A small perturbation theory for cycloidal propellers

A hydromechanical theory is developed for cycloidal propellers for two limiting modes of operation wherein U » ΩR and U « ΩR, with U the rectilinear propeller speed (speed of advance) and ΩR the rotational blade speed. A first order theory is developed from the basic principles of the kinematics and dynamics of fluid motion and proceeds from the point of view of unsteady hydrofoil theory.

Explicit expressions for the instantaneous forces and moments produced by blade motions are presented. On the basis of these results an optimization procedure is carried out which minimizes the energy loss under the constraint of specified mean thrust. Under optimal conditions the propeller is found to possess high Froude efficiencies in both the high and low speed modes of propulsion. This efficiency is defined as the ratio of the average useful work obtained during one cycle of propeller operation to the average power input required to sustain the motion of the propeller during the cycle.

Scalable Methods for Deterministic Integration of Quantum Emitters in Photonic Crystal Cavities

We investigated four unique methods for achieving scalable, deterministic integration of quantum emitters into ultra-high Q{V photonic crystal cavities, including selective area heteroepitaxy, engineered photoemission from silicon nanostructures, wafer bonding and dimensional reduction of III-V quantum wells, and cavity-enhanced optical trapping. In these areas, we were able to demonstrate site-selective heteroepitaxy, size-tunable photoluminescence from silicon nanostructures, Purcell modification of QW emission spectra, and limits of cavity-enhanced optical trapping designs which exceed any reports in the literature and suggest the feasibility of capturing- and detecting nanostructures with dimensions below 10 nm. In addition to process scalability and the requirement for achieving accurate spectral- and spatial overlap between the emitter and cavity, these techniques paid specific attention to the ability to separate the cavity and emitter material systems in order to allow optimal selection of these independently, and eventually enable monolithic integration with other photonic and electronic circuitry.

We also developed an analytic photonic crystal design process yielding optimized cavity tapers with minimal computational effort, and reported on a general cavity modification which exhibits improved fabrication tolerance by relying exclusively on positional- rather than dimensional tapering. We compared several experimental coupling techniques for device characterization. Significant efforts were devoted to optimizing cavity fabrication, including the use of atomic layer deposition to improve surface quality, exploration into factors affecting the design fracturing, and automated analysis of SEM images. Using optimized fabrication procedures, we experimentally demonstrated 1D photonic crystal nanobeam cavities exhibiting the highest Q/V reported on substrate. Finally, we analyzed the bistable behavior of the devices to quantify the nonlinear optical response of our cavities.

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.

Structural and Biophysical Characterization of Variants of the Mechanosensitive Channel of Large Conductance (MSCL)

The ability to sense mechanical force is vital to all organisms to interact with and respond to stimuli in their environment. Mechanosensation is critical to many physiological functions such as the senses of hearing and touch in animals, gravitropism in plants and osmoregulation in bacteria. Of these processes, the best understood at the molecular level involve bacterial mechanosensitive channels. Under hypo-osmotic stress, bacteria are able to alleviate turgor pressure through mechanosensitive channels that gate directly in response to tension in the membrane lipid bilayer. A key participant in this response is the mechanosensitive channel of large conductance (MscL), a non-selective channel with a high conductance of ~3 nS that gates at tensions close to the membrane lytic tension.

It has been appreciated since the original discovery by C. Kung that the small subunit size (~130 to 160 residues) and the high conductance necessitate that MscL forms a homo-oligomeric channel. Over the past 20 years of study, the proposed oligomeric state of MscL has ranged from monomer to hexamer. Oligomeric state has been shown to vary between MscL homologues and is influenced by lipid/detergent environment. In this thesis, we report the creation of a chimera library to systematically survey the correlation between MscL sequence and oligomeric state to identify the sequence determinants of oligomeric state. Our results demonstrate that although there is no combination of sequences uniquely associated with a given oligomeric state (or mixture of oligomeric states), there are significant correlations. In the quest to characterize the oligomeric state of MscL, an exciting discovery was made about the dynamic nature of the MscL complex. We found that in detergent solution, under mild heating conditions (37 °C – 60 °C), subunits of MscL can exchange between complexes, and the dynamics of this process are sensitive to the protein sequence.

Extensive efforts were made to produce high diffraction quality crystals of MscL for the determination of a high resolution X-ray crystal structure of a full length channel. The surface entropy reduction strategy was applied to the design of S. aureus MscL variants and while the strategy appears to have improved the crystallizability of S. aureus MscL, unfortunately the diffraction qualities of these crystals were not significantly improved. MscL chimeras were also screened for crystallization in various solubilization detergents, but also failed to yield high quality crystals.

MscL is a fascinating protein and continues to serve as a model system for the study of the structural and functional properties of mechanosensitive channels. Further characterization of the MscL chimera library will offer more insight into the characteristics of the channel. Of particular interest are the functional characterization of the chimeras and the exploration of the physiological relevance of intercomplex subunit exchange.

Optimum linear coding for additive noise systems using information feedback

The feedback coding problem for Gaussian systems in which the noise is neither white nor statistically independent between channels is formulated in terms of arbitrary linear codes at the transmitter and at the receiver. This new formulation is used to determine a number of feedback communication systems. In particular, the optimum linear code that satisfies an average power constraint on the transmitted signals is derived for a system with noiseless feedback and forward noise of arbitrary covariance. The noisy feedback problem is considered and signal sets for the forward and feedback channels are obtained with an average power constraint on each. The general formulation and results are valid for non-Gaussian systems in which the second order statistics are known, the results being applicable to the determination of error bounds via the Chebychev inequality.

Feedback communication using orthogonal signals

This research is concerned with block coding for a feedback communication system in which the forward and feedback channels are independently disturbed by additive white Gaussian noise and average power constrained. Two coding schemes are proposed in which the messages to be coded for transmission over the forward channel are realized as a set of orthogonal waveforms. A finite number of forward and feedback transmissions (iterations) per message is made. Information received over the feedback channel is used to modify the waveform transmitted on successive forward iterations in such a way that the expected value of forward signal energy is zero on all iterations after the first. Similarly, information is sent over the feedback channel in such a way that the expected value of feedback signal energy is also zero on all iterations after the first. These schemes are shown to achieve a lower probability of error than the best one-way coding scheme at all rates up to the forward channel capacity, provided only that the feedback channel capacity be greater than the forward channel capacity. These schemes make more efficient use of the available feedback power than existing feedback coding schemes, and therefore require less feedback power to achieve a given error performance.