, cost, and power savings promised by photonic integration. In this dissertation we explore new applications of nonlinear optics that can enhance the functionality of integrated lasers. In the first part of this dissertation, we explore the use of additive pulse modelocking (APM) on an integrated platform for generating a high power, low repetition rate modelocked laser to achieve a fully integrated self-referenced frequency comb. We report on simulations that identify key criteria for APM lasers and compare design alternatives for the gain medium and modelocking element. We also report on the progress of experiments towards buliding an APM using semiconductor gain and the challenges associated with this goal. In the second part, we present a new theory for laser linewidth reduction called nonlinear self-injection locking and demonstrate it experimentally using a fiber Brillouin oscillator. This technique combines the gain-narrowing effects from asymmetric nonlinear oscillators like a Brillouin oscillator with the frequency stabilization techniques of self-injection locking to reduce a laser’s linewidth below its Schawlow-Townes limit. We also present future applications of this theory that could be realized on a fully integrated photonic platform.

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Nonlinearities in quantum cascade lasers (QCL¡¯s) have wide applications in wavelength tunability and ultra-short pulse generation. In this thesis, optical nonlinearities in InGaAs/AlInAs-based mid-infrared (MIR) QCL¡¯s with quadruple resonant levels are investigated. Design optimization for the second-harmonic generation (SHG) of the device is presented. Performance characteristics associated with the third-order nonlinearities are also analyzed. The design optimization for SHG efficiency is obtained utilizing techniques from supersymmetric quantum mechanics (SUSYQM) with both material-dependent effective mass and band nonparabolicity. Current flow and power output of the structure are analyzed by self-consistently solving rate equations for the carriers and photons. Nonunity pumping efficiency from one period of the QCL to the next is taken into account by including all relevant electron-electron (e-e) and longitudinal (LO) phonon scattering mechanisms between the injector/collector and active regions. Two-photon absorption processes are analyzed for the resonant cascading triple levels designed for enhancing SHG. Both sequential and simultaneous two-photon absorption processes are included in the rate-equation model. The current output characteristics for both the original and optimized structures are analyzed and compared. Stronger resonant tunneling in the optimized structure is manifested by enhanced negative differential resistance. Current-dependent linear optical output power is derived based on the steady-state photon populations in the active region. The second-harmonic (SH) power is derived from the Maxwell equations with the phase mismatch included. Due to stronger coupling between lasing levels, the optimized structure has both higher linear and nonlinear output powers. Phase mismatch effects are significant for both structures leading to a substantial reduction of the linear-to-nonlinear conversion efficiency. The optimized structure can be fabricated through digitally grading the submonolayer alloys by molecular beam epitaxy (MBE). In addition to the second-order nonlinearity, performance characteristics brought by the third-order nonlinearities are also discussed, which include third-harmonic generation (THG) and intensity dependent (Kerr) refractive index. Linear to third-harmonic (TH) conversion efficiency is evaluated based on the phase-mismatched condition. The enhanced self-mode-locking (SML) effect over a typical three-level laser is predicted, which will stimulate further investigations of pulse duration shortening by structures with multiple harmonic levels.