Nonlinear optics in planar silica-on-silicon disk resonators

Optical frequency combs (OFCs) provide direct phase-coherent link between optical and RF frequencies, and enable precision measurement of optical frequencies. In recent years, a new class of frequency combs (microcombs) have emerged based on parametric frequency conversions in dielectric microresonators. Micocombs have large line spacing from 10's to 100's GHz, allowing easy access to individual comb lines for arbitrary waveform synthesis. They also provide broadband parametric gain bandwidth, not limited by specific atomic or molecular transitions in conventional OFCs. The emerging applications of microcombs include low noise microwave generation, astronomical spectrograph calibration, direct comb spectroscopy, and high capacity telecommunications.

In this thesis, research is presented starting with the introduction of a new type of chemically etched, planar silica-on-silicon disk resonator. A record Q factor of 875 million is achieved for on-chip devices. A simple and accurate approach to characterize the FSR and dispersion of microcavities is demonstrated. Microresonator-based frequency combs (microcombs) are demonstrated with microwave repetition rate less than 80 GHz on a chip for the first time. Overall low threshold power (as low as 1 mW) of microcombs across a wide range of resonator FSRs from 2.6 to 220 GHz in surface-loss-limited disk resonators is demonstrated. The rich and complex dynamics of microcomb RF noise are studied. High-coherence, RF phase-locking of microcombs is demonstrated where injection locking of the subcomb offset frequencies are observed by pump-detuning-alignment. Moreover, temporal mode locking, featuring subpicosecond pulses from a parametric 22 GHz microcomb, is observed. We further demonstrated a shot-noise-limited white phase noise of microcomb for the first time. Finally, stabilization of the microcomb repetition rate is realized by phase lock loop control.

For another major nonlinear optical application of disk resonators, highly coherent, simulated Brillouin lasers (SBL) on silicon are also demonstrated, with record low Schawlow-Townes noise less than 0.1 Hz^2/Hz for any chip-based lasers and low technical noise comparable to commercial narrow-linewidth fiber lasers. The SBL devices are efficient, featuring more than 90% quantum efficiency and threshold as low as 60 microwatts. Moreover, novel properties of the SBL are studied, including cascaded operation, threshold tuning, and mode-pulling phenomena. Furthermore, high performance microwave generation using on-chip cascaded Brillouin oscillation is demonstrated. It is also robust enough to enable incorporation as the optical voltage-controlled-oscillator in the first demonstration of a photonic-based, microwave frequency synthesizer. Finally, applications of microresonators as frequency reference cavities and low-phase-noise optomechanical oscillators are presented.

A model of the olfactory bulb and beyond

The olfactory bulb of mammals aids in the discrimination of odors. A mathematical model based on the bulbar anatomy and electrophysiology is described. Simulations of the highly non-linear model produce a 35-60 Hz modulated activity, which is coherent across the bulb. The decision states (for the odor information) in this system can be thought of as stable cycles, rather than as point stable states typical of simpler neuro-computing models. Analysis shows that a group of coupled non-linear oscillators are responsible for the oscillatory activities. The output oscillation pattern of the bulb is determined by the odor input. The model provides a framework in which to understand the transformation between odor input and bulbar output to the olfactory cortex. This model can also be extended to other brain areas such as the hippocampus, thalamus, and neocortex, which show oscillatory neural activities. There is significant correspondence between the model behavior and observed electrophysiology.

It has also been suggested that the olfactory bulb, the first processing center after the sensory cells in the olfactory pathway, plays a role in olfactory adaptation, odor sensitivity enhancement by motivation, and other olfactory psychophysical phenomena. The input from the higher olfactory centers to the inhibitory cells in the bulb are shown to be able to modulate the response, and thus the sensitivity, of the bulb to odor input. It follows that the bulb can decrease its sensitivity to a pre-existing and detected odor (adaptation) while remaining sensitive to new odors, or can increase its sensitivity to discover interesting new odors. Other olfactory psychophysical phenomena such as cross-adaptation are also discussed.

Investigation of near-collinear degenerated quasi-phase matching optical parametric amplification using PPKTP crystal

The gain properties of near-collinear degenerated phase-matched optical parametric amplification (OPA) using PPKTP crystal are investigated theoretically. The results indicate that the type-0 phase matching of PPKTP has larger accepted angle and better gain spectrum by tuning crystal temperature or rotating crystal angle.

Investigations of noise and of quantum interference in proximity effect bridges

This work reports investigations upon weakly superconducting proximity effect bridges. These bridges, which exhibit the Josephson effects, are produced by bisecting a superconductor with a short (<1µ) region of material whose superconducting transition temperature is below that of the adjacent superconductors. These bridges are fabricated from layered refractory metal thin films whose transition temperature will depend upon the thickness ratio of the materials involved. The thickness ratio is changed in the area of the bridge to lower its transition temperature. This is done through novel photolithographic techniques described in the text, Chapter 2.

If two such proximity effect bridges are connected in parallel, they form a quantum interferometer. The maximum zero voltage current through this circuit is periodically modulated by the magnetic flux through the circuit. At a constant bias current, the modulation of the critical current produces a modulation in the dc voltage across the bridge. This change in dc voltage has been found to be the result of a change in the internal dissipation in the device. A simple model using lumped circuit theory and treating the bridges as quantum oscillators of frequency ω = 2eV/h, where V is the time average voltage across the device, has been found to adequately describe the observed voltage modulation.

The quantum interferometers have been converted to a galvanometer through the inclusion of an integral thin film current path which couples magnetic flux through the interferometer. Thus a change in signal current produces a change in the voltage across the interferometer at a constant bias current. This work is described in Chapter 3 of the text.

The sensitivity of any device incorporating proximity effect bridges will ultimately be determined by the fluctuations in their electrical parameters. He have measured the spectral power density of the voltage fluctuations in proximity effect bridges using a room temperature electronics and a liquid helium temperature transformer to match the very low (~ 0.1 Ω) impedances characteristic of these devices.

We find the voltage noise to agree quite well with that predicted by phonon noise in the normal conduction through the bridge plus a contribution from the superconducting pair current through the bridge which is proportional to the ratios of this current to the time average voltage across the bridge. The total voltage fluctuations are given by <V^2(f ) > = 4kTR^2_d I/V where R_d is the dynamic resistance, I the total current, and V the voltage across the bridge . An additional noise source appears with a strong 1/f^(n) dependence , 1.5 < n < 2, if the bridges are fabricated upon a glass substrate. This excess noise, attributed to thermodynamic temperature fluctuations in the volume of the bridge, increases dramatically on a glass substrate due to the greatly diminished thermal diffusivity of the glass as compared to sapphire.

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.

An in vitro biomolecular breadboard for prototyping synthetic biological circuits

Biomolecular circuit engineering is critical for implementing complex functions in vivo, and is a baseline method in the synthetic biology space. However, current methods for conducting biomolecular circuit engineering are time-consuming and tedious. A complete design-build-test cycle typically takes weeks' to months' time due to the lack of an intermediary between design ex vivo and testing in vivo. In this work, we explore the development and application of a "biomolecular breadboard" composed of an in-vitro transcription-translation (TX-TL) lysate to rapidly speed up the engineering design-build-test cycle. We first developed protocols for creating and using lysates for conducting biological circuit design. By doing so we simplified the existing technology to an affordable ($0.03/uL) and easy to use three-tube reagent system. We then developed tools to accelerate circuit design by allowing for linear DNA use in lieu of plasmid DNA, and by utilizing principles of modular assembly. This allowed the design-build-test cycle to be reduced to under a business day. We then characterized protein degradation dynamics in the breadboard to aid to implementing complex circuits. Finally, we demonstrated that the breadboard could be applied to engineer complex synthetic circuits in vitro and in vivo. Specifically, we utilized our understanding of linear DNA prototyping, modular assembly, and protein degradation dynamics to characterize the repressilator oscillator and to prototype novel three- and five-node negative feedback oscillators both in vitro and in vivo. We therefore believe the biomolecular breadboard has wide application for acting as an intermediary for biological circuit engineering.

I. Electronic processes in α-sulfur. II. Polaron motion in a D.C. electric field

Part I: The mobilities of photo-generated electrons and holes in orthorhombic sulfur are determined by drift mobility techniques. At room temperature electron mobilities between 0.4 cm²/V-sec and 4.8 cm²/V-sec and hole mobilities of about 5.0 cm²/V-sec are reported. The temperature dependence of the electron mobility is attributed to a level of traps whose effective depth is about 0.12 eV. This value is further supported by both the voltage dependence of the space-charge-limited, D.C. photocurrents and the photocurrent versus photon energy measurements.

As the field is increased from 10 kV/cm to 30 kV/cm a second mechanism for electron transport becomes appreciable and eventually dominates. Evidence that this is due to impurity band conduction at an appreciably lower mobility (4.10^-4 cm²/V-sec) is presented. No low mobility hole current could be detected. When fields exceeding 30 kV/cm for electron transport and 35 kV/cm for hole transport are applied, avalanche phenomena are observed. The results obtained are consistent with recent energy gap studies in sulfur.

The theory of the transport of photo-generated carriers is modified to include the case of appreciable thermos-regeneration from the traps in one transit time.

Part II: An explicit formula for the electric field E necessary to accelerate an electron to a steady-state velocity v in a polarizable crystal at arbitrary temperature is determined via two methods utilizing Feynman Path Integrals. No approximation is made regarding the magnitude of the velocity or the strength of the field. However, the actual electron-lattice Coulombic interaction is approximated by a distribution of harmonic oscillator potentials. One may be able to find the “best possible” distribution of oscillators using a variational principle, but we have not been able to find the expected criterion. However, our result is relatively insensitive to the actual distribution of oscillators used, and our E-v relationship exhibits the physical behavior expected for the polaron. Threshold fields for ejecting the electron for the polaron state are calculated for several substances using numerical results for a simple oscillator distribution.

Entanglement negativity in the harmonic chain out of equilibrium

We study the entanglement in a chain of harmonic oscillators driven out of equilibrium by preparing the two sides of the system at different temperatures, and subsequently joining them together. The steady state is constructed explicitly and the logarithmic negativity is calculated between two adjacent segments of the chain. We find that, for low temperatures, the steady-state entanglement is a sum of contributions pertaining to left-and right-moving excitations emitted from the two reservoirs. In turn, the steady-state entanglement is a simple average of the Gibbs-state values and thus its scaling can be obtained from conformal field theory. A similar averaging behaviour is observed during the entire time evolution. As a particular case, we also discuss a local quench where both sides of the chain are initialized in their respective ground states.

Self-Organized Criticality, Plasticity and Sensorimotor Coupling. Explorations with a Neurorobotic Model in a Behavioural Preference Task

During the last two decades, analysis of 1/f noise in cognitive science has led to a considerable progress in the way we understand the organization of our mental life. However, there is still a lack of specific models providing explanations of how 1/f noise is generated in coupled brain-body-environment systems, since existing models and experiments typically target either externally observable behaviour or isolated neuronal systems but do not address the interplay between neuronal mechanisms and sensorimotor dynamics. We present a conceptual model of a minimal neurorobotic agent solving a behavioural task that makes it possible to relate mechanistic (neurodynamic) and behavioural levels of description. The model consists of a simulated robot controlled by a network of Kuramoto oscillators with homeostatic plasticity and the ability to develop behavioural preferences mediated by sensorimotor patterns. With only three oscillators, this simple model displays self-organized criticality in the form of robust 1/f noise and a wide multifractal spectrum. We show that the emergence of self-organized criticality and 1/f noise in our model is the result of three simultaneous conditions: a) non-linear interaction dynamics capable of generating stable collective patterns, b) internal plastic mechanisms modulating the sensorimotor flows, and c) strong sensorimotor coupling with the environment that induces transient metastable neurodynamic regimes. We carry out a number of experiments to show that both synaptic plasticity and strong sensorimotor coupling play a necessary role, as constituents of self-organized criticality, in the generation of 1/f noise. The experiments also shown to be useful to test the robustness of 1/f scaling comparing the results of different techniques. We finally discuss the role of conceptual models as mediators between nomothetic and mechanistic models and how they can inform future experimental research where self-organized critically includes sensorimotor coupling among the essential interaction-dominant process giving rise to 1/f noise.

110-W fiber laser with homemade double-clad fiber

A high-power ytterbium-doped fiber laser (YDFL) with homemade double-clad fiber (DCF) is introduced in this letter. The geometric parameter and laser characteristics of the fiber have been studied. With one-end-pumping scheme, pumped by a high-power laser diode with launching power of 280 W, a maximum continuous wave (CW) output of 110 W is obtained with an optical-to-optical efficiency of 40%.

Higher order vortex gyrotropic modes in circular ferromagnetic nanodots

Magnetic vortex that consists of an in-plane curling magnetization configuration and a needle-like core region with out-of-plane magnetization is known to be the ground state of geometrically confined submicron soft magnetic elements. Here magnetodynamics of relatively thick (50-100 nm) circular Ni80Fe20 dots were probed by broadband ferromagnetic resonance in the absence of external magnetic field. Spin excitation modes related to the thickness dependent vortex core gyrotropic dynamics were detected experimentally in the gigahertz frequency range. Both analytical theory and micromagnetic simulations revealed that these exchange dominated modes are flexure oscillations of the vortex core string with n = 0,1,2 nodes along the dot thickness. The intensity of the mode with n = 1 depends significantly on both dot thickness and diameter and in some cases is higher than the one of the uniform mode with n = 0. This opens promising perspectives in the area of spin transfer torque oscillators.

7.3 W of single-frequency output power at 2.09 μm from an Ho:YAG monolithic nonplanar ring laser

Single-frequency output power of 7.3 W at 2.09 mu m from a monolithic Ho:YAG nonplanar ring oscillator (NPRO) is demonstrated. Resonantly pumped by a Tm-doped fiber laser at 1.91 mu m, the Ho:YAG NPRO produces 71% of slope efficiency with respect to absorbed pump power and nearly diffraction-limited output with a beam quality parameter of M-2 approximate to 1.1. (c) 2008 Optical Society of America

Towards identification of a general model of damping

Characterization of damping forces in a vibrating structure has long been an active area of research in structural dynamics. In spite of a large amount of research, understanding of damping mechanisms is not well developed. A major reason for this is that unlike inertia and stiffness forces it is not in general clear what are the state variables that govern the damping forces. The most common approach is to use `viscous damping' where the instantaneous generalized velocities are the only relevant state variables. However, viscous damping by no means the only damping model within the scope of linear analysis. Any model which makes the energy dissipation functional non-negative is a possible candidate for a valid damping model. This paper is devoted to develop methodologies for identification of such general damping models responsible for energy dissipation in a vibrating structure. The method uses experimentally identified complex modes and complex natural frequencies and does not a-priori assume any fixed damping model (eg., viscous damping) but seeks to determine parameters of a general damping model described by the so called `relaxation function'. The proposed method and several related issues are discussed by considering a numerical example of a linear array of damped spring-mass oscillators.

Energy scattering in weakly non-linear systems.

The Chinese Tam-Tam exhibits non-linear behavior in its vibro-acoustic response. The frequency content of the response during free, unforced vibration smoothly changes, with energy being progressively smeared out over a greater bandwidth with time. This is used as a motivating case for the general study of the phenomenon of energy cascading through weak nonlinearity. Numerical models based upon the Fermi-Pasta-Ulam system of non-linearly coupled oscillators, modified with the addition of damping, have been developed. These were used to study the response of ensembles of systems with randomized natural frequencies. Results from simulations will be presented here. For un-damped systems, individual ensemble members exhibit cyclical energy exchange between linear modes, but the ensemble average displays a steady state. For the ensemble response of damped systems, lightly damped modes can exhibit an effective damping which is higher than predicated by linear theory. The presence of a non-linearity provides a path for energy flow to other modes, increasing the apparent damping spectrum at some frequencies and reducing it at others. The target of this work is a model revealing the governing parameters of a generic system of this type and leading to predictions of the ensemble response.

Far-infrared emission and absorption by hot carriers in superlattices

Some of the earliest theoretical speculation, stimulated by the growth of semiconductor superlattices, focused on novel devices based on vertical transport through engineered band structures; Esaki and Tsu promised Bloch oscillators in narrow mini-band systems and Kazarinov and Suris contemplated electrically stimulated intersubband transitions as sources of infrared radiation. Nearly twenty years later these material systems have been perfected, characterized and understood and experiments are emerging that test some of these original concepts for novel submillimetre wave electronics. Here we describe recent experiments on intersubband emission in quantum wells stimulated by resonant tunnelling currents. A critical issue at this time is devising a way to achieve population inversion. Other experiments explore 'saturation' effects in narrow miniband transport. Thermal saturation may be viewed as a precursor to Bloch oscillation if the same effects can be induced with an applied electric field.