Spin-dependent transport and spin polarization in coupled quantum wells

We theoretically investigate the electron transport and spin polarization of two coupled quantum wells with Dresselhaus spin-orbit interaction. In analogy with the optical dual-channel directional coupler, the resonant tunneling effect is treated by the coupled-mode equations. We demonstrate that spin-up and -down electrons can be completely separated from each other for the system with an appropriate system geometry and a controllable barrier. Our result provides a new approach to construct spin-switching devices without containing any magnetic materials or applying a magnetic field. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.2981204]

On exact boundary controllability for linearly coupled wave equations

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Cavity ring‑up spectroscopy for dissipative and dispersive sensing in a whispering gallery mode resonator

In whispering gallery mode resonator sensing applications, the conventional way to detect a change in the parameter to be measured is by observing the steady-state transmission spectrum through the coupling waveguide. Alternatively, sensing based on cavity ring-up spectroscopy, i.e. CRUS, can be achieved transiently. In this work, we investigate CRUS using coupled mode equations and find analytical solutions with a large spectral broadening approximation of the input pulse. The relationships between the frequency detuning, coupling gap and ring-up peak height are determined and experimentally verified using an ultrahigh Q-factor silica microsphere. This work shows that distinctive dispersive and dissipative transient sensing can be realised by simply measuring the peak height of the CRUS signal, which may improve the data collection rate.

Four-wave mixing self-stability based on photonic crystal fiber and its applications on erbium-doped fiber lasers

The analytic solutions of coupled-mode equations of four-wave mixings (FWMs) are achieved by means of the undepleted approximation and the perturbation method. The self-stability mechanism of the FWM processes is theoretically proved and is applicable to design a new kind of triple-wavelength erbium-doped fiber lasers. The proposed fiber lasers with excellent stability and uniformity are demonstrated by using a flat-near-zero-dispersion high-nonlinear photonic-crystal-fiber. The significant excellence is analyzed in theory and is proved in experiment. Our fiber lasers can stably lase three waves with the power ripple of less than 0.4 dB. (c) 2005 Elsevier B.V. All rights reserved.

Optimization and comparison of single- and dual-pump fiber-optical parametric amplifiers with dispersion fluctuations

Solutions for fiber-optical parametric amplifiers (FOPAs) with dispersion fluctuations are derived using matrix operators. On the basis of the propagation matrix product and the hybrid genetic algorithm, we have optimized and compared single- and dual-pump FOPAs with zero-dispersion-wavelength variations. The simulations prove that the design of FOPAs involves multimodal function optimization problems. The numerical results show that dual-pump FOPAs are highly sensitive to dispersion fluctuations whereas dispersion variations have less impact on the gain of single-pump FOPAs. To increase signal gain and reduce ripple, dual-pump FOPAs, instead of single-pump FOPAs, have to be carefully optimized with a suitable multisegment fiber structure rather than a one-segment fiber structure. The different combinations of multisegment fibers can provide highly different gain properties. The increase in gain is at the cost of the ripple.

Transient and nonlinear analysis of slow-light pulse propagation in an optical fiber via stimulated Brillouin scattering

We investigate slow-light pulse propagation in an optical fiber via transient stimulated Brillouin scattering. Space-time evolution of a generating slow-light pulse is numerically calculated by solving three-wave coupled-mode equations between a pump beam, an acoustic wave, and a counterpropagating signal pulse. Our mathematical treatments are applicable to both narrowband and broadband pump cases. We show that the time delay of 85% pulse width can be obtained for a signal pulse of the order of subnanosecond pulse width by using a broadband pump, while the signal pulse is broadened only by 40% of the input signal pulse. The physical origin of the pulse broadening and distortion is explained in terms of the temporal decay of the induced acoustic field. (C) 2009 Optical Society of America

Advanced fibre gratings and their applications

This thesis describes a detailed study of advanced fibre grating devices using Bragg (FBG) and long-period (LPG) structures and their applications in optical communications and sensing. The major contributions presented in this thesis are summarised below. One of the most important contributions from the research work presented in this thesis is a systematic theoretical study of many distinguishing structures of fibre gratings. Starting from the Maxwell equations, the coupled-mode equations for both FBG and LPG were derived and the mode-overlap factor was analytically discussed. Computing simulation programmes utilising matrix transform method based on the models built upon the coupled-mode equations were developed, enabling simulations of spectral response in terms of reflectivity, bandwidth, sidelobes and dispersion of gratings of different structures including uniform and chirped, phase-shifted, Moiré, sampled Bragg gratings, phase-shifted and cascaded long-period gratings. Although the majority of these structures were modelled numerically, analytical expressions for some complex structures were developed with a clear physical picture. Several apodisation functions were proposed to improve sidelobe suppression, which guided effective production of practical devices for demanding applications. Fibre grating fabrication is the other major part involved in the Ph.D. programme. Both the holographic and scan-phase-mask methods were employed to fabricate Bragg and long-period gratings of standard and novel structures. Significant improvements were particularly made in the scan-phase-mask method to enable the arbitrarily tailoring of the spectral response of grating devices. Two specific techniques - slow-shifting and fast-dithering the phase-mask implemented by a computer controlled piezo - were developed to write high quality phase-shifted, sampled and apodised gratings. A large number of LabVIEW programmes were constructed to implement standard and novel fabrication techniques. In addition, some fundamental studies of grating growth in relating to the UV exposure and hydrogenation induced index were carried out. In particular, Type IIa gratings in non-hydrogenated B/Ge co-doped fibres and a re-generated grating in hydrogenated B/Ge fibre were investigated, showing a significant observation of thermal coefficient reduction. Optical sensing applications utilising fibre grating devices form the third major part of the research work presented in this thesis. Several experiments of novel sensing and sensing-demodulating were implemented. For the first time, an intensity and wavelength dual-coding interrogation technique was demonstrated showing significantly enhanced capacity of grating sensor multiplexing. Based on the mode-splitting measurement, instead of using conventional wavelength-shifting detection technique, successful demonstrations were also made for optical load and bend sensing of ultra-high sensitivity employing LPG structures. In addition, edge-filters and low-loss high-rejection bandpass filters of 50nm stop-band were fabricated for application in optical sensing and high-speed telecommunication systems

Exact solutions of coupled multispecies linear reaction–diffusion equations on a uniformly growing domain

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Normal mode sound propagation in an ocean with random narrow-band surface waves

Normal mode sound propagation in an isovelocity ocean with random narrow-band surface waves is considered, assuming the root-mean-square wave height to be small compared to the acoustic wavelength. Nonresonant interaction among the normal modes is studied straightforward perturbation technique. The more interesting case of resonant interaction is investigated using the method of multiple scales to obtain a pair of stochastic coupled amplitude equations which are solved using the Peano-Baker expansion technique. Equations for the spatial evolution of the first and second moments of the mode amplitudes are also derived and solved. It is shown that, irrespective of the initial conditions, the mean values of the mode amplitudes tend to zero asymptotically with increasing range, the mean-square amplitudes tend towards a state of equipartition of energy, and the total energy of the modes is conserved.

A note on the effect of wall compliance on lowest?order mode propagation in fluid?filled/submerged impedance tubes

Wave propagation in fluid?filled/submerged tubes is of interest in large HVAC ducts, and also in understanding and interpreting the experimental results obtained from fluid?filled impedance tubes. Based on the closed form analytical solution of the coupled wave equations, an eigenequation, which is the determinant of an 8×8 matrix, is derived and solved to obtain the axial wave number of the lowest?order longitudinal modes for cylindrical ducts of various diameter and wall thickness. The dispersion behavior of the wave motion is analyzed. It is observed that the larger the diameter of the duct and/or the smaller its wall thickness, the more flexible the impedance tube leading to more coupling between the waves in the elastic media. Also, it is shown that the wave motion in water?filled ducts submerged in water exhibits anomalous dispersion behavior. The axial attenuation characteristics of plane waves along water?filled tubes submerged in water or air are also investigated. Finally, investigations on the sound intensity level difference characteristics of the wall of the air?filled tubes are reported.

Two-dimensional simulation of high-order laterally-coupled GaAs-AlGaAs DFB laser diodes

Laterally-coupled distributed feedback (LC-DFB) laser diodes made without an epitaxial re-growth process have the advantage of a simple fabrication process. In this paper, two-dimensional optical field distribution of the fundamental quasi TE (transverse electric) mode is calculated by means of a semivectorial finite-difference method (SV-FDM). The dependence of the effective coupling coefficient (kappa(eff)) on the dutycycle of first-, second- and third-order LC-DFB LDs is investigated using modified coupled wave equations.

Multi-mode approximations to wave scattering by an uneven bed

Approximations to the scattering of linear surface gravity waves on water of varying quiescent depth are Investigated by means of a variational approach. Previous authors have used wave modes associated with the constant depth case to approximate the velocity potential, leading to a system of coupled differential equations. Here it is shown that a transformation of the dependent variables results in a much simplified differential equation system which in turn leads to a new multi-mode 'mild-slope' approximation. Further, the effect of adding a bed mode is examined and clarified. A systematic analytic method is presented for evaluating inner products that arise and numerical experiments for two-dimensional scattering are used to examine the performance of the new approximations.

On a linear steady-state system of equations in microcontinuum fluid mechanics

Galerkin representations and integral representations are obtained for the linearized system of coupled differential equations governing steady incompressible flow of a micropolar fluid. The special case of 2-dimensional Stokes flows is then examined and further representation formulae as well as asymptotic expressions, are generated for both the microrotation and velocity vectors. With the aid of these formulae, the Stokes Paradox for micropolar fluids is established.

Convergence feedback and unstable low frequency oscillations in a simple coupled ocean‐atmosphere model

The role of convergence feedback on the stability of a coupled ocean‐atmosphere system is studied using model III of Hirst (1986). It is shown that the unstable coupled mode found by Hirst is greatly modified by the convergence feedback. If the convergence feedback strength exceeds a critical value, several new unstable intraseasonal modes are also introduced. These modes have very weak dependence on the wave number. These results may explain the behaviour of some coupled models and to some extent provide a mechanism for the observed aperiodicity of the El‐Nino and Southern Oscillation (ENSO) events.