Optical mode-coupling in a ring due to a back-scatterer

The coupling of light waves travelling clockwise and counterclockwise along an optical ring due to a back-scattering element is studied. An asymmetric mode splitting occurs as a consequence of the discontinuity suffered by the waves at the scattering point. The mode splitting shows up in an interference pattern and lends itself to an experimental verification.     

Elastic interaction of a dislocation array with a phase boundary

The equilibrium configuration of an array of dislocations in parallel equidistant slip planes under an external shear stress near a welded boundary between two isotropic half-spaces having different elastic constants is computed. For large external stress, the dislocations are arranged into an arc concave when seen from the boundary. It is concluded that such an arc is formed at the tip of a twin or of a martensitic plate near a phase boundary. The tensile stress across the boundary due to an edge dislocation array is discussed in connection with the formation of an interfacial crack.     

Dynamics of a light field in a composite integrable model

The inverse scattering transform method is used to solve the model that describes the evolution of light pulses in an optical system that includes a set of media with different nonlinear optical properties. As a physical example, we analyze a model composed of the systems of equations that describe the resonant interaction of a very short light pulse with an energy transition of the medium and the ensuing propagation of the light field in an optical fiber. The constant boundary value of one of the fields is shown to result in an asymptotic quasi-radiative solution of the model.     

High-Q-preserving coupling between a spiral and a semicircle micro-cavity

We present an efficient design for direct coupling between a spiral-shaped and a semicircle-shaped microcavity (micro-cavity) as an alternative to traditional evanescent wave coupling for planar integrated photonic technology. We observe the preservation of the high Q-value of the spiral oscillator when coupled to a semicircle under current injection using an AlGaAs single-quantum-well heterostructure. With slight alterations to the directly coupled micro-cavity configuration, such as coupling shape and overlap distance, the number of observed modes and output intensity are changed. AlGaAs and InGaN spiral-shaped microcavities have unidirectional emission normal to the spiral notch.     

Solution of a cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula

The Cauchy problem for a class of diffusion equations in a Hilbert space is studied. It is proved that the Cauchy problem in well posed in the class of uniform limits of infinitely smooth bounded cylindrical functions on the Hilbert space, and the solution is presented in the form of the so-called Feynman formula, i.e., a limit of multiple integrals against a gaussian measure as the multiplicity tends to infinity. It is also proved that the solution of the Cauchy problem depends continuously on the diffusion coefficient. A process reducing an approximate solution of an infinite-dimensional diffusion equation to finding a multiple integral of a real function of finitely many real variables is indicated.     

Manipulating a Bose-Einstein condensate with a single photon

We propose a method to create macroscopic superpositions, so-called Schr?dinger cat states, of different motional states of an ideal Bose-Einstein condensate. The scheme is based on the scattering of a freely expanding condensate by the light field of a high-finesse optical cavity in a quantum superposition state of different photon numbers. The atom-photon interaction creates an entangled state of the motional state of the condensate and the photon number, which can be converted into a pure atomic Schr?dinger cat state by operations only acting on the cavity field. We discuss in detail the fully quantised theory and propose an experimental procedure to implement the scheme using short coherent light pulses. Received 26 June 2000 and Received in final form 2nd October 2000     

Density of states in a superconductor carrying a supercurrent

We have measured the tunneling density of states (DOS) in a superconductor carrying a supercurrent or exposed to an external magnetic field. The pair correlations are weakened by the supercurrent, leading to a modification of the DOS and to a reduction of the gap. As predicted by the theory of superconductivity in diffusive metals, we find that this effect is similar to that of an external magnetic field.     

Self-force of a charge in a real current

The analysis of the EM radiation from a single charge shows that the radiated power depends on the retarded acceleration of the charge. Therefore for consistency, an accelerated charge, free from the influence of external forces, should gradually lose its acceleration, until its total energy is radiated. Calculations show that the self force of a charge, which compensates for its radiation, is proportional to the derivative of the acceleration. However, when using this self force in the equation of motion of the charge, one gets a diverging solution, for which the acceleration runs away to infinity. This means that there is an inconsistency in the solution of the single charge problem. However, in the construction of the conserved Maxwell charge density, there is implicitly an integral over the corresponding world line which corresponds to a collection of charged spacetime events. One may therefore consistently think of the “self force” as the force on a charge due to another charge at the retarded position. From this point of view, the energy is evidently conserved and the radiation process appears as an absorbing resistance to the feeding source. The purpose of this work is to learn about the behavior of single charges from the behavior of a real current, corresponding to the set of charges moving on a world line, and to study the analog of the self force of a charge associated with the radiation resistance of a continuum of charges.     

Estimation of a displacement parameter of a quantum system

A displacement parameter such as the angle of rotation or the position of a quantum system, or the phase of a harmonic oscillation, is to be estimated by observing the system with an apparatus that applies to it an operator-valued measure (o.v.m.). The o.v.m. minimizing the average cost of errors in the estimate is determined by quantum estimation theory for a system in a pure state. The best estimate of the parameter is found to be the more accurate, the greater the uncertainty of the dynamical variable serving as the infinitesimal generator of the displacement group. The relation of this result to such uncertainty principles as those between angle and angular momentum, and between oscillator phase and photon number, is discussed. A lower bound to the variance of an unbiased estimate of the time of occurrence of an event in the evolution of a system is derived from the quantum-mechanical Cramér-Rao inequality. It is inversely proportional to the square of the uncertainty of the energy of the system.     

Formation of a high-frequency subpulse upon propagation of a femtosecond pulse in a medium with a saturable potential

On the basis of computer simulation of propagation of femtosecond light pulses in terms of the one-dimensional nonstationary nonlinear Maxwell equations with a saturable restoring force, the possibility of formation of a sequence of subpulses with different carrier frequencies is shown. The formation of frequency-modulated pulses with an asymmetric distribution of spectral components with respect to the center of a local line is demonstrated. Appearance of such pulses indicates that a hysteretic dependence of the frequency of the corresponding local line on the amplitude of an external signal can be realized.     

Synthesis of currents on a disk using a directional diagram

The problem of synthesis of currents using a realizable or unrealizable directional diagram is solved. In the former case, the problem is solved analytically: the current is sought as a series in basis, with each of the basis functions satisfying the Meixner condition on an edge. If the diagram is unrealizable, the current is found from a solution to an integral equation with a small parameter. The solution to the integral equation also satisfies the Meixner condition on an edge.     

Response of a Bloch oscillator to a THz-field

In this paper we report on the observation of response of a Bloch oscillator at room temperature to a THz-field of a frequency larger than the Bloch frequency. The oscillator consisted of a semiconductor superlattice structure, with an applied dc voltage giving rise to a dc electron drift current. Submitting the oscillator to a field at a frequency of 3.3 THz caused a sizeable reduction of the current; the THz-field was generated by use of intense THz-radiation pulses focused on an antenna coupled to the superlattice. We attribute the THz-field induced reduction of the current to a frequency modulation of the Bloch oscillations of electrons at the frequency of the THz-field, leading to reduction of the electron drift velocity and, consequently, of the current.     

Destabilization of a Saffman-Taylor fingerlike pattern in a granular suspension

We study the Saffman-Taylor instability in a granular suspension formed by micrometric beads immersed in a viscous liquid. When using an effective viscosity for the flow of the suspension in the Hele-Shaw cell to define the control parameter of the system, the results for the finger width of stable fingers are found to be close to the classical results of Saffman-Taylor. One observes, however, an early destabilization of the fingers that can be attributed to the discrete nature of the individual grains. Classically, the threshold of destabilization is linked to the noise in the cell and is thus difficult to quantify. We show that the grains represent a "controlled noise" and produce an initial perturbation of the interface with an amplitude proportional to the grain size. The finite amplitude instability mechanism proposed by Bensimon et al. allows us to link this perturbation to the value of the threshold observed.     

Modelling and design of a novel air-spring for a suspension seat

Air-springs used in conjunction with auxiliary volumes provide both spring stiffness and damping. The damping is introduced through the flow restriction connecting the two air volumes. This article presents a simplified model of an air-spring with an auxiliary volume derived from first principles for simulation and design of an air-spring coupled to an auxiliary volume for a suspension seat. Tests were performed on an experimental apparatus to validate the model. The simulation model of the air-spring and auxiliary volume followed the trend predicted by the literature but showed approximately 27% lower transmissibility amplitude and 21% lower system natural frequency than that obtained by tests when using large diameter flow restrictions. This inaccuracy is assumed to be introduced by the simplified mass transfer equations defining the flow restriction between air-spring and auxiliary volume. The model showed closer correlation to the experimental results when the auxiliary volume size was decreased by two-thirds of the volume actually used for the experiment. A procedure, using the developed simulation model, for the design of a prototype air-spring and auxiliary volume, is presented for application in a typical articulated or rigid frame dump truck. The goal of the study was to design a suspension seat for this application and to obtain a SEAT value below 1.1. The design was optimised by varying auxiliary volume size and flow restriction diameters for different loads. A SEAT value of less than 0.9 was achieved, clearly indicating the effectiveness of using an auxiliary volume with an air-spring as seat suspension.     

Investigations of a nonlinear energy harvester with a bistable potential well

This paper investigates a nonlinear energy harvester that uses magnetic interactions to create an inertial generator with a bistable potential well. The motivating hypothesis for this work was that nonlinear behavior could be used to improve the performance of an energy harvester by broadening its frequency response. Theoretical investigations study the harvester's response when directly powering an electrical load. Both theoretical and experimental tests show that the potential well escape phenomenon can be used to broaden the frequency response of an energy harvester.     

Calculation of a triode field-emission system with a modulator

The electrostatic potential of a triode field-emission system with a modulator that represents a circular diaphragm is calculated. A tip field-emission cathode serves as an emitter. The inner part of the system under study is filled with two insulators. In the calculation of the potential distribution, a real field-emission cathode is changed by a virtual cathode whose surface coincides with an equipotential surface, so that the effect of the cathode on the distribution of the electrostatic potential is simulated as the effect of a finite charged wire that is located at the axis of the system. The separation of variables is used to solve the problem. The potential is represented as an expansion in terms of eigenfunctions, and the expansion coefficients are found from the solution to a system of linear algebraic equations.     

The Contributions of a Neutral Vector Boson to the Anomalous Moments of a Fermion in a Plane-Wave Field

The paper deals with the contributions of a neutral vector boson to the anomalous magnetic and to the electric moments (AMM and AEM, respectively) of a polarized fermion moving in a plane-wave electromagnetic field. The contributions are separated by the states of polarization of the fermion spin which allows an investigation of an important problem of the contributions to the anomalous moments of the fermion that result from the transition of the fermion to an intermediate state with or without spin flip.     

Elastic interaction between a dislocation and a near-by inclusion

The study of elastic interaction between a dislocation and an inclusion (i.e., a region transformed without change of elastic constants) in an elastic continuum is extended to the cases when the singular dislocation line intersects or touches the inclusion or is situated inside it. The interaction energy is shown to be a finite and continuous function of position of the inclusion. The interaction of an edge dislocation with a dilatation sphere and of a screw dislocation with a sphere transformed into ellipsoid in isotropic continuum are studied in detail. The spherical inclusion which is considered as a rough model of a point defect (e.g. of carbon atom in iron) has a maximum and minimum energy position near the dislocation line so that the binding energy can be calculated in a consistent way.     

Frequency bistability of a semiconductor laser under a frequency-dependent feedback

The emission frequency of a diode laser submitted to a frequency-dependent optoelectronic feedback is observed to have more than one stable operation point together with a stable power emission. This is, to our knowledge, the first observation of bistability exclusively in the frequency of an optical system. The experiment was carried out with a semiconductor laser coupled to the cesium D2 line by an orthogonally polarized frequency-sensitive optical feedback.     

Transport through a constriction in a FQH-annulus

The flux periodicity of thermodynamic properties of an annulus in the fractional quantum Hall state with a constriction is considered. It is found that -periodicity is obtained due to transfer of fractionally charged particles or composite fermions between the edges of the annulus, respectively. The result for the finite magnitude of the persistent current across a very strong constriction is presented, as obtained with an extension of Wen’s edge state theory.