Transmission spectrum of a double quantum-dot-nanocavity system in photonic crystals

We investigate the optical transmission properties of a combined system which consists of two quantum-dot-nanocavity subsystems indirectly coupled to a waveguide in a planar photonic crystal. A Mollow-like triplet and the growth of sidebands are found, reflecting intrinsic optical responses in the complex microstructure.

Quantum interference in laser-induced nonsequential double ionization in diatomic molecules: Role of alignment and orbital symmetry

We address the influence of the orbital symmetry and the molecular alignment with respect to the laser-field polarization on laser-induced nonsequential double ionization of diatomic molecules, in the length and velocity gauges. We work within the strong-field approximation and assume that the second electron is dislodged by electron-impact ionization, and also consider the classical limit of this model. We show that the electron-momentum distributions exhibit interference maxima and minima due to electron emission at spatially separated centers. The interference patterns survive integration over the transverse momenta for a small range of alignment angles, and are sharpest for parallel-aligned molecules. Due to the contributions of the transverse-momentum components, these patterns become less defined as the alignment angle increases, until they disappear for perpendicular alignment. This behavior influences the shapes and the peaks of the electron-momentum distributions.

Electronic and kinetic processes in the Cu/CuCl double pulse laser

Kinetic and electronic processes in a Cu/CuCl double pulsed laser were investigated by measuring discharge and laser pulse characteristics, and by computer modeling. There are two time scales inherent to the operation of the Cu/CuCl laser. The first is during the interpulse afterglow (tens to hundreds of microseconds). The second is during the pumping pulse (tens of nanoseconds). It was found that the character of the pumping pulse is largely determined by the initial conditions provided by the interpulse afterglow. By tailoring the dissociation pulse to be long and low energy, and by conditioning the afterglow, one may select the desired initial conditions and thereby significantly improve laser performance. With a low energy dissociation pulse, the fraction of metastable copper obtained from a CuCl dissociation is low. By maintaining the afterglow, contributions to the metastable state from ion recombinations are prevented, and the plasma impedance remains low thereby increasing the rate of current rise during the pumping pulse. Computer models for the dissociation pulse, afterglow, pumping pulse and laser pulse reproduced experimentally observed behavior of laser pulse energy and power as a function of time delay, pumping pulse characteristics, and buffer gas pressure. The sensitivity of laser pulse properties on collisional processes (e.g., CuCl reassociation rates) was investigated.

Spin dynamics of pulsed nuclear magnetic double resonance in solids

In the first part of this thesis, experiments utilizing an NMR phase interferometric concept are presented. The spinor character of two-level systems is explicitly demonstrated by using this concept. Following this is the presentation of an experiment which uses this same idea to measure relaxation times of off-diagonal density matrix elements corresponding to magnetic-dipole-forbidden transitions in a ^(13)C-^1H, AX spin system. The theoretical background for these experiments and the spin dynamics of the interferometry are discussed also.

The second part of this thesis deals with NMR dipolar modulated chemical shift spectroscopy, with which internuclear bond lengths and bond angles with respect to the chemical shift principal axis frame are determined from polycrystalline samples. Experiments using benzene and calcium formate verify the validity of the technique in heteronuclear (^(13)C-^1H) systems. Similar experiments on powdered trichloroacetic acid confirm the validity in homonuclear (^1H- ^1H) systems. The theory and spin dynamics are explored in detail, and the effects of a number of multiple pulse sequences are discussed.

The last part deals with an experiment measuring the ^(13)C chemical shift tensor in K_2Pt(CN)_4Br_(0.3) • 3H_2O, a one-dimensional conductor. The ^(13)C spectra are strongly affected by ^(14)N quadrupolar interactions via the ^(13)C - ^(14)N dipolar interaction. Single crystal rotation spectra are shown.

An appendix discussing the design, construction, and performance of a single-coil double resonance NMR sample probe is included.

Double injection: high frequency noise and temperature dependence

Noise measurements from 140°K to 350°K ambient temperature and between 10kHz and 22MHz performed on a double injection silicon diode as a function of operating point indicate that the high frequency noise depends linearly on the ambient temperature T and on the differential conductance g measured at the same frequency. The noise is represented quantitatively by〈i^2〉 = α•4kTgΔf. A new interpretation demands Nyquist noise with α ≡ 1 in these devices at high frequencies. This is in accord with an equivalent circuit derived for the double injection process. The effects of diode geometry on the static I-V characteristic as well as on the ac properties are illustrated. Investigation of the temperature dependence of double injection yields measurements of the temperature variation of the common high-level lifetime τ(τ ∝ T^2), the hole conductivity mobility µ_p (µ_p ∝ T^(-2.18)) and the electron conductivity mobility µ_n(µ_n ∝ T^(-1.75)).

Effects of self energy of the ions on the double layer structure and properties at the dielectric interface

Although numerous theoretical efforts have been put forth, a systematic, unified and predictive theoretical framework that is able to capture all the essential physics of the interfacial behaviors of ions, such as the Hofmeister series effect, Jones-Ray effect and the salt effect on the bubble coalescence remain an outstanding challenge. The most common approach to treating electrostatic interactions in the presence of salt ions is the Poisson-Boltzmann (PB) theory. However, there are many systems for which the PB theory fails to offer even a qualitative explanation of the behavior, especially for ions distributed in the vicinity of an interface with dielectric contrast between the two media (like the water-vapor/oil interface). A key factor missing in the PB theory is the self energy of the ion.

In this thesis, we develop a self-consistent theory that treats the electrostatic self energy (including both the short-range Born solvation energy and the long-range image charge interactions), the nonelectrostatic contribution of the self energy, the ion-ion correlation and the screening effect systematically in a single framework. By assuming a finite charge spread of the ion instead of using the point-charge model, the self energy obtained by our theory is free of the divergence problems and gives a continuous self energy across the interface. This continuous feature allows ions on the water side and the vapor/oil side of the interface to be treated in a unified framework. The theory involves a minimum set of parameters of the ion, such as the valency, radius, polarizability of the ions, and the dielectric constants of the medium, that are both intrinsic and readily available. The general theory is first applied to study the thermodynamic property of the bulk electrolyte solution, which shows good agreement with the experiment result for predicting the activity coefficient and osmotic coefficient.

Next, we address the effect of local Born solvation energy on the bulk thermodynamics and interfacial properties of electrolyte solution mixtures. We show that difference in the solvation energy between the cations and anions naturally gives rise to local charge separation near the interface, and a finite Galvani potential between two coexisting solutions. The miscibility of the mixture can either increases or decreases depending on the competition between the solvation energy and translation entropy of the ions. The interfacial tension shows a non-monotonic dependence on the salt concentration: it increases linearly with the salt concentration at higher concentrations, and decreases approximately as the square root of the salt concentration for dilute solutions, which is in agreement with the Jones-Ray effect observed in experiment.

Next, we investigate the image effects on the double layer structure and interfacial properties near a single charged plate. We show that the image charge repulsion creates a depletion boundary layer that cannot be captured by a regular perturbation approach. The correct weak-coupling theory must include the self-energy of the ion due to the image charge interaction. The image force qualitatively alters the double layer structure and properties, and gives rise to many non-PB effects, such as nonmonotonic dependence of the surface energy on concentration and charge inversion. The image charge effect is then studied for electrolyte solutions between two plates. For two neutral plates, we show that depletion of the salt ions by the image charge repulsion results in short-range attractive and long-range repulsive forces. If cations and anions are of different valency, the asymmetric depletion leads to the formation of an induced electrical double layer. For two charged plates, the competition between the surface charge and the image charge effect can give rise to like- charge attraction.

Then, we study the inhomogeneous screening effect near the dielectric interface due to the anisotropic and nonuniform ion distribution. We show that the double layer structure and interfacial properties is drastically affected by the inhomogeneous screening if the bulk Debye screening length is comparable or smaller than the Bjerrum length. The width of the depletion layer is characterized by the Bjerrum length, independent of the salt concentration. We predict that the negative adsorption of ions at the interface increases linearly with the salt concentration, which cannot be captured by either the bulk screening approximation or the WKB approximation. For asymmetric salt, the inhomogeneous screening enhances the charge separation in the induced double layer and significantly increases the value of the surface potential.

Finally, to account for the ion specificity, we study the self energy of a single ion across the dielectric interface. The ion is considered to be polarizable: its charge distribution can be self-adjusted to the local dielectric environment to minimize the self energy. Using intrinsic parameters of the ions, such as the valency, radius, and polarizability, we predict the specific ion effect on the interfacial affinity of halogen anions at the water/air interface, and the strong adsorption of hydrophobic ions at the water/oil interface, in agreement with experiments and atomistic simulations.

The theory developed in this work represents the most systematic theoretical technique for weak-coupling electrolytes. We expect the theory to be more useful for studying a wide range of structural and dynamic properties in physicochemical, colloidal, soft-matter and biophysical systems.

Origin of the double-peak structure in longitudinal momentum distributions for single ionization of an He atom in strong laser field

The single ionization of an He atom by intense linearly polarized laser field in the tunneling regime is studied by S- matrix theory. When only the first term of the expansion of the S matrix is considered and time, spatial distribution, and fluctuation of the laser pulse are taken into account, the obtained momentum distribution in the polarization direction of laser field is consistent with the semiclassical calculation, which only considers tunneling and the interaction between the free electron and external field. When the second term, which includes the interaction between the core and the free electron, is considered, the momentum distribution shows a complex multipeak structure with the central minimum and the positions of some peaks are independent of the intensity in some intensity regime, which is consistent with the recent experimental result. Based on our analysis, we found that the structures observed in the momentum distribution of an He atom are attributed to the " soft" collision of the tunneled electron with the core.

Topological strings, double affine Hecke algebras, and exceptional knot homology

In this thesis, we consider two main subjects: refined, composite invariants and exceptional knot homologies of torus knots. The main technical tools are double affine Hecke algebras ("DAHA") and various insights from topological string theory.

In particular, we define and study the composite DAHA-superpolynomials of torus knots, which depend on pairs of Young diagrams and generalize the composite HOMFLY-PT polynomials from the full HOMFLY-PT skein of the annulus. We also describe a rich structure of differentials that act on homological knot invariants for exceptional groups. These follow from the physics of BPS states and the adjacencies/spectra of singularities associated with Landau-Ginzburg potentials. At the end, we construct two DAHA-hyperpolynomials which are closely related to the Deligne-Gross exceptional series of root systems.

In addition to these main themes, we also provide new results connecting DAHA-Jones polynomials to quantum torus knot invariants for Cartan types A and D, as well as the first appearance of quantum E6 knot invariants in the literature.

Distortion of beam shape by a rotating double-prism wide-angle laser beam scanner

We describe the rigorous results of a wide-angle laser beam scanner, obtained with the help of the vector refraction theory. Using the rigorous results, the distortion of the beam shape is discussed. The distortion to the beam varies with the different relative angles of double prisms. The scanner expands the beam in some directions while it contracts the beam in other directions. According to the conservation of energy, the distribution of the laser intensity is changed as well. (c) 2006 Society of Photo-Optical Instrumentation Engineers.

The effect of the rotating double-prism wide-angle laser beam scanner on the beam shape

In this paper, we describe a wide-angle laser beam scanner and the rigorous result of the wide-angle laser beam scanner was obtained with the help of the vector refraction theory. Using the rigorous results, the distortion of the beam shape was discussed. The distortion of the beam shape is varying with the different relative angles of the double prisms. According to the conservation of the energy, the distribution of the laser intensity is changed too. (c) 2005 Elsevier GmbH. All rights reserved.

Double refraction and reflection of sequential crystal interfaces with arbitrary orientation of the optic axis and application to optimum design

The general formulation of double refraction or internal double reflection for any directions of incidence and arbitrary orientation of the optic axis in a uniaxial crystal is analysed in terms of Huygens' principle. Then double refraction and double reflection along the sequential interfaces in a crystal are discussed. On this basis, if the parameters of the interface are chosen appropriately, the range of angular separation between the ordinary ray and extraordinary ray can be much greater, It is useful for crystal element design. Finally, as an example, an optimum design of the Output end interface for a 2 x 2 electro-optic switch is given.

Characteristics of an add-drop filter composed of a Mach-Zehnder interferometer and double ring resonators

A planar lightwave circuit (PLC) add-drop filter is proposed and analyzed, which consists of a symmetric Mach-Zehnder interferometer (MZI) combined with double microring resonators. A critical coupling condition is derived for a better box-like drop spectrum. Comparisons of its characteristics with other schemes, such as a MZI with a single ring resonator, arepresented, and some of the issues about device design and fabrication are also discussed.