<p>Imaging distant objects at a high resolution has always presented a challenge due to the diffraction limit. Larger apertures improve the resolution, but at some point the cost of engineering, building, and correcting phase aberrations of large apertures become prohibitive. Interferometric imaging uses the Van Cittert-Zernike theorem to form an image from measurements of spatial coherence. This effectively allows the synthesis of a large aperture from two or more smaller telescopes to improve the resolution. We apply this method to imaging geosynchronous satellites with a ground-based system. Imaging a dim object from the ground presents unique challenges. The atmosphere creates errors in the phase measurements. The measurements are taken simultaneously across a large bandwidth of light. The atmospheric piston error, therefore, manifests as a linear phase error across the spectral measurements. Because the objects are faint, many of the measurements are expected to have a poor signal-to-noise ratio (SNR). This eliminates possibility of use of commonly used techniques like closure phase, which is a standard technique in astronomical interferometric imaging for making partial phase measurements in the presence of atmospheric error. The bulk of our work has been focused on forming an image, using sub-Nyquist sampled data, in the presence of these linear phase errors without relying on closure phase techniques. We present an image reconstruction algorithm that successfully forms an image in the presence of these linear phase errors. We demonstrate our algorithm?s success in both simulation and in laboratory experiments.

The quantum nature of light at the single photon level allows for unique applications that classical physics neither predicts nor describes. Most notably, appropriate conditions may cause the states of photons with indistinguishable properties to become entangled, enabling novel approaches to quantum computation, secure communications, and metrology. Any operational quantum information network transporting entangled-photon states must establish a high-fidelity link between its distant nodes despite the inherent fragility of entangled states. However, the lack of a universal operating wavelength for all optical devices makes this a substantial challenge. Telecommunication fibers, entangled photon pair sources, quantum optical memories, and quantum repeaters all function in disparate spectral windows dictated by the properties of the materials used to fabricate them. Quantum frequency conversion (QFC), the single-photon limit of nonlinear parametric sum and difference frequency generation in optics, offers a bridge between spectral regions with full preservation of quantum state character, including entanglement. Periodically poled optical waveguides in ferroelectric crystals are versatile tools in nonlinear optics. Confining the nonlinear interaction to a waveguide greatly enhances its efficiency compared to bulk optics. Periodic poling, the process of periodically inverting the domains of a ferroelectric medium using a strong electric field, enables a variety of quasi-phase matching configurations to engineer a desired nonlinear interaction. This work concentrates on the design, development, fabrication, and characterization of a titanium-diffused periodically poled lithium niobate (Ti:PPLN) waveguide device. This device is designed to execute single-step quantum frequency conversion from 369.5nm to 1550nm in order to facilitate a quantum state transfer between standard fiber telecommunication wavelengths and an atomic quantum memory system employing trapped ytterbium ions. The creation of phase matching conditions for such an extreme distance in frequency demands precise control of high magnitude electric fields on the single-micron scale. As the first demonstration of its kind in Ti:PPLN, the development of these devices included novel improvements to existing fabrication methods, improving the state-of-the-art of precision, quality, and yield for poling of ferroelectric crystals.

Optical microscopy is an indispensable tool in biomedical laboratories since it is minimum invasive and can provide high spatiotemporal resolution when imaging biological tissues and organisms. However, recent advancements in biological and neurological sciences impose new challenges on optical microscopes, where one wants to image over extended volumes at high speeds, or deep inside scattering tissues. Conventional wide-field fluorescence microscopy (WFM) is able to image a 2D field-of-view at high speeds, but suffers from degrading contrast due to out-of-focus fluorescence. Two-photon microscopy can image deep inside scattering tissue compared to WFM, but the maximum attainable penetration depth is still limited by signal contrast. The presence of tissue scattering also incurs inaccuracy in point spread function (PSF) estimation, which is critical in deconvolution microscopy for contrast enhancement. In chapter 2 we describe a widefield-based extended depth-of-field (EDOF) fluorescence microscopy for high-speed high-contrast volumetric imaging. The system makes use of a digital micromirror device (DMD) to target illumination only on in-focus sample features within the imaging volume, significantly reducing the out-of-focus fluorescent background that plagues the typical widefield, and particularly EDOF, microscopes. This technique greatly enhances the image contrast and signal-to-noise ratio, while reducing the light dosage delivered to the sample. Image quality is further improved by the application of a robust deconvolution algorithm. These advantages are demonstrated for in vivo calcium imaging in the mouse brain. In chapter 3 we describe a variant of two-photon microscopy for high contrast imaging in deep tissue. The technique is based on the previously proposed differential aberration imaging (DAI) strategy where image contrast is enhanced by subtracting an aberrated image from an unaberrated one. This technique, though simple and effective, compromises imaging speed because two images must be taken sequentially. A new strategy for two-photon DAI based on near-instantaneous temporal multiplexing is proposed here, enabling high-speed imaging with pixel rates limited only by fluorescence lifetime and laser repetition rate. It can be implemented with standard two-photon microscopes since it does not require active optical elements and it is based on a synchronized sampling strategy that does not require specialized hardware. The resultant contrast improvement is demonstrated by imaging fluorescently-labeled mouse brain at video-rate. In chapter 4 we describe a theoretical model for imaging fluorescent objects embedded inside scattering medium. The model provides a simple analytical solution for estimating PSF within the forward scattering limit, which can be used for contrast improvement in deconvolution microscopy. We verify the results using Monte Carlo simulation. We also apply the model to a partitioned aperture detection system, demonstrate both theoretically and experimentally that one can use strongly scattered light for quantitative 3D localization of fluorescent objects in scattering medium with micrometer-level precision, up to the depth approaching transport mean free path.

Multiphoton microscopy has become an extremely valuable tool for peering deeply into thick, scattering media such as biological tissue. However, the traditional multiphoton beam-scanning approach is held back because only one thin plane is observed at a time. The reverberation loop elegantly overcomes this limitation by generating an infinite series of foci at depths spanning the sample, all sampled individually but near-simultaneously. With the inclusion of some additional interleave steps, it is possible to quickly scan a sample at video rates – allowing volumetric imaging at or near the rate one would traditionally image planes. In neural imaging, this enables a reverberation multiphoton microscope to simultaneously monitor relationships in neuronal activity not only horizontally across samples, but vertically across many layers of the brain. In imaging of engineered cardiac tissues, this enables high resolution observation of three-dimensional structures in a live sample, even as it actively beats and moves.

Multi-photon fluorescence microscopy has become a primary tool for high-resolution deep tissue imaging because of its sensitivity to ballistic excitation photons in comparison to scattered excitation photons. The imaging depth of multi-photon microscopes in tissue imaging is limited primarily by background fluorescence that is generated by scattered light due to the random fluctuations in refractive index inside the media, and by reduced intensity in the ballistic focal volume due to aberrations within the tissue and at its interface. We built two multi-photon adaptive optics (AO) correction systems, one for combating scattering and aberration problems, and another for compensating interface aberrations. For scattering correction a MEMS segmented deformable mirror (SDM) was inserted at a plane conjugate to the objective back-pupil plane. The SDM can pre-compensate for light scattering by coherent combination of the scattered light to make an apparent focus even at a depths where negligible ballistic light remains (i.e. ballistic limit). This problem was approached by investigating the spatial and temporal focusing characteristics of a broad-band light source through strongly scattering media. A new model was developed for coherent focus enhancement through or inside the strongly media based on the initial speckle contrast. A layer of fluorescent beads under a mouse skull was imaged using an iterative coherent beam control method in the prototype two-photon microscope to demonstrate the technique. We also adapted an AO correction system to an existing in three-photon microscope in a collaborator lab at Cornell University. In the second AO correction approach a continuous deformable mirror (CDM) is placed at a plane conjugate to the plane of an interface aberration. We demonstrated that this “Conjugate AO” technique yields a large field-of-view (FOV) advantage in comparison to Pupil AO. Further, we showed that the extended FOV in conjugate AO is maintained over a relatively large axial misalignment of the conjugate planes of the CDM and the aberrating interface. This dissertation advances the field of microscopy by providing new models and techniques for imaging deeply within strongly scattering tissue, and by describing new adaptive optics approaches to extending imaging FOV due to sample aberrations.

Brillouin scattering is a nonlinear optical process via which light waves or photons scatter from density fluctuations or acoustic phonons in a medium to generate new optical fields. At sufficient optical intensities, the incident and scattered optical fields interfere to generate density fields, such that the acoustic and scattered light fields reinforce each other’s growth, thereby resulting in stimulated Brillouin scattering (SBS). The scattered light due to SBS is typically frequency-downshifted or Stokes-shifted in the counter-propagating direction to the incident light, due to the linear momentum and energy conservation requirements between light and the available acoustic phonons in most media. SBS is of both fundamental and technological importance since on one hand, it sheds light on the light-matter interactions at the quantum level as well as on the mechanical properties of matter, on the other hand, it has found utility in a variety of applications such as distributed sensing, signal processing, beam combination via phase conjugation and optical storage by slowing down light. In addition, SBS is an important consideration for long-haul fiber communication networks as well as high-power single frequency lasers since it can limit the amount of transmitted optical power through a medium. The primary means to tailor SBS interactions till now have involved designing guided-wave and resonator structures to control and alter the waveguiding properties of both light and sound fields, as well as the overlap between them. Such waveguide designs have led to the demonstration of several distinctive properties such as SBS gain suppression, anti-Stokes cooling and forward SBS, to name a few. In this thesis, we show that controlling the angular momentum (AM) of light and sound yields an entirely new toolbox with which to tailor SBS. In light fields, angular momentum can result from helical phase or orbital angular momentum (OAM) as well as from circular polarization or spin angular momentum (SAM), whereas in sound fields, only OAM exists. OAM states, in particular, have received tremendous attention in the past couple of decades due to the new degree of freedom afforded by the existence of theoretically infinite number of states encoded in their helicity. More recently, interaction between SAM and OAM, termed spin-orbit coupling, which is observed only in confined geometries such as waveguides, has received enormous interest on account of the remarkable phenomena enabled by such interactions, such as optical super-resolution and spin-Hall effects. Here, we demonstrate that SBS of AM-carrying light in waveguides such as optical fibers, where light experiences the above-mentioned spin-orbit coupling, results in unique acousto-optic interactions. For light fields with the same helical charge; hence the same effective area that usually controls the strength of the nonlinear interaction, we show that different combinations of the signs of OAM and SAM results in dramatically different behavior due to the requirement to conserve angular momentum. The SBS gain can be lowered by almost a factor of 2 just by the aforementioned choice of OAM and SAM combinations, yielding an alternate means of scaling power of fiber lasers. Alternatively, high-degree spatial phase conjugation is observed for unaberrated coherent optical fields for the first time. This is realized via a fundamentally new mechanism of polarization-mediated angular momentum selectivity, unlocking potential applications in aberration correction in vortex lasers, optical trapping and manipulation of microscopic particles as well as signal processing. Finally, we observe that OAM and SAM control results in the efficient generation of record high (order ~22) OAM acoustic vortices, which, by itself, would usher applications in high-density acoustic communications and acoustic rheology

In the last decade, metalenses have become an increasingly popular topic of research, partly due to their ability to reduce the physical space that would otherwise by occupied by traditional lenses, thereby reducing the length of the optical system. However, metalenses do not reduce the largest contributor to optical system length: the propagation of the light between optical elements. We present a novel optic, which we call a “spaceplate,” that can replicate propagation distance of light greater than its thickness, without changing the magnification. We demonstrate the capabilities of spaceplates via proof of concept experiments that use two distinct types of spaceplate; the “low-index” spaceplate is based on Snell’s Law, while the “uniaxial” spaceplate utilizes the anisotropy of birefringent crystals. The 11 mm thick low-index spaceplate reduced light propagation by (4.7 ± 0.2) mm and the 15 mm thick uniaxial spaceplate reduced light propagation by (1.2 ± 0.2) mm. Future spaceplates, especially in conjunction with metalenses, could vastly decrease the length of optical systems, including imaging systems like cameras, and has the potential to make such systems monolithic.

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Recent burgeoning machine learning has revolutionized our ways of looking at the world. Being extraordinarily good at pattern recognition, machine learning has been widely applied to many fields to solve challenging problems. This dissertation demonstrates the applications of machine learning on scanning-free fiber-optic imaging systems (FOISs), and on the design of anti-resonant fibers. In the first part, we propose a semi-supervised learning framework called the adaptive inverse mapping (AIP) to stabilize the imaging performance through multimode fibers (MMFs). We show that if the state of the MMF is traced closely, the output images can be used as probes to correct the image reconstruction inverse mapping. Robustness is increased through the AIP method but still quite limited by the intrinsic sensitivity of the MMFs to perturbations. To further increase the robustness and the image quality of FOISs, we investigate an alternative optical fiber called glass-air Anderson localizing optical fibers (GALOFs), where randomness is intentionally introduced in the fiber cross-section. Enabled by the transverse Anderson localization (TAL), the modes in the GALOF are well confined, robust and wavelength-independent. We illustrate robust full-color cellular high-fidelity imaging through the GALOF with unsupervised learning. In the second part, I demonstrate the use of reinforcement learning in capillary structure design in hollow-core anti-resonant fibers (HC-ARFs). Moreover, inspired by the loss and dispersion spectra of the HC-ARFs, we propose a solid-core anti-resonant fiber (SC-ARF) design for fiber lasers at 2 microns. Power upscaling for fiber lasers at 2 microns requires a novel design of an all-solid active fiber that operates in the normal dispersion regime by compensating the material dispersion with the waveguide dispersion, while achieves a large mode area, low losses, single mode operations and robustness. We utilize a genetic algorithm (GA) to optimize the design parameters of the SC-ARF in terms of these multiple objectives.