From the viewpoint of quantum mechanics, a system must always be Hermitian since all its corresponding eigenvalues must be real. In contrast, the eigenvalues of open systems-unrestrained because of either decay or amplification-can be in general complex. Not so long ago, a certain class of non-Hermitian Hamiltonians was discovered that could have a completely real eigenvalue spectrum. This special class of Hamiltonians was found to respect the property of commutation with the parity-time (PT) operator. Translated into optics, this implies a balance between regions exhibiting gain and loss. Traditionally, loss has been perceived as a foe in optics and something that needs to be avoided at all costs. As we will show, when used in conjunction with gain, the presence of loss can lead to a host of counterintuitive outcomes in such non-Hermitian configurations that would have been otherwise unattainable in standard arrangements. We will study PT symmetric phase transitions in various optical settings that include semiconductor microrings and coupled fiber cavities, and show how they can allow mode-selectivity in lasers. One of the key outcomes of this effort was the realization of higher order degeneracies in a three-cavity laser configuration that can exhibit orders-of-magnitude larger sensitivity to external perturbations. We will also consider systems that display nonlinear effects such as gain saturation, thus allowing novel phase transitions. Some interesting properties associated with degeneracies in non-Hermitian settings will be investigated as well. Such degeneracies, called exceptional points (EPs), are much more drastic compared to standard degeneracies of eigenvalues because the corresponding eigenvectors also coalesce, which in turn reduces the dimensionality of the phase space. We will show that dynamic parameter contours enclosing or close to EPs can lead to a robust chiral mode conversion process – something that can be potentially used to realize omni-polarizing optical devices.

Properties of light such as amplitude and phase, temporal and spatial coherence, polarization, etc. are abundantly used for sensing and imaging. Regardless of the passive or active nature of the sensing method, optical intensity fluctuations are always present! While these fluctuations are usually regarded as noise, there are situations where one can harness the intensity fluctuations to enhance certain attributes of the sensing procedure. In this thesis, we developed different sensing methodologies that use statistical properties of optical fluctuations for gauging specific information. We examine this concept in the context of three different aspects of computational optical imaging and sensing. First, we study imposing specific statistical properties to the probing field to image or characterize certain properties of an object through a statistical analysis of the spatially integrated scattered intensity. This offers unique capabilities for imaging and sensing techniques operating in highly perturbed environments and low-light conditions. Next, we examine optical sensing in the presence of strong perturbations that preclude any controllable field modification. We demonstrate that inherent properties of diffused coherent fields and fluctuations of integrated intensity can be used to track objects hidden behind obscurants. Finally, we address situations where, due to coherent noise, image accuracy is severely degraded by intensity fluctuations. By taking advantage of the spatial coherence properties of optical fields, we show that this limitation can be effectively mitigated and that a significant improvement in the signal-to-noise ratio can be achieved even in one single-shot measurement. The findings included in this dissertation illustrate different circumstances where optical fluctuations can affect the efficacy of computational optical imaging and sensing. A broad range of applications, including biomedical imaging and remote sensing, could benefit from the new approaches to suppress, enhance, and exploit optical fluctuations, which are described in this dissertation.

Space division multiplexing (SDM) is the most promising way of increasing the capacity of a single fiber. To enable the few mode fiber (FMF) or multi-mode fiber (MMF) transmission system, several major challenges have to be overcome. One is the urgent need of ideal mode multiplexer, the second is the perfect amplification for all spatial modes, another one is the modal delay spread (MDS) due to group velocity difference of spatial modes. The main subject of this dissertation is to model, fabricate and characterize the mode multiplexer for FMF transmission. First, we designed a novel resonant mode coupler (structured directional coupler pair). After that, we studied the adiabatic mode multiplexer (photonic lantern). 6-mode photonic lantern using graded-index (GI) MMFs is proposed and demonstrated, which alleviates the adiabatic require-ment and improves mode selectivity. Then, 10-mode photonic lantern is demonstrated using novel double cladding micro-structured drilling-hole preform, which alleviates the adiabatic requirement and demonstrate a feasible way to scale up the lantern modes. Also, multi-mode photonic lantern is studied for high order input modes. In addition, for the perfect amplification of the modes, cladding pump method is demonstrated. The mode selective lantern designed and fabricated can be used for the characterization of few mode amplifier with swept wavelength interferometer (SWI). Also, we demonstrated the application of the use of the few mode amplifier for the turbulence-resisted preamplified receiver. Besides, for the reduction of MDS, the long period grating for introducing strong mode mixing is demonstrated.

The observation of any atomic and molecular dynamics requires a probe that has a timescale comparable to the dynamics itself. Ever since the invention of laser, the temporal duration of the laser pulse has been incrementally reduced from several nanoseconds to just attoseconds. Picosecond and femtosecond laser pulses have been widely used to study molecular rotation and vibration. In 2001, the first single isolated attosecond pulse (1 attosecond = 10^-18 seconds.) was demonstrated. Since this breakthrough, "attoscience" has become a hot topic in ultrafast physics. Attosecond pulses typically have span between EUV to X-ray photon energies and sub-femtosecond pulse duration. It becomes an ideal tool for experimentalists to study ultrafast electron dynamics in atoms, molecules and condensed matter. The conventional scheme for generating attosecond pulses is focusing an intense femtosecond laser pulse into inert gases. The bound electrons are ionized into continuum through tunneling ionization under the strong electrical field. After ionization, the free electron will be accelerated by the laser field away from the parent ion and then recombined with its parent ion and releases its kinetic energy as a photon burst that lasts for a few hundred attoseconds. According to the classical "three-step model", high order harmonic will have a higher cutoff photon energy when driven by a longer wavelength laser field. Compared to Ti:sapphire lasers center at a wavelength of 800 nm, an optical parametric amplifier could offer a broad bandwidth at infrared range, which could support few cycle pulses for driving high harmonic generation in the X-ray spectrum range. In this work, an optical parametric chirped-pulse amplification system was developed to deliver CEP-stable 3-mJ, 12-fs pulses centered at 1.7 micron. We implement a chirped-pump technique to phase match the board parametric amplification bandwidth with high conversion efficiency. Using such a laser source, isolated attosecond pulses with photon exceeding 300 eV are achieved by applying the polarization gating technique at 1.7 micron. The intrinsic positive chirp of the attosecond pulses is measured by the attosecond streak camera and retrieved with our PROOF technique. Sn metal filters with negative dispersion were chosen to compensate the intrinsic attochirp. As a result, isolated 53-attosecond soft x-ray pulses are achieved. Such water window attosecond source will be a powerful tool for studying charge distribution/migration in bio-molecules and will bring opportunities to study high field physics or attochemistry.

The goal of this thesis is to design a tabletop coherent soft X-ray source for attosecond high resolution imaging. We collect signals from gas cells with different length and lens with different focal length. A spectrometer with a grating and a CCD camera is applied to observe and measure the spectrum of the X-ray attosecond pulses. This thesis first introduces the theory background of ultrafast lasers, then mainly explains high harmonic generation, which is the key method for attosecond pulses generation, subsequently presents the experiment system and analyzes the results from the experiment, also compares different combinations of parameters of the devices.

This dissertation reports on design and fabrication of various optical elements in Photo-thermo-refractive (PTR) glass. An ability to produce complex holographic optical elements (HOEs) for the visible spectral region appears very beneficial for variety of applications, however, it is limited due to photosensitivity of the glass confined within the UV region. First two parts of this dissertation present two independent approaches to the problem of holographic recording using visible radiation. The first method involves modification of the original PTR glass rendering it photosensitive to radiation in the visible spectral region and, thus, making possible the recording of holograms in PTR glass with visible radiation. The mechanism of photoionization in this case is based on an excited state absorption upconversion process in the glass when doped with Tb3+. By contrast, the second approach uses the original Ce3+ doped PTR glass and introduces a new modified technique for hologram formation that allows for holographic recording with visible light. Complex HOEs including holographic lenses and holographic curved mirrors were fabricated in PTR glass with visible light using both techniques. The third part of the dissertation takes a step in a different direction and discusses the development of the methods for fabrication of phase masks in PTR glass. A method for relatively straightforward and inexpensive fabrication of phase masks with the aid of a Digital Micromirror Device is presented. This method enabled to produce phase masks containing complex greyscale phase distributions for generation of vortex (helical) beams. A phase mask can be holographically encoded into a transmission Bragg grating where a holographic phase mask (HPM) is formed. HPM has an advantage over a regular phase mask of being capable of multi-wavelength operation. All optical elements recorded in PTR glass preserve the advantages peculiar to VBGs recorded in PTR glass such as stability to heating and illumination with high-power laser beams.

Even though fiber-optic communication systems have been engineered to nearly approach the Shannon capacity limit, they still cannot meet the exponentially-growing bandwidth demand of the Internet. Space-division multiplexing (SDM) has attracted considerable attention in recent years due to its potential to address this capacity crunch. In SDM, the transmission channels support more than one spatial mode, each of which can provide the same capacity as a single-mode fiber. To make SDM practical, crosstalk among modes must be effectively managed. This dissertation presents three techniques for crosstalk management for SDM. In some cases such as intra-datacenter interconnects, even though mode crosstalk cannot be completely avoided, crosstalk among mode groups can be suppressed in properly-designed few-mode fibers to support mode group-multiplexed transmission. However, in most cases, mode coupling is unavoidable. In free-space optical (FSO) communication, mode coupling due to turbulence manifests as wavefront distortions. Since there is almost no modal dispersion in FSO, we demonstrate the use of few-mode pre-amplified receivers to mitigate the effect of turbulence without using adaptive optics. In fiber-optic communication, multi-mode fibers or long-haul few-mode fibers not only suffer from mode crosstalk but also large modal dispersion, which can only be compensated electronically using multiple-input-multiple-output (MIMO) digital signal processing (DSP). In this case, we take the counterintuitive approach of introducing strong mode coupling to reduce modal group delay and DSP complexity.

Metal halide perovskites (simplified as perovskites as below), particularly those in nanocrystal forms, have recently emerged as highly efficient, bandgap tunable photonics materials that can be easily solution processed at low cost for display, lighting or other energy conversion applications. However, the quick degradation of perovskite nanocrystals under external stresses or upon colloidal aggregations has been a major challenge for most applications where high reliability is normally required. In this thesis, we have explored a polymer swelling-deswelling microencapsulation (SDM) process that enables the dispersion, in-situ crystallization and subsequent surface passivation of perovskite nanocrystals in polymer matrices, and leads to ultrastable metal halide perovskites - polymer composites (PPCs) with outstanding optical properties for various efficient and highly reliable photonics applications. In chapter two, we have proved the SDM concept by synthesizing green emitting CH3NH3PbBr3 PPCs with high photoluminescence (PL) efficiency and pure color emission, which can survive boiling water treatment for 30 min with less than 7% PL efficiency decay. In the third chapter, we extend the SDM principle to inorganic perovskites and synthesized CsPbBr3 nanorods in a polymer matrix (NRs-PM), which show polarized emission due to dielectric contrast and anisotropic shape. The NRs-PM can be aligned in macroscale through mechanical stretching at elevated temperature. In chapter four, we demonstrate that with ligand assisted SDM, PPCs of various emitting colors ranging from blue to near-infrared can be obtained, and high efficiency ( > 70%) can be achieved for PPCs of a wide range of optical density (0.05 to 0.78) without concentration quenching. The high efficiency, wide tunability and outstanding stability of these SDM-derived PPCs could enable a broad range of photonics applications. In chapter five, we propose to use a hybrid downconverter system comprising green PPC films and state-of-the-art red emitting downconverters for LCD backlight to realize wide color gamut. Beyond conventional displays, in chapter six, we introduce three novel applications that may be enabled by PPCs: 1) Tailored lighting that can provide delicate spectral control, 2) Highly transparent emissive projection display with high ambient contrast, low haze level and wide viewing angle, and 3) X-ray scintillators with high resolution and fast response.

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.