The field of integrated photonics aims at compressing large and environmentally-sensitive optical systems to micron-sized circuits that can be mass-produced through existing semiconductor fabrication facilities. The integration of optical components on single chips is pivotal to the realization of miniature systems with high degree of complexity. Such novel photonic chips find abundant applications in optical communication, spectroscopy and signal processing. This work concentrates on harnessing nonlinear phenomena to this avail. The first part of this dissertation discusses, both from component and system level, the development of a frequency comb source with a semiconductor mode-locked laser at its heart. New nonlinear devices for supercontinuum and second-harmonic generations are developed and their performance is assessed inside the system. Theoretical analysis of a hybrid approach with synchronously-pumped Kerr cavity is also provided. The second part of the dissertation investigates stimulated Brillouin scattering (SBS) in integrated photonics. A fully-tensorial open-source numerical tool is developed to study SBS in optical waveguides composed of crystalline materials, particularly silicon. SBS is demonstrated in an all-silicon optical platform.

In the last few years, optics has witnessed the emergence of two fields namely metasurfaces and parity-time (PT) symmetry. Optical metasurfaces are engineered structures that provide unique responses to electromagnetic waves, absent in natural materials. On the other hand, PT symmetry has emerged from quantum mechanics, when a new class of non-Hermitian Hamiltonian quantum systems was shown to have real eigenvalues. In this work, we demonstrate how PT-symmetric diffractive structures are capable of eliminating diffraction orders in specific directions, while maintaining/enhancing the remaining orders. In the second part of this work, we emphasize on supersymmetry (SUSY) and its applications in optics. Even though the full ramification of SUSY in high-energy physics is still a matter of debate that awaits experimental validation, supersymmetric techniques have already found their way into low-energy physics. In this work, we apply certain isospectral techniques in order to achieve single mode lasing in multi-element waveguide systems, where multimode chaotic emission is expected. In the third part of this dissertation, we emphasize on dynamically reconfigurable nanoparticle platforms. By exploiting the dielectrophoresis effect, we demonstrate how controllable lasing can be achieved in random photonic arrangements. Although this work focuses on the case of controlling random lasers, we expect that the proposed nanoparticle architecture can incorporate heterogeneous materials of a wide range of optical functionalities, including gain, scattering, plasmonic resonance, and nonlinearity. In the last part of the dissertation, we demonstrate the capability of synthesizing space-time (ST) wave packets, based on new propagation-invariant elementary solutions of the wave equation identified through a complexification of the spatial and temporal degrees of freedom. By establishing the connection between ST propagation-invariant pulses and tilted-pulse-front pulses, a path is opened to exploiting the unique attributes of such wave packets both in nonlinear and quantum optics.

Driven by the advances in signal processing and ubiquitous availability of high-speed low-cost computing resources over the past decade, computational imaging has seen the growing interest. Improvements on spatial, temporal, and spectral resolutions have been made with novel designs of imaging systems and optimization methods. However, there are two limitations in computational imaging. 1), Computational imaging requires full knowledge and representation of the imaging system called the forward model to reconstruct the object of interest. This limits the applications in the systems with a parameterized unknown forward model such as range imaging systems. 2), the regularization in the optimization process incorporates strong assumptions which may not accurately reflect the a priori distribution of the object. To overcome these limitations, we propose 1) novel optimization frameworks for applying computational imaging on active and passive range imaging systems and achieve 5-10 folds improvement on temporal resolution in various range imaging systems; 2) a data-driven method for estimating the distribution of high dimensional objects and a framework of adaptive sensing for maximum information gain. The adaptive strategy with our proposed method outperforms Gaussian process-based method consistently. The work would potentially benefit high-speed 3D imaging applications such as autonomous driving and adaptive sensing applications such as low-dose adaptive computed tomography(CT).

Since their invention in 1960, lasers have revolutionized modern technology, and tremendous amounts of innovation and development has gone into advancing their properties and efficiencies. This dissertation reports on further innovations by presenting novel solid state laser systems based on the volume Bragg gratings (VBGs) and the newly developed holographic phase mask (HPMs) for brightness enhancement, dual wavelength operation, and mode conversion. First, a new optical element was created by pairing the HPM with two surface gratings creating an achromatic holographic phase mask. This new optical device successfully performed transverse mode conversion of multiple narrow line laser sources operating from 488 to 1550 nm and a broadband mode locked femtosecond source with no angular tuning. Also, two types of HPMs were tested on high power Yb fiber lasers to demonstrate high energy mode conversion. Secondly, the effects of implementing VBGs for brightness enhancement of passively Q-switched systems with large Fresnel numbers was investigated. Implementing VBGs for angular mode selection allowed for higher pulse energies to be extracted without sacrificing brightness and pulse duration. This technique could potentially be applied to construct compact cavities with 1 cm diameter beams and nearly diffraction limited beam quality. Lastly, a spectral beam combining approach was applied to create Tm3+ and Yb3+ based narrowband dual-wavelength pump sources for terahertz generation, using VBGs as frequency selectors and beam combiners. Comparison of pulse duration and synchronization was done between passive and active Q-switching operation. An experimental set up for THz generation and detection using high sensitive detectors was created, and modeling of terahertz conversion efficiencies were done

Small-sized vertical-cavity surface-emitting laser (VCSEL) may offer very low power consumption along with high reliability for cryogenic data transfer. Cryogenic data transfer has application in supercomputers and superconducting for efficient computing and also focal plane array cameras operating at 77 K, and at the lower temperature of 4 K for data extraction from superconducting circuits. A theoretical analysis is presented for 77 K and 4 K operation based on small cavity, oxide-free VCSEL sizes of 2 to 6 µm, that have been shown to operate efficiently at room temperature. Temperature dependent operation for optimally-designed VCSELs are studied by calculating the response of the laser at 77 K and 4 K to estimate their bias conditions needed to reach modulation speed for cryogenic optical links. The temperature influence is to decrease threshold for reducing temperature, and to increase differential gain for reducing temperature. The two effects predict very low bias currents for small cavity VCSELs to reach needed data speed for cryogenic optical data links. Projections are made for different cavity structures (half-wave cavity and full-wave cavity) shown that half-wave cavity structure has better performance. Changing the number of top-mirror pairs has also been studied to determine how cavity design impacts speed and bit energy. Our design and performance predictions paves the way for realizing highly efficient, ultra-small VCSEL arrays with applications in optical interconnects.

Wearable near-eye display has found widespread applications in education, gaming, entertainment, engineering, military training, and healthcare, just to name a few. However, the visual experience provided by current near-eye displays still falls short to what we can perceive in the real world. Three major challenges remain to be overcome: 1) limited dynamic range in display brightness and contrast, 2) inadequate angular resolution, and 3) vergence-accommodation conflict (VAC) issue. This dissertation is devoted to addressing these three critical issues from both display panel development and optical system design viewpoints. A high-dynamic-range (HDR) display requires both high peak brightness and excellent dark state. In the second and third chapters, two mainstream display technologies, namely liquid crystal display (LCD) and organic light emitting diode (OLED), are investigated to extend their dynamic range. On one hand, LCD can easily boost its peak brightness to over 1000 nits, but it is challenging to lower the dark state to < 0.01 nits. To achieve HDR, we propose to use a mini-LED local dimming backlight. Based on our simulations and subjective experiments, we establish practical guidelines to correlate the device contrast ratio, viewing distance, and required local dimming zone number. On the other hand, self-emissive OLED display exhibits a true dark state, but boosting its peak brightness would unavoidably cause compromised lifetime. We propose a systematic approach to enhance OLED's optical efficiency while keeping indistinguishable angular color shift. These findings will shed new light to guide future HDR display designs. In Chapter four, in order to improve angular resolution, we demonstrate a multi-resolution foveated display system with two display panels and an optical combiner. The first display panel provides wide field of view for peripheral vision, while the second panel offers ultra-high resolution for the central fovea. By an optical minifying system, both 4x and 5x enhanced resolutions are demonstrated. In addition, a Pancharatnam-Berry phase deflector is applied to actively shift the high-resolution region, in order to enable eye-tracking function. The proposed design effectively reduces the pixelation and screen-door effect in near-eye displays. The VAC issue in stereoscopic displays is believed to be the main cause of visual discomfort and fatigue when wearing VR headsets. In Chapter five, we propose a novel polarization-multiplexing approach to achieve multiplane display. A polarization-sensitive Pancharatnam-Berry phase lens and a spatial polarization modulator are employed to simultaneously create two independent focal planes. This method enables generation of two image planes without the need of temporal multiplexing. Therefore, it can effectively reduce the frame rate by one-half. In Chapter six, we briefly summarize our major accomplishments.

The capability of retrieving the image/signal of interest from extremely low photon flux is attractive in scientific, industrial, and medical imaging applications. Conventional imaging modalities and reconstruction algorithms rely on hundreds to thousands of photons per pixel (or per measurement) to ensure enough signal-to-noise (SNR) ratio for extracting the image/signal of interest. Unfortunately, the potential of radiation or photon damage prohibits high SNR measurements in dose-sensitive diagnosis scenarios. In addition, imaging systems utilizing inherently weak signals as contrast mechanism, such as X-ray scattering-based tomography, or attosecond pulse retrieval from the streaking trace, entail prolonged integration time to acquire hundreds of photons, thus rendering high SNR measurement impractical. This dissertation addresses the problem of imaging from limited photon budget when high SNR measurements are either prohibitive or impractical. A statistical image reconstruction framework based on the knowledge of the image-formation process and the noise model of the measurement system has been constructed and successfully demonstrated on two imaging platforms – photon-counting X-ray imaging, and attosecond pulse retrieval. For photon-counting X-ray imaging, the statistical image reconstruction framework achieves high-fidelity X-ray projection and tomographic image reconstruction from as low as 16 photons per pixel on average. The capability of our framework in modeling the reconstruction error opens the opportunity of designing the optimal strategies to distribute a fixed photon budget for region-of-interest (ROI) reconstruction, paving the way for radiation dose management in an imaging-specific task. For attosecond pulse retrieval, a learning-based framework has been incorporated into the statistical image reconstruction to retrieve the attosecond pulses from the noisy streaking traces. Quantitative study on the required signal-to-noise ratio for satisfactory pulse retrieval enabled by our framework provides a guideline to future attosecond streaking experiments. In addition, resolving the ambiguities in the streaking process due to the carrier envelop phase has also been demonstrated with our statistical reconstruction framework.

Frequency combs have revolutionized metrology and demonstrated numerous applications in science and technology. Combs operating in the mid-infrared region could be beneficial for molecular spectroscopy for several reasons. First, numerous molecules have their spectroscopic signatures in this region. Furthermore, the atmospheric window (3-5μm and 8-14μm) is located here. Additionally, a mid-infrared frequency comb could be employed as a diagnostic tool for the many components of human breath, as well as for detection of harmful gases and contaminants in the atmosphere. In this thesis, I used synchronously pumped subharmonic optical parametric oscillators (OPOs) operating at degeneracy to produce ultra-broadband outputs near half of the pump laser frequency. One attractive property of the subharmonic OPOs is that the signal/idler waves of the OPO are frequency- and phase-locked to the pump frequency comb. We explored three new nonlinear materials in the subharmonic OPO and demonstrated a broadband spectrum for mid-infrared frequency comb generation. (1) Orientation-patterned (OP) gallium arsenide (GaAs) was selected as the first material because it has high nonlinearity. We found that the OP-GaAs based OPO yielded an approximately two-octave wide spectrum (2.8–11μm). (2) Gallium phosphide (GaP) has near zero group velocity dispersion (GVD) at 4.7 μm and a large bandgap. The OP-GaP OPO yielded a spectrum of more than two octaves (3–12.5μm). Also, because of the large bandgap, GaP is suitable for telecom 1.56-μm pumping, having the advantage of much smaller GVD than in periodically-poled-lithium-niobite (PPLN). The telecom laser (1.56μm) pumped OP-GaP OPO was demonstrated with more than one octave wide spectrum. (3) Finally, we explored the phenomenon of random phase matching in the zinc selenide (ZnSe) polycrystalline material. The first random phase matched OPO was demonstrated with more than one octave spectrum (3.1– 9μm), which is also the first OPO based on ZnSe.

The last two decades have witnessed tremendous advancements in the area of nanophotonics and plasmonics, which has helped propel the development of integrated photonic sources. Of central importance to such circuits is compact, scalable, low threshold, and efficient coherent sources that can be driven at high modulation frequencies. In this regard, metallic nanolasers offer a unique platform. Their introduction has enabled confinement of light at a subwavelength scale and the ultra-small size of the modes afforded by these structures allows for cavity enhancing effects that can help facilitate thresholdless lasing and large direct modulation bandwidths. In this report, I present my work on the study of the fundamental properties of metallic nanolasers. I start with a rate equation model to predict threshold behavior and the modulation response of metallic nanolasers. Next, I explain the second-order coherence measurement setup that was built, based on a modified Hanbury-Brown and Twiss experiment, to assess the intensity autocorrelation of various optically pumped metallic nanolasers. These studies concluded that metallic coaxial and disk-shaped nanolasers are capable of generating truly coherent radiation. Subsequently, design considerations are taken into account for electrically pumped coaxial nanolasers. This has led to the demonstration of electrically injected coaxial and disk-shaped nanolasers at cryogenic temperatures. Lastly, the appearance of collective behaviors in metallic nanolasers lattices is explored. Individually supporting modes that are highly vectorial by nature, when such cavities are fabricated in close proximity to one another, coupling through their overlapping fields results in the formation of a set of supermodes. The tendency of the system to minimize the overall loss leads to each element of the lattice having a geometric dependent field distribution and helps promotes single-mode lasing. We show both through simulations and experimentally that this effect can lead to the direct generation of vector vortices.

Infrared transparent glassy and crystalline materials often have unique and complex processing requirements but are an important class of materials for such applications as optical windows, lenses, waveplates, polarizers and beam splitters. This thesis investigates two specific materials, one amorphous and one crystalline, that are candidates for use in the short and midwave-infrared and mid and longwave infrared, respectively. It is demonstrated that an innovative uniaxial sintering process, which uses a sacrificial pressure-transmitting medium, can be used to fully densify a 70TeO2-20WO3-10La2O3 (TWL) glass powder. The characteristics of the sintered TWL glass is compared to that of a parent glass produced through a conventional melt/quench process to ascertain the impact of process-specific property changes on the resulting material. Additionally, the design, construction and characterization of a custom-made transparent Bridgman crystal growth furnace is undertaken to enable growth of highly birefringent tellurium single crystal. The key obstacles that need to be overcome to scale up the size of the grown crystals are summarized with the end goal of producing commercial grade optical elements.