Multi-Gaussian Ultrasonic Beam Modeling for Multiple Curved Interfaces—an ABCD Matrix Approach

ABSTRACT

A multi-Gaussian beam model uses a superposition of Gaussian beams to simulate the waves radiated from an ultrasonic transducer. We show that propagation and reflection/transmission laws for Gaussian beams in fluids and elastic solids can be written in the form of A , B , C , D matrices that are analogous to the A, B, C, D scalars used in Gaussian optics. This representation leads to simple expressions for a Gaussian beam even after that beam has been transmitted or reflected at multiple curved interfaces and produces a highly modular multi-Gaussian beam model that is also computationally very efficient. Some examples of the use of this model for both planar and curved interfaces are given.     

Rings, chains and planes: Variation ofT g with composition in chalcogenide glasses

We propose a microscopic, phenomenological model for the decrease in the viscosity observed at glass transition. Our model is primarily applicable to chalcogenide glasses. According to this model, the decrease in the viscosity at glass transition is mainly due to the breaking of the Van der Waals bonds in the chalcogenides. Using this model, we derive a relationship between the glass transition temperature,T _g ,and the molar volume V _m.The validity of this relation is checked using experimental data available in the literature for two binary systems (Ge-Se and As-S) and a pseudo-binary system (As ₄₀ Se _x Te _60-x .     

Efficiency of spontaneous emission from planar microcavities

Abstract

We use a computational model to investigate the different routes by which power is lost by an optical emitter placed in a microcavity environment. We make a quantitative investigation of the 1/2n ² model used by many workers in evaluating the fraction of power radiated from a thin film of emitting material. We show the limitations of the 1/2n ² model, emphasizing the important role of the orientation of the dipole moment of the emitters. Multi-layer systems, involving dielectric Bragg stack reflectors and metal mirrors, are compared for their efficiency in producing useful radiation. We consider both a standard Bragg reflector and the recently developed omni-directional Bragg stack. We show that metal mirrors, although lossy, may still be effective for producing useful radiation from microcavities. We focus our attention on parameters appropriate for organic microcavity light emitting diode structures.     

Optical Activity of Photonic Crystals

Abstract

We consider optically active photonic crystals. We propose a model structure and discuss the factors which determine optical activity by reference to this model.     

States prepared by decay

Abstract

We consider the time evolution of a discrete state embedded in a continuum. Results from scattering theory can be utilized to solve the initial value problem and to discuss the system as a model of wave packet preparation. Extensive use is made of the analytic properties of the propagators, and simple model systems are evaluated to illustrate the argument. We verify the exponential appearence of the continuum state and its propagation as a localized wave packet.     

Sensor Network Localization,Euclidean Distance Matrix completions,and graph realization

We study Semidefinite Programming, SDP, relaxations for Sensor Network Localization, SNL, with anchors and with noisy distance information. The main point of the paper is to view SNL as a (nearest) Euclidean Distance Matrix, EDM, completion problem that does not distinguish between the anchors and the sensors. We show that there are advantages for using the well studied EDM model. In fact, the set of anchors simply corresponds to a given fixed clique for the graph of the EDM problem.     

Analysis and Comparison of Birefringent Fibre Ring Resonator Types

Abstract

We present a theoretical model that can be used to determine the output of fibre ring resonators made with birefringent fibre, and with different types of polarization-selective or polarization-insensitive couplers. We derive tolerances for the coupler polarization crosstalk, splice alignment, and input polarization mode purity necessary for optimum operation of each type.     

Quantum State Diffusion Theory and a Quantum Jump Experiment

Abstract

We use a recent stochastical diffusion model of quantum evolution to represent the evolution of a three-level quantum system undergoing quantum jumps. This is possible because the continuous change in the quantum state in this diffusion model is so rapid that it appears to be instantaneous in comparison with the time between transitions. Experimental data from a study of the intermittent fluorescence of a single trapped ²⁴Mg⁺ ion and equivalent theoretical data are shown to be strikingly similar. Statistical comparisons of the data are also made.     

Nonlinear quantum optical computing via measurement

Abstract

We show how the measurement induced model of quantum computation proposed by Raussendorf and Briegel (2001, Phys. Rev. Letts., 86, 5188) can be adapted to a nonlinear optical interaction. This optical implementation requires a Kerr nonlinearity, a single photon source, a single photon detector and fast feed forward. Although nondeterministic optical quantum information proposals such as that suggested by KLM (2001, Nature, 409, 46) do not require a Kerr nonlinearity they do require complex reconfigurable optical networks. The proposal in this paper has the benefit of a single static optical layout with fixed device parameters, where the algorithm is defined by the final measurement procedure.     

Phase Behaviour in Diffuse Light Bands from Diffraction Gratings

Abstract

We have measured the phase in diffuse light bands generated by the surface electromagnetic waves on diffraction gratings. We confront the result with a simple theoretical model.     

A Model for the Optical Transistor and Optical Switching

Abstract

We propose a model for the optical transistor which can also be used for optical switching. We consider the ‘resonant optical tunnel effect’ and we show that the amplification of a modulation may be obtained by acting on the index of refraction of the intermediate nonlinear layer of a multilayer optical film. Parameters can be chosen in a technically possible range and we give a numerical estimation of these parameters when using CdS as amplifier. These results are compared with those which could be expected with a nonlinear Fabry-Perot.     

Twisted Gaussian Schell-model Beams: A Superposition Model

Abstract

We present a simple model in which a twisted Gaussian Schell-model beam is produced by an incoherent superposition of ordinary Gaussian beams. The meaning and some direct consequences of the model are given.     

Photo-excitation of a Structured Continuum: A Soluble Model

Abstract

The photoexcitation of a structured continuum of states from a single ground state is considered. We investigate an analytically soluble model in which the dipole matrix elements between the ground state and the continuum vary sinusoidally between zero and a maximum. The time-evolution of the ground-state population still exhibits the periodic disruption observed in the Bixon-Jortner model, although the disruption is much reduced. We allow the ground state to be resonant with an arbitrary place in the continuum; population trapping is observed in the case of resonance with a zero in the continuum. We compare and contrast the results obtained with this model with those of quasi-continuum excitation. Lastly, we examine the final-state spectrum.     

Characterization of a grating-coupled liquid crystal cell using a rigorous theoretical model

Abstract

We use a rigorous differential formalism to model the optical response of a multilayer structure having both a surface-relief grating and containing uniaxial materials. The uniaxial material is, in this case, a layer of liquid crystal that has its uniaxial axis defined by its director. By fitting experimental angle dependent reflectivity data to a multilayer grating model we are able to determine the spatial profile of the liquid crystal director, and show how accurately the optical response of such a system may be modelled.     

State vector approximations for the resonant two-photon jaynes-cummings model

Abstract

We report improved approximate state vectors for the resonant two-photon Jaynes-Cummings model. The results show that conventional practice of approximating the state vector via a Taylor series expansion up to the second-order term can be dramatically improved by the addition of a third-order term. Our new approximation is no more difficult to use than the conventional one.     

Using magnetic birefringence to determine the molecular arrangement of supramolecular nanostructures

Abstract

Supramolecular aggregates can be aligned in solution using a magnetic field. Because of the optical anisotropy of the molecular building blocks, the alignment results in an anisotropic refractive index of the solution parallel and perpendicular to the magnetic field. We present a model for calculating the magnetic birefringence, using solely the magnetic susceptibilities and optical polarizabilities of the molecules, for any molecular arrangement. We demonstrate that magnetic birefringence is a very sensitive tool for determining the molecular organization within supramolecular aggregates.     

Photon filters in a microwave cavity

Abstract

In an earlier paper we concluded that time-dependent parameters in the atom-mode interaction can be utilized to modify the quantum field in a cavity. When an atom shoots through the cavity field, it is expected to experience a trigonometric time dependence of its coupling constant. We investigate the possibilities this offers to modify the field. As a point of comparison we use the solvable Rosen-Zener model, which has parameter dependences roughly similar to the ones expected in a real cavity. We do confirm that by repeatedly sending atoms through the cavity, we can obtain filters on the photon states. Highly non-classical states can be obtained. We find that the Rosen-Zener model is more sensitive to the detuning than the case of a trigonometric coupling.     

Optomechanical effect on the Dicke quantum phase transition and quasi-particle damping in a Bose–Einstein condensate: a new tool to measure weak force

Abstract

We make a semi-classical steady state analysis of the influence of mirror motion on the quantum phase transition for an optomechanical Dicke model in the thermodynamic limit. An additional external mechanical pump is shown to modify the critical value of atom–photon coupling needed to observe the quantum phase transition. We further show how to choose the mechanical pump frequency and cavity–laser detuning to produce extremely cold condensates. The present system can be used as a quantum device to measure weak forces.     

Counter-rotating Contributions in the Jaynes-Cummings Model

Abstract

We present several perturbative approaches to the Jaynes-Cummings model of optical resonance with the counter-rotating terms included. We find that there exists a hitherto overlooked phase-dependence of the atomic inversion which is due to an interference between the rotating wave and counter-rotating contributions.     

Fock states generation in a kicked cavity with a nonlinear medium

Abstract

We discuss a model of a cavity filled with a passive nonlinear ?Kerr‘ medium and periodically kicked by a series of ultra-short laser pulses. The nonlinear medium is described by the (2q ? 1)th nonlinearity X ^(2q?1). We find analytical formulas describing the field states inside the cavity. We show that such a system can produce, depending on the order of the nonlinearity, superpositions of several Fock states with the small photon numbers (0,1; 0,1,2; etc). In particular, the one-photon state can be approached during the evolution of the system with X ⁽³⁾ nonlinearity provided the cavity losses are negligible. The purity of states generated in this process, however, can be seriously degraded by the cavity damping. We perform numerical calculations to validate our analytical results.