Doctor of Philosophy / Department of Physics / Kristan L. Corwin / Portable frequency references are crucial for many practical on-site applications, for example, the Global Position System (GPS) navigation, optical communications, and remote sensing. Fiber laser optical frequency combs are a strong candidate for portable reference systems. However, the conventional way of locking the comb repetition rate, frep, to an RF reference leads to large multiplied RF instabilities in the optical frequency domain. By stabilizing a comb directly to an optical reference, the comb stability can potentially be enhanced by four orders of magnitude. The main goal of this thesis is to develop techniques for directly referencing optical frequency combs to optical references toward an all-fiber geometry. A big challenge for direct fiber comb spectroscopy is the low comb power. With an 89 MHz fiber ring laser, we are able to optically amplify a single comb tooth from nW to mW (by a factor of 10^6) by building multiple filtering and amplification stages, while preserving the comb signal-to-noise ratio. This amplified comb tooth is directly stabilized to an optical transition of acetylene at ~ 1539.4 nm via a saturated absorption technique, while the carrier-envelope offset frequency, f0, is locked to an RF reference. The comb stability is studied by comparing to a single wavelength (or CW) reference at 1532.8 nm. Our result shows a short term instability of 6 x10^(-12) at 100 ms gate time, which is over an order of magnitude better than that of a GPS-disciplined Rb clock. This implies that our optically-referenced comb is a suitable candidate for a high precision portable reference. In addition, the direct comb spectroscopy technique we have developed opens many new possibilities in precision spectroscopy for low power, low repetition rate fiber lasers. For single tooth isolation, a novel cross-VIPA (cross-virtually imaged phase array) spectrometer is proposed, with a high spectral resolution of 730 MHz based on our simulations. In addition, the noise dynamics for a free space Cr:forsterite-laser-based frequency comb are explored, to explain the significant f0 linewidth narrowing with knife insertion into the intracavity beam. A theoretical model is used to interpret this f0 narrowing phenomenon, but some unanswered questions still remain.

This dissertation begins with a study of some of the linear and nonlinear optical properties of composite materials consisting of CdSₓSe₁₋ₓ microcrystallites embedded in a host glass matrix. These studies investigate changes in absorption, refractive index and nonlinear response time under a variety of experimental conditions. The data demonstrates that this class of materials exhibit: a strong saturation of absorption due to band filling; a large n₂ which also saturates; response times which range from <100ps to many nanoseconds; and a permanent darkening and change of n₂ induced by extended exposure to high energy pulses. These measurements were used to identify the optimum sample of the semiconductor doped glasses to demonstrate an efficient degenerate four-wave mixing process within a planar waveguide. High quality single mode waveguides were fabricated from the semiconductor doped glass by K⁺-ion exchange. Four wave mixing was performed in the waveguide that produced a peak reflectivity of ≅.003, which is 8 orders of magnitude larger than that achieved previously in a similar experiment where CS₂ was used as the nonlinear medium.

Because of their compatibility with the planar concept of integrated optics, grating couplers offer the most satisfactory means of coupling light into thin film optical waveguides. The purpose of this dissertation has been to study the behaviour, both theoretically and experimentally, and fabrication of grating couplers in nonlinear waveguides. A theory of nonlinear grating couplers is presented based on a coupled-mode approach. The dependence of coupling efficiency on incident beam intensity, beam size, beam position, incident angle, chirp rate, and waveguide losses have been examined all in the presence of nonlinearities in the waveguide. It is reported that, in the presence of nonlinearities, the coupling efficiency decreases with increasing incident power. Different ways of optimizing the coupling efficiency at high incident power levels are presented. These include adjusting the beam size, the coupling angle, and chirping the grating. A new technique is reported for fabrication of regular period, chirped, and curved photoresist gratings. The experimental arrangement is essentially based on Lloyd's mirror fringes and is characterized by its stability, simplicity, and versatility. We also report on successful use of Reactive Ion-Beam Etching (RIBE) with C₂F₆ gas in producing very smooth and deep gratings with high aspect ratios in different waveguide structures. Experimental coupling efficiencies of up to 40% are reported in polystyrene waveguides using etched grating couplers. Experiments are reported in support of the theoretical findings of this dissertation using a polystyrene waveguide with thermal nonlinearity.

A study of the application of single-mode fiber optics to the multiple-beam interferometric recombination problem is presented. In the laboratory, the fibers have been used in wide bandwidth, two-arm, Mach-Zehnder test interferometers as well as a 5-telescope imaging interferometer connected to an all-fiber beam combiner. Based upon these experiments and some theoretical studies it is shown that fiber optics and fiber optic components such as directional couplers provide an excellent alternative to conventional optics such as mirrors, beamsplitters, and relay lenses. The equations describing the measurement of the complex degree of coherence in an interferometer with a single-mode fiber in each arm are derived. The equations reveal an important feature of the fibers: they filter phase fluctuations due to aberrations and turbulence at the input and convert them to intensity fluctuations at the output. This leads to a simplification of the calibration of measured visibilities. The coupling efficiency of light which has passed through a turbulent atmosphere is also studied as a function of fiber parameters and turbulence conditions for both image motion stabilized and non-stabilized cases. For the former case, coupling efficiency remains greater than 50% as long as telescope diameter is no larger than the turbulence coherence length. Beam combination architectures using arrays of directional couplers are fully discussed. Arrays accommodating up to 20 input beams are presented. The arrays require only N detector pixels for N input beams. A scheme of temporal multiplexing of the phase of each beam is used to identify individual fringe pairs. One possible scheme allows wide bandwidths even for large numbers of beams. A 5-telescope interferometer has been constructed and connected to an all-fiber beam combiner. Two extended objects were observed and reconstructed using standard radio astronomy VLBI software. The interferometer and beam combiner had good thermal and polarization stability and high throughput. Reconstructed images had dynamic ranges of about 50.

Two spectral regions of gain exist for a weak probe beam propagating through a medium of two-level-atoms pumped by a strong near-resonance field. Experimentally a cw ring-dye laser is used to explore this gain at the Na D₂ resonance in a vapor. Plane-wave calculations of probe-gain spectra which include the Doppler broadening inherent in a vapor agree well with experimental spectra obtained with a Fabry-Perot interferometer. Such two-beam-coupling gain might have applications as optical pre- or power amplifiers. The gain is also the primary step in four-wave-mixing. Mixing of the pump and sideband which experiences gain produces the medium polarization from which the fourth-wave arises. For phase-matched propagation the fourth-wave, which is at a frequency that experiences little or negative probe-gain (i.e., absorption), grows at nearly the same rate as the primary sideband. Together the two sidebands extract far more than twice as much energy from the pump than does the primary sideband acting alone. Experimentally four-wave-mixing which arises from noise at the gain-sideband-frequency is sometimes accompanied by conical emission at the fourth-wave sideband. Since this sideband is also seen on axis the explanation cannot be simply phase-matching. Simulations which include the full transverse nature of the experiment are currently running on a CRAY supercomputer. These simulations indicate that the radial variation of the medium index of refraction is responsible for conical emission.

QC 351 A7 no. 59 / The optical properties of two prisms combined as a single anamorphic element are discussed. There is a family of solutions for which the angular magnification versus field angle is U-shaped. Thus there are regions for which the angular magnification is almost constant. The distortions associated with these regions are explored. It is shown how distortion can be effectively eliminated over a restricted field by cascading a negative and a positive anamorphic element.

<p>The nonlinear interaction between light and atoms is an extensive field of study with a broad range of applications in quantum information science and condensed matter physics. Nonlinear optical phenomena occurring in cold atoms are particularly interesting because such slowly moving atoms can spatially organize into density gratings, which allows for studies involving optical interactions with structured materials. In this thesis, I describe a novel nonlinear optical effect that arises when cold atoms spatially bunch in an optical lattice. I show that employing this spatial atomic bunching provides access to a unique physical regime with reduced thresholds for nonlinear optical processes and enhanced material properties. Using this method, I observe the nonlinear optical phenomenon of transverse optical pattern formation at record-low powers. These transverse optical patterns are generated by a wave- mixing process that is mediated by the cold atomic vapor. The optical patterns are highly multimode and induce rich non-equilibrium atomic dynamics. In particular, I find that there exists a synergistic interplay between the generated optical pat- terns and the atoms, wherein the scattered fields help the atoms to self-organize into new, multimode structures that are not externally imposed on the atomic sample. These self-organized structures in turn enhance the power in the optical patterns. I provide the first detailed investigation of the motional dynamics of atoms that have self-organized in a multimode geometry. I also show that the transverse optical patterns induce Sisyphus cooling in all three spatial dimensions, which is the first observation of spontaneous three-dimensional cooling. My experiment represents a unique means by which to study nonlinear optics and non-equilibrium dynamics at ultra-low required powers.</p> / Dissertation

This thesis investigates two thematic lines of research, both underpinned by non-Markovian system-reservoir interactions in quantum optics. The overarching focus is on modelling the open system dynamics in a non-perturbative fashion, broadly on - though not restricted to - instances when the environment is structured. A theory is developed by means of enlarging the open system over environmental degrees of freedom to include memory effects in its dynamics. This is achieved using an established technique that involves mapping a bosonic environment onto a 1D chain of harmonic oscillators. Within this setting, we apply a Heisenberg equation-of-motion approach to derive an exact set coupled differential equations for the open system and a single auxiliary oscillator of the chain. The combined equations are shown to have their interpretation rooted in a quantum Markov stochastic process. Including the auxiliary chain oscillator as part of the original system then enables us to obtain an exact master equation for the enlarged system, avoiding any need for the Born-Markov approximations. Our method is valid for a dissipative two-state system, with cases of multiple excitations and added driving discussed. Separately, we apply the framework of quantum Darwinism to an atom-cavity system, and, subsequently, to a more general multiple-environment model. In both cases, the time-dependent spread of correlations between the open system and fractions of the environment is analysed during the course of the decoherence process. The degree to which information is redundant across different fractions is checked to infer the emergence of classicality. In the second case, we go further and present a decomposition of information in terms of its quantum and classical correlations. A quantitative measure of redundancy is also studied with regard to its ability to witness non-Markovian behaviour. Besides fundamental interest, our results have application to quantum information processing and quantum technologies, keeping in mind the potential beneficial use of non-Markovian effects in reservoir engineering.

The objective of this thesis is to develop the quantum theory of the motional degrees of freedom of a charged particle in a Penning trap. The theory is treated within the formalism of quantum optics, and explores the use of dressed-atom methods by exploiting the threefold SU(N) algebraic structure of the problem. The quantum form of the experimental techniques of sideband coupling and driving to the ultra-elliptical regime are examined in this context, and resulting future applications considered. Interpretation of the quantum dynamics of the separate x and y motions of an electron is discussed, motivated by the desire to modify the trapping potential without changing the basic experimental configuration. A detailed discussion of operator methods which exploit the algebraic structure of the problem is given. This results in a clearer understanding of the physical manifestations of a range of unitary transformations upon a general three-dimensional system, and a novel interpretation of the mapping between canonical angular momentum components of isotropic and anisotropic trapping systems. The results highly promote future use of these methods in Penning trap theory, detailing a robust formulation of unitary operations which can be used to prepare the quantum state of a charged particle. The majority of the results can be applied to any Penning trap, but the theory is based throughout upon the “Geonium Chip" trap at Sussex; the scalability and planar design of this trap promotes it as natural candidate in experimental quantum optics and Gaussian quantum information studies. The work in this thesis aims to provide framework for such future applications.

Chan, Yun San = 光子晶格系統中相干行為的研究 / 陳潤燊. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 109-112). / Abstracts in English and Chinese. / Chan, Yun San = Guang zi jing ge xi tong zhong xiang gan xing wei de yan jiu / Chen Runshen. / Abstract --- p.i / 摘要 --- p.iii / Acknowledgements --- p.V / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Periodic system and photonic crystal --- p.1 / Chapter 1.1.1 --- Properties and Applications --- p.1 / Chapter 1.1.2 --- Coherent Phenomena --- p.2 / Chapter 1.1.3 --- Quantum Optical Analogue --- p.9 / Chapter 1.2 --- Coupled Optical Waveguides --- p.11 / Chapter 1.2.1 --- Coupled-mode Theory --- p.11 / Chapter 1.2.2 --- Field Evolution Analysis (FEA) --- p.14 / Chapter 1.2.3 --- Hamiltonian Optics (HO) --- p.15 / Chapter 1.3 --- Experimental Realization --- p.17 / Chapter 1.4 --- Objectives --- p.17 / Chapter 2 --- Parabolic Optical Waveguide Array --- p.19 / Chapter 2.1 --- Introduction --- p.19 / Chapter 2.1.1 --- Generalized Bloch Oscillation --- p.19 / Chapter 2.1.2 --- DO-BO Transition --- p.20 / Chapter 2.2 --- Model and Formalism --- p.20 / Chapter 2.3 --- Results --- p.25 / Chapter 2.3.1 --- Dipole Oscillation --- p.29 / Chapter 2.3.2 --- Bloch Oscillation --- p.29 / Chapter 2.3.3 --- Right Reflection --- p.31 / Chapter 2.3.4 --- Mechanical Analogue --- p.32 / Chapter 2.3.5 --- Lift-n-Shift Process --- p.33 / Chapter 2.4 --- Summary --- p.39 / Chapter 3 --- Binary POWA --- p.40 / Chapter 3.1 --- Introduction --- p.40 / Chapter 3.2 --- Model and Formalism --- p.41 / Chapter 3.3 --- Results --- p.45 / Chapter 3.3.1 --- Dipole Oscillation --- p.48 / Chapter 3.3.2 --- Bloch-dipole-Zener Oscillation --- p.51 / Chapter 3.3.3 --- Bloch-Zener oscillation --- p.54 / Chapter 3.4 --- Viable Experimental Realization --- p.57 / Chapter 3.5 --- Summary --- p.58 / Chapter 4 --- Parabolically Graded Square Lattice --- p.60 / Chapter 4.1 --- Introduction --- p.60 / Chapter 4.2 --- Model and Formalism --- p.61 / Chapter 4.3 --- Results --- p.65 / Chapter 4.3.1 --- Orthogonal Coupling --- p.65 / Chapter 4.3.2 --- Weak Diagonal Coupling --- p.76 / Chapter 4.4 --- Summary --- p.81 / Chapter 5 --- Elliptical Optical Waveguide Array --- p.82 / Chapter 5.1 --- Introduction --- p.82 / Chapter 5.2 --- Model and Formalism --- p.83 / Chapter 5.2.1 --- Kac Matrix --- p.83 / Chapter 5.2.2 --- Kac Matrix and Spin --- p.85 / Chapter 5.2.3 --- System Configuration --- p.86 / Chapter 5.3 --- Results --- p.91 / Chapter 5.3.1 --- Upper Dipole Oscillation --- p.92 / Chapter 5.3.2 --- Lower Dipole Oscillation --- p.94 / Chapter 5.3.3 --- Bloch Oscillation --- p.95 / Chapter 5.3.4 --- Upper Reflection --- p.96 / Chapter 5.3.5 --- Lower Reflection --- p.98 / Chapter 5.3.6 --- Harmonic Oscillations --- p.98 / Chapter 5.3.7 --- Lift-n-Shift Process --- p.101 / Chapter 5.4 --- Summary --- p.102 / Chapter 6 --- Conclusion --- p.104 / Chapter 6.1 --- Suggestion of Future Works --- p.106 / Chapter 6.1.1 --- POWA --- p.106 / Chapter 6.1.2 --- BPOWA --- p.106 / Chapter 6.1.3 --- PGSL --- p.107 / Chapter 6.1.4 --- EOWA --- p.107 / Chapter A --- List of abbreviations --- p.108 / Bibliography --- p.109