Filaments are self-guided plasma channels generated from laser pulses with power above a critical value. They can propagate several times the Rayleigh length for diffraction and can travel through adverse atmospheric conditions. As such, filaments are useful in applications such as long wavelength electromagnetic and electric discharge guiding, and weather manipulation to name a few. Arrays of filaments can be useful to these applications, particularly in the generation of waveguides. However, understanding the filament-induced plasma dynamics of two closely propagating beams is crucial in designing the ideal waveguide. One common way to characterize a filament is through the electron density of the plasma channel, a property which has previously been proven to be clamped for a single filament. This work will show how the electron density can be enhanced through the use of two co-propagating beams, taking advantage of their interaction. Three cases were studied: two sub-critical beams, one subcritical beam and one filament, and two filaments. The separations and focusing conditions of the beams were also varied. Enhancement of the electron density and lengthening of the plasma lifetime will be discussed for each case.

As a label-free, non-destructive, high-resolution, and quantitative imaging technique, optical diffraction tomography (ODT) has been widely used to image biological samples and microstructures, such as cells, tissues, and optical fibers. The refractive-index (RI) distribution of an object is reconstructed from multi-view measurements of diffracted fields emerging from the object. Typical ODT setups include the object rotating configuration (ORC) and the illumination scanning configuration (ISC). One major limitation of ODT is that it is only applicable to weakly-scattering objects. In this dissertation, novel methods have been developed to overcome the reconstruction difficulty caused by multiple scattering, so as to extend ODT applications. First, an iterative ODT (iODT) algorithm has been developed by iteratively reducing the differences between the forward and backward propagation fields through the scattering area. The perturbative correction to the reconstructed object is computed from the field discrepancies by use of the Rytov-based inversion. iODT as originally designed for ORC, can also be applied to ISC with an appropriate coherent transfer function normalization. Both simulation and experimental results demonstrate that iODT provides accurate and efficient reconstructions of multiply-scattering phase objects with high RI contrasts, large optical path-length differences (OPDs), and/or complicated structures. Furthermore, with the same prior knowledge, iODT also outperforms ODT in resolving the missing-angle problem, in terms of convergence and reconstruction quality. For imaging multiply-scattering objects with complex RI distributions, iODT is prone to crosstalk-like artifacts between the real and imaginary parts. An error subtraction (ES) method has been developed, serving as an add-on module to iODT, to simultaneously reconstruct the RI and the absorption/gain distributions of multiply-scattering objects, even from noisy measurements with signal-to-noise ratio of 20 dB. Finally, we have explored the complementarity of iODT and optimization-based ODT in terms of their advantages and disadvantages, and proposed a combined strategy — iODT initialization for optimization-based ODT. Because the perturbative correction in iODT relies on the Rytov-based inversion instead of a generic gradient method, iODT has a physics-based component that alleviates the trapping in local minima. Numerical results demonstrate that reconstruction only under this combined strategy can accurately converge to the global minimum, especially for multiply-scattering objects with large OPDs.

Filamentation is a complex process that gives rise to many nonlinear interactions. However, the fundamentals of filament formation and propagation can be explained in terms of two dominant mechanisms: Kerr self-focusing and plasma defocusing. The first to occur, self-focusing, is responsible for an increase in irradiance through beam collapse. This process requires sufficient initial peak power, on the order of gigawatts for near infrared beams in air. Plasma defocusing then arrests the collapse process once the irradiance reaches the ionization threshold of the medium. These two processes balance each other in an extended plasma channel known as a filament. A beam's collapse behavior is strongly influenced by the initial beam conditions, especially in applications that require power scaling to terawatt levels where the Kerr effect is more pronounced. Therefore, understanding and controlling the collapse process is essential in this regime. For this reason, an exploration of the wavefront evolution of filamenting beams is of great interest and the topic of this thesis, which has three parts. First, it reviews the filamentation process and describes characteristics of filaments. Next, experimental measurements of the wavefronts of filamenting beams are given in two separate regimes. The first regime is the Kerr self-focusing that takes place before beam collapse is arrested. This data is then contrasted with wavefront measurements within a filament after collapse has occurred.

In order to extend the capabilities and applications of silicon photonics, other materials and compatible technologies have been developed and integrated on silicon substrates. A particular class of integrable materials are those with high second- and third-order nonlinear optical properties. This work presents contributions made to nonlinear integrated photonics on silicon substrates, including chalcogenide waveguides for over an octave supercontinuum generation, and rib-loaded thin-film lithium niobate waveguides for highly efficient second-harmonic generation. Through the pursuit of hybrid integration of the two types of waveguides for applications such as on-chip self-referenced optical frequency combs, we have experimentally demonstrated fabrication integrability of chalcogenide and thin-film lithium niobate waveguides in a single chip and a pathway for both second- and third-order nonlinearities occurring therein. Accordingly, design specifications for an efficient nonlinear integrated waveguide are reported, showing over an octave supercontinuum generation and frequency selectivity for second-harmonic generation, enabling potentials of on-chip interferometry techniques for carrier-envelope offset detection, and hence stabilized optical combs.

The next generation fiber transmission system is limited by fiber nonlinearity. A distributed nonlinearity compensation method, known as Digital Backward Propagation (DBP), is necessary for effective compensation of the joint effect of dispersion and nonlinearity. However, in order for DBP to be accurate, a large number of steps are usually required for long-haul transmission, resulting in a heavy computational load. In real time DBP implementation, the FIR filters can be used for dispersion compensation and account for most of the computation per step. A method of designing a complementary filter pair is proposed. The individual errors in the frequency response of the two filters in a complementary filter pair cancel each other. As a result, larger individual filter error can be tolerated and the required filter length is significantly reduced. Unequal step size can be used in DBP to minimize the number of steps. For unrepeatered transmission with distributed Raman amplification, the Raman gain as a function of the distance and the effective fiber length of each DBP step need to be calculated by solving the differential equations of Raman amplification. The split-step DBP is performed only for transmission where the signal power is high. In comparison with solving the nonlinear Schrodinger equation (NLSE) for the total field of the WDM signal, solving the coupled NLSE requires a smaller step number and a lower sampling rate. In addition, the phase-locking between the local IV oscillators is not necessary for solving the coupled NLSE. The XPM compensation of WDM long-haul transmission by solving the coupled NLSE is experimentally demonstrated. At the optimum power level of fiber transmission, the total nonlinear phase shift is on the order of 1 radian. Therefore, for transoceanic fiber transmission systems which consist of many ( > 100) amplified fiber spans, the nonlinear effects in each span are weak. As a result, the optical waveform evolution is dominated by the dispersion. Taking advantage of the periodic waveform evolution in periodically dispersion managed fiber link, the DBP of K fiber spans can be folded into one span with K times the nonlinearity. This method can be called "distance-folded DBP". Under the weakly nonlinear assumption, the optical waveform repeats at locations where accumulated dispersions are identical. Consequently, the nonlinear behavior of the optical signal also repeats at locations of identical accumulative dispersion. Hence for a fiber link with arbitrary dispersion map, the DBP steps can be folded according to the accumulated dispersion. Experimental results show considerable savings in computation using this "dispersion-folded DBP" method. Simulation results show that the dramatically reduced computational load makes the nonlinearity-compensated dispersion-managed fiber link a competitive candidate for the next-generation transmission systems.

A thorough understanding of laser-materials interactions is crucial when designing and building optical systems. An ideal test method would probe both the thermal and optical properties simultaneously for materials under large optical loads where detrimental thermal effects emerge. An interesting class of materials are those used for infrared wavelengths due to their wide spectral transmission windows and large optical nonlinearities. Since coherent sources spanning the mid-wave and long-wave infrared wavelength regions have only become widely available in the past decade, data regarding their thermal and optical responses is lacking in literature. Photothermal Lensing (PTL) technique is an attractive method for characterizing the optical and thermal properties of mid-infrared materials as it is nondestructive and can be implemented using both continuous wave and pulsed irradiation. Analogous to the well-known Z-scan, the PTL technique involves creating a thermal lens within a material and subsequently measuring this distortion with a probe beam. By translating the sample through the focus of the pump laser, information can be obtained regarding the nonlinear absorption, thermal diffusivity and thermo-optic coefficient. This thesis evaluates the effectiveness and scope of the PTL method using numerical simulations of low loss infrared materials. Specifically, the response of silicon, germanium, and As2Se3 glass is explored. The 2 µm pump and 4.55 µm probe beam geometries are optimized in order to minimize experimental error. Methodologies for estimating the thermal diffusivity, nonlinear absorption coefficient and thermo-optic coefficient directly from the experimentally measured PTL signal are presented. Finally, the ability to measure the nonlinear absorption coefficient without the need for high-energy or ultrashort optical pulses is demonstrated.

Laser ablation of GaAs by a combination of femtosecond and nanosecond pulses is investigated as a means of enhancing material removal by a femtosecond pulse in the filamentation intensity regime. We demonstrate for the first time increased ablation of GaAs by ultrafast laser pulse plasmas augmented by nanosecond pulse radiation from a secondary laser. Material removal during laser ablation is a complex process that occurs via multiple mechanisms over several timescales. Due to different pulse durations, ablation by femtosecond and nanosecond pulses are dominated by different mechanisms. Ablation can be enhanced by optimally combining a femtosecond and nanosecond pulse in time. In this work, the craters generated by combinations of pulses are investigated for inter-pulse delays ranging from -50ns to +1?s, with the fs pulse preceding the ns pulse corresponding to a positive delay. The Ti:Sapph Multi-Terawatt Femtosecond Laser (MTFL) in the Laser Plasma Laboratory (LPL) provides 50fs pulses at 800nm with intensities of 1014W/cm^2 at the sample. An Nd:YAG laser (Quantel CFR200) provides 8ns pulses at 1064nm with intensities of 109W/cm^2. Crater profilometry with white-light interferometry and optical microscopy determine the structure and surface features of the craters and the volume of material removed. Ultrafast shadowgraphy of the ejected plasma provides insight to the dual-pulse ablation dynamics. Sedov-Taylor analysis of the generated shockwave reveals the energy coupled to the sample or preceding plasma. It was found that inter-pulse delays between +40 and +200ns yielded craters 2.5x greater in volume than that of the femtosecond pulse alone, with a maximum enhancement of 2.7x at +100ns. Shadowgraphy of -40 to +40ns delays revealed that enhancement occurs when the nanosecond pulse couples to plasma generated by the fs pulse. This work provides a possible means of enhancing ablation by femtosecond filaments, which propagate long distances with clamped intensity, advancing long-range stand-off ablation

Liquid crystal spatial phase modulator plays an important role in laser beam steering, wave-front shaping and correction, optical communication, optical computation and holography. One fundamental limitation lays in the response time of liquid crystal reorientation. To achieve fast response time, polymer-network liquid crystals are therefore proposed. By incorporating polymer network in a liquid crystal host, the response time can be reduced by a factor of 100. However, the polymer network introduces hysteresis, light scattering, and high voltage. The motivation for a fast-response liquid crystal phase modulator will be discussed in the first chapter. In the second chapter, we introduce our discovery that by modifying the polymer network structure with C12A, the hysteresis from the network can be eliminated, while keeping response time at the same order. In the third chapter, we introduce a new route toward fast response time. Instead of randomly generated network, we propose to utilize two-photon-polymerization method to create well-defined polymer scaffold. By introducing polymer scaffold, we demonstrated a 7-fold faster response in comparison with traditional phase modulators, while hysteresis, scattering, and high driving voltage are all eliminated. In the fourth chapter, we introduce phase modulation based on Pancharatnam-Berry (PB) phase principle. In this type of phase modulation, the defect at 2π phase reset in conventional phase modulators can be avoided. Therefore, a higher optical quality can be achieved, making them suitable for display and imaging applications. We demonstrated a fast PB lens with response time less than 1 ms, and using which we realized the first PB lens-based additive light field display to generate true (monocular) 3D content with computationally rendered images. In chapter five, we demonstrate the resolution enhancement based on pixel-shifting of fast PB gratings. By synchronizing display content with shifting pixels, we demonstrated ~2x enhanced resolution and significantly reduced screen-door artifact. In chapter six, we report our discovery of reflective polarization volume gratings (PVGs) based on self-organized liquid crystal helix. We achieved a large deflection angle ( > 50° in glass), high diffraction efficiency ( > 95%), and unique polarization selectivity (distinction ratio > 100:1). A system integrating PB optical elements is described in chapter seven. Finally, we will summarize our major accomplishments in chapter eight.

Thulium- and holmium-doped fiber lasers (TDF and HDF) emitting at 2 micron offer unique benefits and applications compared to common ytterbium-doped 1 micron lasers. This dissertation details the concepts, limitations, design, and performance of four 2 micron fiber laser systems. While these lasers were developed for various end-uses, they also provide further insight into two major power scaling limitations. The first limitation is optical nonlinearities: specifically stimulated Brillouin scattering (SBS) and modulation instability (MI). The second limitation is thermal failure due to inefficient pump conversion. First, a 21.5 W single-frequency, single-mode laser with adjustable output from continuous-wave to nanosecond pulses is developed. Measuring the SBS threshold versus pulse duration enables the Brillouin gain coefficient and gain bandwidth to be determined at 2 micron. Second, a 23 W spectrally-broadband, nanosecond pulsed laser is constructed for materials processing applications. The temporally incoherent multi-kW peak power pulses can also efficiently produce MI and supercontinuum generation by adjusting the input spectral linewidth. Third, the measured performance of in-band pumped TDF and HDF lasers are compared with simulations. HDF displays low efficiencies, which is explained by including ion clustering in the simulations. The TDF operates with impressive > 90% slope efficiencies. Based on this result, a system design for > 1 kW average power TDF amplifier is described. The designed final amplifier will be in-band pumped to enable high efficiency and low thermal load. The amplifier efficiency, operating bandwidth, thermal load, and nonlinear limits are modeled and analyzed to provide a framework for execution. Overall, this dissertation provides further insight and understanding on the various processes that limit power scaling of 2 micron fiber lasers.

Thulium fiber lasers have the broadest emission wavelength bandwidth out of any rare-earth doped fiber lasers. The emission wavelength starts from 1.75μm and ends at around 2.15μm, covering a vast swath of the eye safe wavelength region and intersecting with a large portion of mid-infrared atmospheric transmission window. Also, thulium fiber lasers provide the highest average output power of any other rare-earth doped fiber lasers in these wavelength regimes, making them uniquely suited for applications such as remote sensing. At the moment, high power beam propagation of continuous wave laser through the atmosphere in the mid-infrared range is yet to be investigated anywhere. In particular, the effects of atmospheric water vapors on the thulium fiber laser propagation are unknown and are of great research interest. This dissertation identifies the stringent requirements in constructing a high power, single frequency, wavelength tunable, continuous wave thulium fiber laser with the aim of using it to study various atmospheric transmission effects. A fine spectral control scheme using diffraction gratings is explored and improvements are made. Moreover, a fiber numerical simulation model is presented and is used for designing and implementing the thulium fiber laser system. The current limitations of the implemented system are discussed and an improved system is proposed. This will lay the foundation for the future high power atmospheric propagation studies.