Bragg diffraction is a natural phenomenon that arises from the coherent interference of scattered waves in multilayer structures with a well-defined periodicity. In practice, the physical size of these multilayer structures varies depending on the intended application, from micrometer-thick dielectric mirrors with tens of layers to centimeter-long Bragg gratings with ten-thousands of layers. The scope of this work centers around a unique class of multilayer elements developed in bulk photo-thermo-refractive (PTR) glass – the volume Bragg grating (VBG). The content of this thesis places an emphasis on the volume nature of these Bragg devices, implying a three-dimensional structure whereupon arbitrary spatial phase information can be embedded for laser-beam shaping, or the distribution of Bragg periods across each element is instead engineered to yield diffracted light with distinct spatio-temporal properties. In Chapter 1, operating principles, and fabrication technique of a conventional VBG are introduced. Owning to the principles of Bragg diffraction, the desired spatial and/or spectral phase information can be encoded onto the interference of scattered waves, reflecting from different sections along a grating volume. In Chapter 2, this principle is implemented in the form of phase-shifted volume Bragg gratings, whereby desired phase information is holographically engineered into the relative shift between neighboring Bragg substructures. Unlike other known active or passive phase-shaping tools, these phase-shifted elements can reconstruct the encoded phase profiles over a broad range of wavelengths that meet the Bragg condition of the VBG. On the other hand, the chirped volume Bragg grating, identified by a unique variation in grating periods across its volume, presents an alternative mean upon which phase information can be encoded – i.e., the Bragg-period distribution. Gratings of this kind are addressed in detail through Chapter 3. Due to the adaptability of holographic technique employed for the fabrication of volume gratings, a new class of Bragg elements is explored, capable of inscribing phase information into both (1) the relative shift among local Bragg elements, and (2) the Bragg-period variation across the grating volume. Chapter 4 reports on the construction of these hybrid structures, referred to as the phase-shifted, chirped volume Bragg gratings. Their unique ability to double as distributed feedback lasers, when recorded into the optically active volume of doped PTR glass, is discussed, paving the way for a novel source of light – the chirped, distributed feedback laser.

Infrared (IR) imaging has been a widely used method for chemical imaging of a variety of samples. Traditional infrared imaging method that is directly measuring IR absorption such as Fourier transform infrared (FTIR) microscopy has limited resolution due to the intrinsic long wavelength of the IR beam. Atomic force microscope-infrared (AFM-IR) spectroscopy was developed to break the IR diffraction-limited resolution of FTIR. However, it has limited speed and is only applicable for dry and flat samples. In recent years, mid-infrared photothermal (MIP) microscopy was invented to overcome the limitations of FTIR and AFM-IR. The first developed point-scanning-based MIP achieved sub-micron resolution and depth-resolved IR imaging of live biological samples. Later, wide-field-based MIP schemes were developed and dramatically improved the imaging speed of MIP. In Chapter One, this dissertation introduces the MIP development background and the MIP signal formation mechanism for general samples. In Chapters Two, Three, and Four, this dissertation further developed wide-field MIP and achieved optimal detection of three different specific types of samples by three different methodologies, which are described as follows. (1) Chapter Two, bond-selective interferometric scattering microscopy. (2) Chapter Three, back-ground suppressed high-throughput mid-infrared photothermal microscopy via pupil engineering. (3) Chapter Four, bond-selective full-field optical coherence tomography. In Chapter Five, this dissertation summarizes the work and provides an outlook of future work on video-rate bond-selective intensity diffraction tomography. In the first methodology, we describe a bond-selective interferometric scattering microscope where the mid-IR induced photothermal signal is detected by a visible beam in a wide-field common-path interferometry configuration. Single-particle interferometric reflectance imaging sensor (SP-IRIS) has been a very promising technology for highly sensitive label-free imaging of a broad spectrum of biological nanoparticles from proteins to viruses in a high-throughput manner. Although it can reveal the specimen's size and shape information, the chemical composition is inaccessible in interferometric measurements. IR spectroscopic imaging provides chemical specificity based on inherent chemical bond vibrations of specimens but lacks the ability to image and resolve individual nanoparticles due to long IR wavelengths. Here, a bond-selective interferometric scattering microscope is achieved by detecting the mid-IR-induced photothermal modulation of a visible beam in a wide-field common-path interferometry configuration. A thin film layered substrate is utilized to reduce the reflected light and provide a reference field for the interferometric detection of the weakly scattered field. A pulsed mid-IR laser is employed to modulate the interferometric signal. Subsequent demodulation via a virtual lock-in camera offers simultaneous chemical information about tens of micro- or nano-particles. The chemical contrast arises from a minute change in the particle's scattered field as a consequence of the vibrational absorption at the target molecule. We characterize the system with sub-wavelength polymer beads and highlight biological applications by chemically imaging several microorganisms including Staphylococcus aureus, Escherichia coli, and Candida albicans. A theoretical framework is established to extend bond-selective interferometric scattering microscopy to a broad range of biological micro- and nano-particles. In the second methodology, we demonstrate a back-ground suppressed high-throughput mid-infrared photothermal microscopy via pupil engineering. MIP microscopy has been a promising label-free chemical imaging technique for functional characterization of specimens owing to its enhanced spatial resolution and high specificity. Recently developed wide-field MIP imaging modalities have drastically improved speed and enabled high-throughput imaging of micron-scale subjects. However, the weakly scattered signal from subwavelength particles becomes indistinguishable from the shot-noise as a consequence of the strong background light, leading to limited sensitivity. Here, we demonstrate background-suppressed chemical fingerprinting at a single nanoparticle level by selectively attenuating the reflected light through pupil engineering in the collection path. Our technique provides over 3 orders of magnitude background suppression by quasi-darkfield illumination in the epi-configuration without sacrificing lateral resolution. We demonstrate 6-fold signal-to-background noise ratio improvement, allowing for simultaneous detection and discrimination of hundreds of nanoparticles across a field of view of 70 μm × 70 μm. A comprehensive theoretical framework for photothermal image formation is provided and experimentally validated with 300 and 500 nm PMMA beads. The versatility and utility of our technique are demonstrated via hyperspectral dark-field MIP imaging of S. aureus and E. coli bacteria and MIP imaging of subcellular lipid droplets inside C. albicans and cancer cells. In the third methodology, we present a bond-selective full-field optical coherence tomography. Optical coherence tomography (OCT) is a label-free, non-invasive 3D imaging tool widely used in both biological research and clinical diagnosis. Conventional OCT modalities can only visualize specimen tomography without chemical information. Here, we report a bond-selective full-field OCT (BS-FF-OCT), in which a pulsed mid-infrared laser is used to modulate the OCT signal through the photothermal effect, achieving label-free bond-selective 3D sectioned imaging of highly scattering samples. We first demonstrate BS-FF-OCT imaging of 1 µm PMMA beads embedded in agarose gel. Next, we show 3D hyperspectral imaging of up to 75 µm of polypropylene fiber mattress from a standard surgical mask. We then demonstrate BS-FF-OCT imaging on biological samples, including cancer cell spheroids and C. elegans. Using an alternative pulse timing configuration, we finally demonstrate the capability of BS-FF-OCT on imaging a highly scattering myelinated axons region in a mouse brain tissue slice.

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Recent advancements in flat-optics, metamaterials research, and integrated optical devices have established the need for more efficient, spectrally tunable, and Si-compatible optical media and nanostructures with designed linear/nonlinear responses that can enable high-density integration of ultrafast photonic-plasmonic functionalities on the chip. Traditional methodologies for nanoscale photon manipulation utilize lossy materials, such as noble metals, which lack significant optical tunablility and compatibility with complementary metal-oxide-semiconductor technologies. In this dissertation, we propose, develop, and characterize alternative plasmonic materials that overcome these limitations while providing novel opportunities for significant optical nonlinear enhancement. Specifically, we investigate the plasmonic resonant regime and the nonlinear optical responses of Si- and O2- doped titanium nitride, SiO2- doped indium oxide, and Sn-doped indium oxide with engineered structural and optical dispersion behavior. We study a number of novel passive metaphotonic devices that leverage refractive index control in low-loss materials for near-field engineering and nanoscale nonlinear optical enhancement. Moreover, we integrate the developed alternative plasmonic materials into active metaphotonic surfaces for electro-optical modulation, enhanced light absorption, and ultrafast photon detection. Furthermore, utilizing the double-beam accurate Z-scan technique, we characterize the intrinsic nonlinear susceptibility χ(3) of optical nanolayers with epsilon-near-zero behavior as a function of their microstructural properties that we largely control by post-deposition annealing. A main objective of this work is to establish robust structure-property relationships for the control of optical dispersion, Kerr nonlinearity, and near-field resonances that extend from the visible to the infrared. This work substantially expands and diversifies the reach of plasmonics, flat-optics, and nonlinear optics across multiple spectral regions within scalable and Si-compatible novel material platforms.

Scientists have long recognized the importance of modes in describing and utilizing the intricate properties of light, as modes are characterized by coherence and orthogonality. Any of the spatial, temporal, frequency, or polarization modes is considered an individual quantum degree of freedom (DoF). Building upon previous innovations, we introduce new perspectives on utilizing modes in the characterization of random media, LiDARs, and photonic processing units. First, we address wavefront distortions of light propagating through random media. We propose to characterize the transfer matrix of coupled multimode transmission channels by representing the wavefronts as superpositions of spatial modes and deploying naturally occurring Rayleigh scattering properties. Our method is beneficial for many applications such as imaging (e.g., endoscopy) and focusing inside random media where the distal end of the optical channel is inaccessible or non-cooperative. Although coherent distributed channel characterization can provide a powerful platform for LiDARs, the applications of spatial and frequency modes in improving LiDAR precision and measurement range will not stop here. We show that using a few-mode local oscillator (LO) with spatial modes at different frequencies at the receiver can significantly enhance the LiDAR detection range. The required signal-to-noise ratio (SNR) for the frequency-modulated continuous wave (FMCW) LiDAR decreases with the number of LO modes. In the few-mode frequency modulated receiver, every spatial mode contributes to the signal detection as an individual element resulting in an improved LiDAR performance by parallelizing the process. In general, optics is scalable and offers many dimensions to parallelize every function. This scalability can also be applied in other applications than LiDARs such as tensor acceleration to escalate the speed and computation power of the photonic processing units. Optics and photonics have great potential to further enhance the performance of neural networks by contributing to three major building blocks of ANNs and deep neural networks (DNNs) including interconnects, matrix multiplication, and nonlinearity. Here, as another application of DoF of light, we demonstrate a photonic tensor accelerator (PTA) based on multidimensional encoding, for the first time. The proposed PTA can perform matrix-vector, matrix-matrix, and batch matrix multiplications in a single clock cycle. The PTA can offer both significantly higher computing power and energy efficiency than state-of-the-art electronic or photonic accelerators.

Multi-plane light conversion (MPLC) has recently been developed as a versatile tool for manipulating spatial distributions of the optical field through repeated phase modulations. An MPLC Device consists of a series of phase masks separated by free-space propagation. It can convert one orthogonal set of beams into another orthogonal set through unitary transformation, which is useful for a number of applications. In telecommunication, for example, mode-division multiplexing (MDM) is a promising technology that will enable continued scaling of capacity by employing spatial modes of a single fiber. MPLC has shown great potential in MDM devices with ultra-wide bandwidth, low insertion loss (IL), low mode-dependent loss (MDL), and low crosstalk. This dissertation presents MPLC devices for (de)multiplexing, coupling, routing, optical signal processing, and wavefront synthesis. First, fundamentals in the design, simulation, and characterization of MPLC devices are introduced. In the area of MPLC devices, a coupler based on MPLC was demonstrated to bridge between few-mode fibers and waveguides. A reconfigurable broadband mode router for multi-port mode-to-space mapping was proposed using the MPLC technique, compatible with existing wavelength division multiplexed (WDM) systems. In the area of MPLC signal processing, an ultrabroadband polarization-insensitive optical 90° hybrid, which is a two-input four-output device, was demonstrated. In the area of system application, we demonstrated the use of a pair of 45-mode MPLC (de)multiplexers and high-sensitivity superconducting nanowire single-photon detectors (SNSPDs) to measure the differential mode group delay (DMDG), distributed mode crosstalk, and cladding modes of a commercial graded-index multimode fiber (GI-MMF). A compact, large-area, non-mode selective MPLC coherent beam combiner using curved mirrors is also presented for high-power wavefront synthesis.