Deep tissue fluorescence imaging with time-reversed light

Advances in optical techniques have enabled many breakthroughs in biology and medicine. However, light scattering by biological tissues remains a great obstacle, restricting the use of optical methods to thin ex vivo sections or superficial layers in vivo. In this thesis, we present two related methods that overcome the optical depth limit—digital time reversal of ultrasound encoded light (digital TRUE) and time reversal of variance-encoded light (TROVE). These two techniques share the same principle of using acousto-optic beacons for time reversal optical focusing within highly scattering media, like biological tissues. Ultrasound, unlike light, is not significantly scattered in soft biological tissues, allowing for ultrasound focusing. In addition, a fraction of the scattered optical wavefront that passes through the ultrasound focus gets frequency-shifted via the acousto-optic effect, essentially creating a virtual source of frequency-shifted light within the tissue. The scattered ultrasound-tagged wavefront can be selectively measured outside the tissue and time-reversed to converge at the location of the ultrasound focus, enabling optical focusing within deep tissues. In digital TRUE, we time reverse ultrasound-tagged light with an optoelectronic time reversal device (the digital optical phase conjugate mirror, DOPC). The use of the DOPC enables high optical gain, allowing for high intensity optical focusing and focal fluorescence imaging in thick tissues at a lateral resolution of 36 µm by 52 µm. The resolution of the TRUE approach is fundamentally limited to that of the wavelength of ultrasound. The ultrasound focus (~ tens of microns wide) usually contains hundreds to thousands of optical modes, such that the scattered wavefront measured is a linear combination of the contributions of all these optical modes. In TROVE, we make use of our ability to digitally record, analyze and manipulate the scattered wavefront to demix the contributions of these spatial modes using variance encoding. In essence, we encode each spatial mode inside the scattering sample with a unique variance, allowing us to computationally derive the time reversal wavefront that corresponds to a single optical mode. In doing so, we uncouple the system resolution from the size of the ultrasound focus, demonstrating optical focusing and imaging between highly diffusing samples at an unprecedented, speckle-scale lateral resolution of ~ 5 µm. Our methods open up the possibility of fully exploiting the prowess and versatility of biomedical optics in deep tissues.

Fluorescence optofluidic microscopy and fluorescence microscopy based on the Talbot effect

Light microscopy has been one of the most common tools in biological research, because of its high resolution and non-invasive nature of the light. Due to its high sensitivity and specificity, fluorescence is one of the most important readout modes of light microscopy. This thesis presents two new fluorescence microscopic imaging techniques: fluorescence optofluidic microscopy and fluorescent Talbot microscopy. The designs of the two systems are fundamentally different from conventional microscopy, which makes compact and portable devices possible. The components of the devices are suitable for mass-production, making the microscopic imaging system more affordable for biological research and clinical diagnostics.

Fluorescence optofluidic microscopy (FOFM) is capable of imaging fluorescent samples in fluid media. The FOFM employs an array of Fresnel zone plates (FZP) to generate an array of focused light spots within a microfluidic channel. As a sample flows through the channel and across the array of focused light spots, a filter-coated CMOS sensor collects the fluorescence emissions. The collected data can then be processed to render a fluorescence microscopic image. The resolution, which is determined by the focused light spot size, is experimentally measured to be 0.65 μm.

Fluorescence Talbot microscopy (FTM) is a fluorescence chip-scale microscopy technique that enables large field-of-view (FOV) and high-resolution imaging. The FTM method utilizes the Talbot effect to project a grid of focused excitation light spots onto the sample. The sample is placed on a filter-coated CMOS sensor chip. The fluorescence emissions associated with each focal spot are collected by the sensor chip and are composed into a sparsely sampled fluorescence image. By raster scanning the Talbot focal spot grid across the sample and collecting a sequence of sparse images, a filled-in high-resolution fluorescence image can be reconstructed. In contrast to a conventional microscope, a collection efficiency, resolution, and FOV are not tied to each other for this technique. The FOV of FTM is directly scalable. Our FTM prototype has demonstrated a resolution of 1.2 μm, and the collection efficiency equivalent to a conventional microscope objective with a 0.70 N.A. The FOV is 3.9 mm × 3.5 mm, which is 100 times larger than that of a 20X/0.40 N.A. conventional microscope objective. Due to its large FOV, high collection efficiency, compactness, and its potential for integration with other on-chip devices, FTM is suitable for diverse applications, such as point-of-care diagnostics, large-scale functional screens, and long-term automated imaging.

Nonlinear optics and wavelength translation via cavity-optomechanics

The field of cavity-optomechanics explores the interaction of light with sound in an ever increasing array of devices. This interaction allows the mechanical system to be both sensed and controlled by the optical system, opening up a wide variety of experiments including the cooling of the mechanical resonator to its quantum mechanical ground state and the squeezing of the optical field upon interaction with the mechanical resonator, to name two.

In this work we explore two very different systems with different types of optomechanical coupling. The first system consists of two microdisk optical resonators stacked on top of each other and separated by a very small slot. The interaction of the disks causes their optical resonance frequencies to be extremely sensitive to the gap between the disks. By careful control of the gap between the disks, the optomechanical coupling can be made to be quadratic to first order which is uncommon in optomechanical systems. With this quadratic coupling the light field is now sensitive to the energy of the mechanical resonator and can directly control the potential energy trapping the mechanical motion. This ability to directly control the spring constant without modifying the energy of the mechanical system, unlike in linear optomechanical coupling, is explored.

Next, the bulk of this thesis deals with a high mechanical frequency optomechanical crystal which is used to coherently convert photons between different frequencies. This is accomplished via the engineered linear optomechanical coupling in these devices. Both classical and quantum systems utilize the interaction of light and matter across a wide range of energies. These systems are often not naturally compatible with one another and require a means of converting photons of dissimilar wavelengths to combine and exploit their different strengths. Here we theoretically propose and experimentally demonstrate coherent wavelength conversion of optical photons using photon-phonon translation in a cavity-optomechanical system. For an engineered silicon optomechanical crystal nanocavity supporting a 4 GHz localized phonon mode, optical signals in a 1.5 MHz bandwidth are coherently converted over a 11.2 THz frequency span between one cavity mode at wavelength 1460 nm and a second cavity mode at 1545 nm with a 93% internal (2% external) peak efficiency. The thermal and quantum limiting noise involved in the conversion process is also analyzed and, in terms of an equivalent photon number signal level, are found to correspond to an internal noise level of only 6 and 4 times 10x^-3 quanta, respectively.

We begin by developing the requisite theoretical background to describe the system. A significant amount of time is then spent describing the fabrication of these silicon nanobeams, with an emphasis on understanding the specifics and motivation. The experimental demonstration of wavelength conversion is then described and analyzed. It is determined that the method of getting photons into the cavity and collected from the cavity is a fundamental limiting factor in the overall efficiency. Finally, a new coupling scheme is designed, fabricated, and tested that provides a means of coupling greater than 90% of photons into and out of the cavity, addressing one of the largest obstacles with the initial wavelength conversion experiment.

Cu2O substrates and epitaxial Cu2O/ZnO thin film hetero-structures for solar energy conversion

Future fossil fuel scarcity and environmental degradation have demonstrated the need for renewable, low-carbon sources of energy to power an increasingly industrialized world. Solar energy with its infinite supply makes it an extraordinary resource that should not go unused. However with current materials, adoption is limited by cost and so a paradigm shift must occur to get everyone on the same page embracing solar technology. Cuprous Oxide (Cu2O) is a promising earth abundant material that can be a great alternative to traditional thin-film photovoltaic materials like CIGS, CdTe, etc. We have prepared Cu2O bulk substrates by the thermal oxidation of copper foils as well Cu2O thin films deposited via plasma-assisted Molecular Beam Epitaxy. From preliminary Hall measurements it was determined that Cu2O would need to be doped extrinsically. This was further confirmed by simulations of ZnO/Cu2O heterojunctions. A cyclic interdependence between, defect concentration, minority carrier lifetime, film thickness, and carrier concentration manifests itself a primary reason for why efficiencies greater than 4% has yet to be realized. Our growth methodology for our thin-film heterostructures allow precise control of the number of defects that incorporate into our film during both equilibrium and nonequilibrium growth. We also report process flow/device design/fabrication techniques in order to create a device. A typical device without any optimizations exhibited open-circuit voltages Voc, values in excess 500mV; nearly 18% greater than previous solid state devices.

Catalytic conversion of nitrogen to ammonia by an iron model complex

Threefold symmetric Fe phosphine complexes have been used to model the structural and functional aspects of biological N₂ fixation by nitrogenases. Low-valent bridging Fe-S-Fe complexes in the formal oxidation states Fe(II)Fe(II), Fe(II)/Fe(I), and Fe(I)/Fe(I) have been synthesized which display rich spectroscopic and magnetic behavior. A series of cationic tris-phosphine borane (TPB) ligated Fe complexes have been synthesized and been shown to bind a variety of nitrogenous ligands including N₂H₄, NH₃, and NH₂-. These complexes are all high spin S = 3/2 and display EPR and magnetic characteristics typical of this spin state. Furthermore, a sequential protonation and reduction sequence of a terminal amide results in loss of NH₃ and uptake of N₂. These stoichiometric transformations represent the final steps in potential N₂ fixation schemes.

Treatment of an anionic FeN₂ complex with excess acid also results in the formation of some NH₃, suggesting the possibility of a catalytic cycle for the conversion of N₂ to NH₃ mediated by Fe. Indeed, use of excess acid and reductant results in the formation of seven equivalents of NH₃ per Fe center, demonstrating Fe mediated catalytic N₂ fixation with acids and protons for the first time. Numerous control experiments indicate that this catalysis is likely being mediated by a molecular species.

A number of other phosphine ligated Fe complexes have also been tested for catalysis and suggest that a hemi-labile Fe-B interaction may be critical for catalysis. Additionally, various conditions for the catalysis have been investigated. These studies further support the assignment of a molecular species and delineate some of the conditions required for catalysis.

Finally, combined spectroscopic studies have been performed on a putative intermediate for catalysis. These studies converge on an assignment of this new species as a hydrazido(2-) complex. Such species have been known on group 6 metals for some time, but this represents the first characterization of this ligand on Fe. Further spectroscopic studies suggest that this species is present in catalytic mixtures, which suggests that the first steps of a distal mechanism for N₂ fixation are feasible in this system.

Nanostructured tungsten trioxide photoanodes for solar energy conversion

Nanostructured tungsten trioxide (WO₃) photoelectrodes are potential candidates for the anodic portion of an integrated solar water-splitting device that generates hydrogen fuel and oxygen from water. These nanostructured materials can potentially offer improved performance in photooxidation reactions compared to unstructured materials because of enhancements in light scattering, increases in surface area, and their decoupling of the directions of light absorption and carrier collection. To evaluate the presence of these effects and their contributions toward energy conversion efficiency, a variety of nanostructured WO₃ photoanodes were synthesized by electrodeposition within nanoporous templates and by anodization of tungsten foils. A robust fabrication process was developed for the creation of oriented WO₃ nanorod arrays, which allows for control nanorod diameter and length. Films of nanostructured WO₃ platelets were grown via anodization, the morphology of the films was controlled by the anodization conditions, and the current-voltage performance and spectral response properties of these films were studied. The observed photocurrents were consistent with the apparent morphologies of the nanostructured arrays. Measurements of electrochemically active surface area and other physical characteristics were correlated with observed differences in absorbance, external quantum yield, and photocurrent density for the anodized arrays. The capability to quantify these characteristics and relate them to photoanode performance metrics can allow for selection of appropriate structural parameters when designing photoanodes for solar energy conversion.

Bright-field and fluorescence chip-scale microscopy for biological imaging

Optical microscopy is an essential tool in biological science and one of the gold standards for medical examinations. Miniaturization of microscopes can be a crucial stepping stone towards realizing compact, cost-effective and portable platforms for biomedical research and healthcare. This thesis reports on implementations of bright-field and fluorescence chip-scale microscopes for a variety of biological imaging applications. The term “chip-scale microscopy” refers to lensless imaging techniques realized in the form of mass-producible semiconductor devices, which transforms the fundamental design of optical microscopes.

Our strategy for chip-scale microscopy involves utilization of low-cost Complementary metal Oxide Semiconductor (CMOS) image sensors, computational image processing and micro-fabricated structural components. First, the sub-pixel resolving optofluidic microscope (SROFM), will be presented, which combines microfluidics and pixel super-resolution image reconstruction to perform high-throughput imaging of fluidic samples, such as blood cells. We discuss design parameters and construction of the device, as well as the resulting images and the resolution of the device, which was 0.66 µm at the highest acuity. The potential applications of SROFM for clinical diagnosis of malaria in the resource-limited settings is discussed.

Next, the implementations of ePetri, a self-imaging Petri dish platform with microscopy resolution, are presented. Here, we simply place the sample of interest on the surface of the image sensor and capture the direct shadow images under the illumination. By taking advantage of the inherent motion of the microorganisms, we achieve high resolution (~1 µm) imaging and long term culture of motile microorganisms over ultra large field-of-view (5.7 mm × 4.4 mm) in a specialized ePetri platform. We apply the pixel super-resolution reconstruction to a set of low-resolution shadow images of the microorganisms as they move across the sensing area of an image sensor chip and render an improved resolution image. We perform longitudinal study of Euglena gracilis cultured in an ePetri platform and image based analysis on the motion and morphology of the cells. The ePetri device for imaging non-motile cells are also demonstrated, by using the sweeping illumination of a light emitting diode (LED) matrix for pixel super-resolution reconstruction of sub-pixel shifted shadow images. Using this prototype device, we demonstrate the detection of waterborne parasites for the effective diagnosis of enteric parasite infection in resource-limited settings.

Then, we demonstrate the adaptation of a smartphone’s camera to function as a compact lensless microscope, which uses ambient illumination as its light source and does not require the incorporation of a dedicated light source. The method is also based on the image reconstruction with sweeping illumination technique, where the sequence of images are captured while the user is manually tilting the device around any ambient light source, such as the sun or a lamp. Image acquisition and reconstruction is performed on the device using a custom-built android application, constructing a stand-alone imaging device for field applications. We discuss the construction of the device using a commercial smartphone and demonstrate the imaging capabilities of our system.

Finally, we report on the implementation of fluorescence chip-scale microscope, based on a silo-filter structure fabricated on the pixel array of a CMOS image sensor. The extruded pixel design with metal walls between neighboring pixels successfully guides fluorescence emission through the thick absorptive filter to the photodiode layer of a pixel. Our silo-filter CMOS image sensor prototype achieves 13-µm resolution for fluorescence imaging over a wide field-of-view (4.8 mm × 4.4 mm). Here, we demonstrate bright-field and fluorescence longitudinal imaging of living cells in a compact, low-cost configuration.

Innovations of wide-field optical-sectioning fluorescence microscopy : toward high-speed volumetric bio-imaging with simplicity

Optical microscopy has become an indispensable tool for biological researches since its invention, mostly owing to its sub-cellular spatial resolutions, non-invasiveness, instrumental simplicity, and the intuitive observations it provides. Nonetheless, obtaining reliable, quantitative spatial information from conventional wide-field optical microscopy is not always intuitive as it appears to be. This is because in the acquired images of optical microscopy the information about out-of-focus regions is spatially blurred and mixed with in-focus information. In other words, conventional wide-field optical microscopy transforms the three-dimensional spatial information, or volumetric information about the objects into a two-dimensional form in each acquired image, and therefore distorts the spatial information about the object. Several fluorescence holography-based methods have demonstrated the ability to obtain three-dimensional information about the objects, but these methods generally rely on decomposing stereoscopic visualizations to extract volumetric information and are unable to resolve complex 3-dimensional structures such as a multi-layer sphere.

The concept of optical-sectioning techniques, on the other hand, is to detect only two-dimensional information about an object at each acquisition. Specifically, each image obtained by optical-sectioning techniques contains mainly the information about an optically thin layer inside the object, as if only a thin histological section is being observed at a time. Using such a methodology, obtaining undistorted volumetric information about the object simply requires taking images of the object at sequential depths.

Among existing methods of obtaining volumetric information, the practicability of optical sectioning has made it the most commonly used and most powerful one in biological science. However, when applied to imaging living biological systems, conventional single-point-scanning optical-sectioning techniques often result in certain degrees of photo-damages because of the high focal intensity at the scanning point. In order to overcome such an issue, several wide-field optical-sectioning techniques have been proposed and demonstrated, although not without introducing new limitations and compromises such as low signal-to-background ratios and reduced axial resolutions. As a result, single-point-scanning optical-sectioning techniques remain the most widely used instrumentations for volumetric imaging of living biological systems to date.

In order to develop wide-field optical-sectioning techniques that has equivalent optical performance as single-point-scanning ones, this thesis first introduces the mechanisms and limitations of existing wide-field optical-sectioning techniques, and then brings in our innovations that aim to overcome these limitations. We demonstrate, theoretically and experimentally, that our proposed wide-field optical-sectioning techniques can achieve diffraction-limited optical sectioning, low out-of-focus excitation and high-frame-rate imaging in living biological systems. In addition to such imaging capabilities, our proposed techniques can be instrumentally simple and economic, and are straightforward for implementation on conventional wide-field microscopes. These advantages together show the potential of our innovations to be widely used for high-speed, volumetric fluorescence imaging of living biological systems.

Fluorescence microscopy of nicotinic acetylcholine receptors

Neuronal nicotinic acetylcholine receptors (nAChRs) are pentameric ligand gated ion channels abundantly expressed in the central nervous system. Changes in the assembly and trafficking of nAChRs are pertinent to disease states including nicotine dependence, autosomal dominant nocturnal frontal lobe epilepsy (ADNFLE), and Parkinson’s disease (PD). Here we investigate the application of high resolution fluorescence techniques for the study of nAChR assembly and trafficking. We also describe the construction and validation of a fluorescent α5 subunit and subsequent experiments to elucidate the cellular mechanisms through which α5 subunits are expressed, assembled into mature receptors, and trafficked to the cell surface. The effects of a known single nucleotide polymorphism (D398N) in the intracellular loop of α5 are also examined.

Additionally, this report describes the development of a combined total internal reflection fluorescence (TIRF) and lifetime imaging (FLIM) technique and the first application of this methodology for elucidation of stochiometric composition of nAChRs. Many distinct subunit combinations can form functional receptors. Receptor composition and stoichiometry confers unique biophysical and pharmacological properties to each receptor sub-type. Understanding the nature of assembly and expression of each receptor subtype yields important information about the molecular processes that may underlie the mechanisms through which nAChR contribute to disease and addiction states.

Part I. Efforts directed towards the total synthesis of shionone. Part II. Conversion of estrone to androst-4-EN-3-ONE: a new method for activating the C-9 and C-10 positions of estrogenic steroids for substitution

Part I: An approach to the total synthesis of the triterpene shionone is described, which proceeds through the tetracyclic ketone i. The shionone side chain has been attached to this key intermediate in 5 steps, affording the olefin 2 in 29% yield. A method for the stereo-specific introduction of the angular methyl group at C-5 of shionone has been developed on a model system. The attempted utilization of this method to convert olefin 2 into shionone is described.

Part II: A method has been developed for activating the C-9 and C-10 positions of estrogenic steroids for substitution. Estrone has been converted to 4β,5β-epoxy-10β-hydroxyestr-3-one; cleavage of this epoxyketone using an Eschenmoser procedure, and subsequent modification of the product afforded 4-seco-9-estren-3,5-dione 3-ethylene acetal. This versatile intermediate, suitable for substitution at the 9 and/or 10 position, was converted to androst-4-ene-3-one by known procedures.

Resonance cones and mode conversion in a warm magnetized bounded plasma

The warm plasma resonance cone structure of the quasistatic field produced by a gap source in a bounded magnetized slab plasma is determined theoretically. This is initially determined for a homogeneous or mildly inhomogeneous plasma with source frequency lying between the lower hybrid frequency and the plasma frequency. It is then extended to the complicated case of an inhomogeneous plasma with two internal lower hybrid layers present, which is of interest to radio frequency heating of plasmas.

In the first case, the potential is obtained as a sum of multiply reflected warm plasma resonance cones, each of which has a similar structure, but a different size, amplitude, and position. An important interference between nearby multiply-reflected resonance cones is found. The cones are seen to spread out as they move away from the source, so that this interference increases and the individual resonance cones become obscured far away from the source.

In the second case, the potential is found to be expressible as a sum of multiply-reflected, multiply-tunnelled, and mode converted resonance cones, each of which has a unique but similar structure. The effects of both collisional and collisionless damping are included and their effects on the decay of the cone structure studied. Various properties of the cones such as how they move into and out of the hybrid layers, through the evanescent region, and transform at the hybrid layers are determined. It is found that cones can tunnel through the evanescent layer if the layer is thin, and the effect of the thin evanescent layer is to subdue the secondary maxima of cone relative to the main peak, while slightly broadening the main peak and shifting it closer to the cold plasma cone line.

Energy theorems for quasistatic fields are developed and applied to determine the power flow and absorption along the individual cones. This reveals the points of concentration of the flow and the various absorption mechanisms.

A study of a new electromechanical energy conversion process using superconducting frequency modulated resonators

Experimental demonstrations and theoretical analyses of a new electromechanical energy conversion process which is made feasible only by the unique properties of superconductors are presented in this dissertation. This energy conversion process is characterized by a highly efficient direct energy transformation from microwave energy into mechanical energy or vice versa and can be achieved at high power level. It is an application of a well established physical principle known as the adiabatic theorem (Boltzmann-Ehrenfest theorem) and in this case time dependent superconducting boundaries provide the necessary interface between the microwave energy on one hand and the mechanical work on the other. The mechanism which brings about the conversion is another known phenomenon - the Doppler effect. The resonant frequency of a superconducting resonator undergoes continuous infinitesimal shifts when the resonator boundaries are adiabatically changed in time by an external mechanical mechanism. These small frequency shifts can accumulate coherently over an extended period of time to produce a macroscopic shift when the resonator remains resonantly excited throughout this process. In addition, the electromagnetic energy in s ide the resonator which is proportional to the oscillation frequency is al so accordingly changed so that a direct conversion between electromagnetic and mechanical energies takes place. The intrinsically high efficiency of this process is due to the electromechanical interactions involved in the conversion rather than a process of thermodynamic nature and therefore is not limited by the thermodynamic value.

A highly reentrant superconducting resonator resonating in the range of 90 to 160 MHz was used for demonstrating this new conversion technique. The resonant frequency was mechanically modulated at a rate of two kilohertz. Experimental results showed that the time evolution of the electromagnetic energy inside this frequency modulated (FM) superconducting resonator indeed behaved as predicted and thus demonstrated the unique features of this process. A proposed usage of FM superconducting resonators as electromechanical energy conversion devices is given along with some practical design considerations. This device seems to be very promising in producing high power (~10W/cm^3) microwave energy at 10 - 30 GHz.

Weakly coupled FM resonator system is also analytically studied for its potential applications. This system shows an interesting switching characteristic with which the spatial distribution of microwave energies can be manipulated by external means. It was found that if the modulation was properly applied, a high degree (>95%) of unidirectional energy transfer from one resonator to the other could be accomplished. Applications of this characteristic to fabricate high efficiency energy switching devices and high power microwave pulse generators are also found feasible with present superconducting technology.

Nanofabrication for On-Chip Optical Levitation, Atom-Trapping, and Superconducting Quantum Circuits

Researchers have spent decades refining and improving their methods for fabricating smaller, finer-tuned, higher-quality nanoscale optical elements with the goal of making more sensitive and accurate measurements of the world around them using optics. Quantum optics has been a well-established tool of choice in making these increasingly sensitive measurements which have repeatedly pushed the limits on the accuracy of measurement set forth by quantum mechanics. A recent development in quantum optics has been a creative integration of robust, high-quality, and well-established macroscopic experimental systems with highly-engineerable on-chip nanoscale oscillators fabricated in cleanrooms. However, merging large systems with nanoscale oscillators often require them to have extremely high aspect-ratios, which make them extremely delicate and difficult to fabricate with an "experimentally reasonable" repeatability, yield and high quality. In this work we give an overview of our research, which focused on microscopic oscillators which are coupled with macroscopic optical cavities towards the goal of cooling them to their motional ground state in room temperature environments. The quality factor of a mechanical resonator is an important figure of merit for various sensing applications and observing quantum behavior. We demonstrated a technique for pushing the quality factor of a micromechanical resonator beyond conventional material and fabrication limits by using an optical field to stiffen and trap a particular motional mode of a nanoscale oscillator. Optical forces increase the oscillation frequency by storing most of the mechanical energy in a nearly loss-less optical potential, thereby strongly diluting the effects of material dissipation. By placing a 130 nm thick SiO₂ pendulum in an optical standing wave, we achieve an increase in the pendulum center-of-mass frequency from 6.2 to 145 kHz. The corresponding quality factor increases 50-fold from its intrinsic value to a final value of Q_m = 5.8(1.1) x 10⁵, representing more than an order of magnitude improvement over the conventional limits of SiO₂ for a pendulum geometry. Our technique may enable new opportunities for mechanical sensing and facilitate observations of quantum behavior in this class of mechanical systems. We then give a detailed overview of the techniques used to produce high-aspect-ratio nanostructures with applications in a wide range of quantum optics experiments. The ability to fabricate such nanodevices with high precision opens the door to a vast array of experiments which integrate macroscopic optical setups with lithographically engineered nanodevices. Coupled with atom-trapping experiments in the Kimble Lab, we use these techniques to realize a new waveguide chip designed to address ultra-cold atoms along lithographically patterned nanobeams which have large atom-photon coupling and near 4π Steradian optical access for cooling and trapping atoms. We describe a fully integrated and scalable design where cold atoms are spatially overlapped with the nanostring cavities in order to observe a resonant optical depth of d₀ ≈ 0.15. The nanodevice illuminates new possibilities for integrating atoms into photonic circuits and engineering quantum states of atoms and light on a microscopic scale. We then describe our work with superconducting microwave resonators coupled to a phononic cavity towards the goal of building an integrated device for quantum-limited microwave-to-optical wavelength conversion. We give an overview of our characterizations of several types of substrates for fabricating a low-loss high-frequency electromechanical system. We describe our electromechanical system fabricated on a Si₃N₄ membrane which consists of a 12 GHz superconducting LC resonator coupled capacitively to the high frequency localized modes of a phononic nanobeam. Using our suspended membrane geometry we isolate our system from substrates with significant loss tangents, drastically reducing the parasitic capacitance of our superconducting circuit to ≈ 2.5$ fF. This opens up a number of possibilities in making a new class of low-loss high-frequency electromechanics with relatively large electromechanical coupling. We present our substrate studies, fabrication methods, and device characterization.

Injection Locked Clocking and Transmitter Equalization Techniques for Chip to Chip Interconnects

Semiconductor technology scaling has enabled drastic growth in the computational capacity of integrated circuits (ICs). This constant growth drives an increasing demand for high bandwidth communication between ICs. Electrical channel bandwidth has not been able to keep up with this demand, making I/O link design more challenging. Interconnects which employ optical channels have negligible frequency dependent loss and provide a potential solution to this I/O bandwidth problem. Apart from the type of channel, efficient high-speed communication also relies on generation and distribution of multi-phase, high-speed, and high-quality clock signals. In the multi-gigahertz frequency range, conventional clocking techniques have encountered several design challenges in terms of power consumption, skew and jitter. Injection-locking is a promising technique to address these design challenges for gigahertz clocking. However, its small locking range has been a major contributor in preventing its ubiquitous acceptance.

In the first part of this dissertation we describe a wideband injection locking scheme in an LC oscillator. Phase locked loop (PLL) and injection locking elements are combined symbiotically to achieve wide locking range while retaining the simplicity of the latter. This method does not require a phase frequency detector or a loop filter to achieve phase lock. A mathematical analysis of the system is presented and the expression for new locking range is derived. A locking range of 13.4 GHz–17.2 GHz (25%) and an average jitter tracking bandwidth of up to 400 MHz are measured in a high-Q LC oscillator. This architecture is used to generate quadrature phases from a single clock without any frequency division. It also provides high frequency jitter filtering while retaining the low frequency correlated jitter essential for forwarded clock receivers.

To improve the locking range of an injection locked ring oscillator; QLL (Quadrature locked loop) is introduced. The inherent dynamics of injection locked quadrature ring oscillator are used to improve its locking range from 5% (7-7.4GHz) to 90% (4-11GHz). The QLL is used to generate accurate clock phases for a four channel optical receiver using a forwarded clock at quarter-rate. The QLL drives an injection locked oscillator (ILO) at each channel without any repeaters for local quadrature clock generation. Each local ILO has deskew capability for phase alignment. The optical-receiver uses the inherent frequency to voltage conversion provided by the QLL to dynamically body bias its devices. A wide locking range of the QLL helps to achieve a reliable data-rate of 16-32Gb/s and adaptive body biasing aids in maintaining an ultra-low power consumption of 153pJ/bit.

From the optical receiver we move on to discussing a non-linear equalization technique for a vertical-cavity surface-emitting laser (VCSEL) based optical transmitter, to enable low-power, high-speed optical transmission. A non-linear time domain optical model of the VCSEL is built and evaluated for accuracy. The modelling shows that, while conventional FIR-based pre-emphasis works well for LTI electrical channels, it is not optimum for the non-linear optical frequency response of the VCSEL. Based on the simulations of the model an optimum equalization methodology is derived. The equalization technique is used to achieve a data-rate of 20Gb/s with power efficiency of 0.77pJ/bit.

Investigations of group IVA transition metal mediated carbon-carbon bond forming reactions

Zirconocene aldehyde and ketone complexes were synthesized in high yield by treatment of zirconocene acyl complexes with trimethylaluminum or diisobutylaluminum hydride. These complexes, which are activated by dialkylaluminum chloride ligands, inserted unsaturated substrates such as alkynes, allenes, ethylene, nitriles, ketenes, aldehydes, ketones, lactones, and acid chlorides with moderate to high conversion. Insertion of aldehyde substrates yielded zirconocene diolate complexes with up to 20:1 (anti:syn) diastereoselectivity. The zirconocene diolates were hydrolyzed to afford unsymmetrical 1,2-diols in 40-80% isolated yield. Unsymmetrical ketones gave similar insertion yields with little or no diastereoselectivity. A high yielding one-pot method was developed that coupled carbonyl substrates with zirconocene aldehyde complexes that were derived from olefins by hydrozirconation and carbonylation. The zirconocene aldehyde complexes also inserted carbon monoxide and gave acyloins in 50% yield after hydrolysis.

The insertion reaction of aryl epoxides with the trimethylphoshine adduct of titanocene methylidene was examined. The resulting oxytitanacyclopentanes were carbonylated and oxidatively cleaved with dioxygen to afford y-lactones in moderate yields. Due to the instability and difficult isolation of titanocene methylidene trimethylphoshine adducts, a one-pot method involving the addition of catalytic amounts of trimethylphosphine to β,β-dimethyltitanacyclobutane was developed. A series of disubstituted aryl epoxides were examined which gave mixtures of diastereomeric insertion products. Based on these results, as well as earlier Hammett studies and labeling experiments, a biradical transition state intermediate is proposed. The method is limited to aryl substituted epoxide substrates with aliphatic examples showing no insertion reactivity.

The third study involved the use of magnesium chloride supported titanium catalysts for the Lewis acid catalyzed silyl group transfer condensation of enol silanes with aldehydes. The reaction resulted in silylated aldol products with as many as 140 catalytic turnovers before catalyst inactivation. Low diastereoselectivities favoring the anti-isomer were consistent with an open transition state involving a titanium atom bound to the catalyst surface. The catalysts were also used for the aldol group transfer polymerization of t-butyldimethylsilyloxy-1-ethene resulting in polymers with molecular weights of 5000-31,000 and molar mass dispersities of 1.5-2.8. Attempts to polymerize methylmethacrylate using GTP proved unsuccessful with these catalysts.