Optical waveguide analysis using modified Airy functions

We review a little-used but powerful method of solving the scalar wave equation. It uses a modification of the well-known Airy functions, which are easily calculated on desktop computers. The techniques are reminiscent of the WKBJ methodology, but the solution, although approximate, is much more useful than the traditional WKBJ solution and can be used with almost as much ease. Re method is extremely powerful but, to our knowledge, is not used in the optics community. It is useful in analyzing integrated optical waveguide components.     

一维双方势垒量子隧穿的研究及其数值模拟

量子隧穿效应在实际技术中具有重要应用,本文首先展示了如何求解一维任意边界非对称以及对称双方势垒的透射系数,然后研究了对称双方势垒透射系数对垒宽、垒间距以及微观粒子入射能量与垒高比值(E/U 0)的变化依赖关系.最终得出以下结论,随着双方势垒垒宽的增加,透射系数从最大值1衰减至最小值0.随着垒间距的增加,透射系数呈现周期振荡,本文首次推导得出透射系数最大时对应的垒间距解析表达式,并给出振荡的周期,进一步证明得到它等于微观粒子的德布罗意波长.当垒宽越小时,随着E/U 0的增大,透射系数更容易达到1,并且保持不变,当垒间距越大时,随着E/U 0的增大,透射系数振荡周期变大,而振幅变小,粒子更容易实现共振隧穿.     

Uniform light emission from electrically driven plasmonic grating using multilayer tunneling barriers

Light emission by inelastic tunneling(LEIT)from a metal-insulator-metal tunnel junction is an ultrafast emission process.It is a promising platform for ultrafast transduction from electrical signal to optical signal on integrated circuits.However,existing procedures of fabricating LEIT devices usually involve both top-down and bottom-up techniques,which reduces its compatibility with the modern microfabrication streamline and limits its potential applications in industrial scale-up.Here in this work,we lift these restrictions by using a multilayer insulator grown by atomic layer deposition as the tunnel barrier.For the first time,we fabricate an LEIT device fully by microfabrication techniques and show a stable performance under ambient conditions.Uniform electroluminescence is observed over the entire active region,with the emission spectrum shaped by metallic grating plasmons.The introduction of a multilayer insulator into the LEIT can provide an additional degree of freedom for engineering the energy band landscape of the tunnel barrier.The presented scheme of preparing a stable ultrathin tunnel barrier may also find some applications in a wide range of integrated optoelectronic devices.     

Derivation of an optical potential for deuterons

A general interpolation scheme is described which allows to determine the different eigenvaluesE _n(κ) for a given value of κ by solving an eigenvalue problem of small rank. The elements of the corresponding matrix, not yet restricted by symmetry requirements, may be determined from calculated energy valuesE _n (κ) along the directions of high symmetry. In addition for different bands connected with one another a new set of Wannier functions is defined.     

Quantum tunneling: A general study in multi-dimensional potential barriers with and without dissipative coupling

Quantum tunneling is formulated in terms of the time evolution of a localized state and thus shown to be dependent upon the eigenspectrum of the system Hamiltonian. A number of exactly solvable models with local and non-local double-well potentials are discussed, and it is shown how, for local potentials, other solvable models can be generated by using Gelfand-Levitan and Darboux transformations. Tunneling in multi-dimensional potential barriers is investigated under semi-classical approximation by developing the method of asymptotic expansion of the wave function for large quantum numbers and the WKB approximation for separable systems. General expressions for the imaginary-time tunneling trajectory are obtained in both methods and specific applications are discussed. Approximation schemes for non-separable systems are also presented. A general study of dissipative multi-dimensional tunneling is carried out by using the Gisin equation, the Schrödinger-Langevin equation and the complex potential model. It is shown that, in general, different models of dissipation are not equivalent in the tunneling context. Using these models one can show (a) the existence of critical damping beyond which no tunneling can occur, (b) that tunneling trajectories are dependent on the damping constant and (c) that dissipation may stabilize the excited state rather than the ground state. Finally the tunneling time delay in one-dimensional systems for undamped and for dissipative systems is formulated in terms of the phase shift, and this has been used to show that the effect of damping on the time delay is ignorable.     

A general modelling method for functionally graded materials with an arbitrarily oriented crack

In order to analytically solve crack problems regarding functionally graded materials (FGMs), some ideal assumptions are often made. They are: (1) the properties of FGMs are usually assumed to be described by very particular functions; (2) the crack is assumed to be vertical to (or parallel to) the gradient of FGMs. However, these assumptions may not be practical for actual FGMs. Since the controlling differential equations with general mechanical properties are very difficult to solve and the arbitrarily oriented crack causes great trouble in the analytical procedure, a general piecewise-exponential model (GPE model) is proposed to investigate the fracture behaviour of FGMs with general mechanical properties and an arbitrarily oriented crack. “General mechanical properties” means that the mechanical properties in the GPE model are not required to be very particularly pre-defined functions but arbitrary functions determined by fitting the experimental results of FGMs. The studied FGMs are divided into some sub-layers with each layer’s properties varying exponentially so that the general mechanical properties can be approximated by a series of exponential functions and hence the stresses and displacements of each layer which may contain a mixed-mode crack can be solved analytically. By use of integral transform methods, principle of superposition, residual theorem and theory of singular integral equations, the mixed-mode crack problem can be turned into solving a group of singular integral equations from which mixed-mode stress intensity factors (SIFs) can be obtained. Finally, the influences of the nonhomogeneous and geometric parameters on the mixed-mode SIFs are analysed.     

Fundamental view on the calculation of internal partition functions using occupational probabilities

From first principles, the author gathers a few general rules that need to be abided by in the calculation of the internal partition functions (IPFs) of individual molecules. These rules are violated in many schemes in the literature where occupational probabilities are used including those using the Planck–Larkin partition function (PLPF) within the chemical picture. Considering these rules is useful from conceptual and practical points of view. A solution is introduced to assure fulfilling the above mentioned rules when using occupational probabilities. Sample calculations are performed showing quantitative significance of inaccuracies caused by dishonoring such rules.     

Transmission times of wave packets tunneling through barriers

The transmission of wave packets through barriers by tunneling is studied in detail by the method of quantum molecular dynamics. The distribution of the arrival times of a tunneling packet in front of and behind a barrier and the momentum distribution function of the packet are calculated. The average position and average momentum of the packet and their spread are investigated. It is found that below the barrier a part of the packet is reflected, and a Gaussian barrier increases the average momentum of the transmitted packet and its spread in momentum space. Zh. éksp. Teor. Fiz. 115, 1872–1889 (May 1999)     

Spin-dependent tunneling in nanostructures consisting of magnetic barriers

We study the spin-dependent transport properties of the nanostructures consisting of realistic magnetic barriers produced by the deposition of ferromagnetic stripes on heterostructures. It is shown that, only in the nanostructures with symmetric magnetic field with respect to the magnetic-modulation direction, electrons exhibit a considerable spin-polarization. It is also shown that the degree of the electron spin polarization is greatly dependent on the ferromagnetic stripe and its position relative to the 2DEG. A much larger electron-spin polarization can be obtained by properly fabricating the ferromagnetic stripe and by adjusting its distance above the 2DEG. Received 27 December 2001 and Received in final form 13 March 2002 Published online 25 June 2002     

General correlation functions of the Clauser-Horne-Shimony-Holt inequality for arbitrarily high-dimensional systems

We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to arbitrarily high-dimensional systems. Based on this generalization, we construct the general CHSH inequality for bipartite quantum systems of arbitrarily high dimensionality, which takes the same simple form as CHSH inequality for two dimensions. This inequality is optimal in the same sense as the CHSH inequality for two-dimensional systems, namely, the maximal amount by which the inequality is violated consists of the maximal resistance to noise. We also discuss the physical meaning and general definition of the correlation functions. Furthermore, by giving another specific set of the correlation functions with the same physical meaning, we realize the inequality presented by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)]].     

The dynamical image potential for tunneling electrons

The exchange-correlation (XC) potential (image potential) felt by an electron tunneling from a metal through a classically forbidden region into vacuum is calculated by a Green's function technique. The resulting XC-potential reduces to the classical image potential if x, where $\text{x}\textcolor{red}{}\text{2}\text{m}\text{ω}{}_{\mathrm{s}}\text{κ}$ and $\text{κ = {2}\text{m}\text{(}\text{V}\text{?ω)}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, is large. For small x dynamical corrections to the classical result become important.     

Derivation of the effective potential

A simple derivation of the effective potential for single and composite operators is given. Green functions under general constraints are considered and compact expressions for derivatives of the effective potential are given.     

推导粒子数态波函数的厄米多项式算符法

引入厄米多项式算符并用其正规乘积展开式推导出了粒子数态|n〉在坐标表象和动量表象下的波函数,并由此得出了坐标和动量本征态的福克(Fock)表示形式,这是一个简洁而全新的推导方法.     

Resonant tunneling of a few-body cluster through repulsive barriers

A model for quantum tunnelling of a cluster comprised of A identical particles, interacting via oscillator-type potential, through short-range repulsive barrier potentials is introduced for the first time in symmetrized-coordinate representation and numerically studied in the s-wave approximation. A constructive method for symmetrizing or antisymmetrizing the (A ? 1)-dimensional harmonic oscillator basis functions in the new symmetrized coordinates with respect to permutations of coordinates of A identical particles is described. The effect of quantum transparency, manifesting itself in nonmonotonic resonance-type dependence of the transmission coefficient upon the energy of the particles, their number A = 2, 3, 4 and the type of their symmetry, is analyzed. It is shown that the total transmission coefficient demonstrates the resonance behavior due to the existence of barrier quasi-stationary states, embedded in the continuum.     

Derivation of reference distribution functions for Tokamak-plasmas by statistical thermodynamics

A general approach for deriving the expression of reference distribution functions by statistical thermodynamics is illustrated, and applied to the case of a magnetically confined plasma. The local equilibrium is defined by imposing the minimum entropy production, which applies only to the linear regime near a stationary thermodynamically non-equilibrium state and the maximum entropy principle under the scale invariance restrictions. This procedure may be adopted for a system subject to an arbitrary number of thermodynamic forces, however, for concreteness, we analyze, afterwords, a magnetically confined plasma subject to three thermodynamic forces, and three energy sources: (i) the total Ohmic heat, supplied by the transformer coil; (ii) the energy supplied by neutral beam injection (NBI); and (iii) the RF energy supplied by ion cyclotron resonant heating (ICRH) system which heats the minority population. In this limit case, we show that the derived expression of the distribution function is more general than that one, which is currently used for fitting the numerical steady-state solutions obtained by simulating the plasma by gyro-kinetic codes. An application to a simple model of fully ionized plasmas submitted to an external source is discussed. Through kinetic theory, we fixed the values of the free parameters linking them with the external power supplies. The singularity at low energy in the proposed distribution function is related to the intermittency in the turbulent plasma.     

Photoluminescence of InAs quantum dots embedded in graded InGaAs barriers

The effects of the top barrier and the dot density on photoluminescence (PL) of the InAs quantum dots (QDs) sandwiched by the graded In_xGa_1−xAs barriers grown by metal-organic vapor phase epitaxy (MOVPE) have been studied. Two emission peaks corresponding to the ground state and the 1st excited state transitions of the QD structures have been observed, which matches well to the theoretical calculation. The PL emission linewidth and intensity of the InAs QDs structure are improved by reducing the Indium/Gallium composition variation of the graded In_xGa_1−xAs top barrier layer of the structure. The QDs’ ground states filling excitation power depends on the crystal quality of the InGaAs barrier layer and the QD density. The extracted thermal activation energy for the QDs’ PL emission is sensitive to the QD size.