Quasi-bound states determination using a perturbed wavenumbersmethod in a large quantum box

A perturbed wavenumbers method (PWM) is presented that is capable of determining the quasi-bound-state eigenenergies and their lifetimes for quantum heterostructures having arbitrary potential profiles. The numerical method presented solves the single-band effective-mass Schrodinger equation without using complex energies. It is applicable to quantum structures that are symmetric, asymmetric, unbiased, or biased. For multiple quantum heterostructures, extensive comparisons of this numerical method with other currently used techniques are included. In addition, a modified density of states formulation is presented and applied to these example cases     

Efficient solution of eigenvalue equations of optical waveguidingstructures

A general numerical method is presented that is capable of extracting all the zeros of a complex equation. This method allows accurate determination of the complex propagation constants of general multilayer optical and microwave planar waveguides, the computation of energy states and their lifetimes of semiconductor heterostructures, and the roots of complex transcendental equations from other scientific disciplines. The method differs from previous approaches in that the time-consuming differentiation of the complex function is not required. Furthermore, the present method is not affected by the presence of complex poles and so can be used for the solution of meromorphic transcendental equations. In practice, the method is found to be much faster than other rigorous approaches     

A novel numerical technique for solving the one-dimensionalSchroedinger equation using matrix approach-application to quantum wellstructures

A numerical technique that allows straightforward determination of bound-state and quasi-bound-state energy eigenvalues (and lifetimes of the latter) for arbitrary one-dimensional potentials is presented. The method involves straightforward multiplication of 2×2 matrices and does not involve any iterations. The applicability of the technique to analysis of the quantum-well structures is also shown. Since the Schroedinger equation for a spherically symmetric potential can be transformed to a one-dimensional equation, all such problems can also be solved using this method     

Resonance in a superstrate-loaded cylindrical-rectangularmicrostrip structure

The complex resonant frequencies of the cylindrical-rectangular microstrip structure loaded with a dielectric superstrate layer is studied using a rigorous full-wave analysis, and the numerical results are obtained using the Galerkin moment method calculation. The numerical convergence for the selected sinusoidal basis functions with and without the edge singularity condition is also discussed. Numerical results for the dependence of the real and imaginary parts of the complex resonant frequencies on the superstrate permittivity and thickness are calculated and analyzed, and are compared with those obtained for the planar microstrip structure     

Polynomial factorization using the routh criterion

A method is presented for polynomial factorization using a search method. The method used is to search for real parts of roots by iteratively applying the Routh test to a shifted polynomial. Imaginary parts of roots are found in a similar manner after using some polynomial manipulations to convert imaginary parts of the roots of the original polynomial to real parts in a new polynomial. Real and imaginary parts can then be paired. Experimental results indicate that the method is competitive with several common algorithms on both the accuracy and the computation time basis.     

High-frequency base-transport factor and transit time of graded-base transistors

Closed expressions are derived for the modulus and argument, as well as for the real and imaginary parts of the complex base-transport factor (β) of diffusion and uniform drift-field transistors. Since these expressions involve only trigonometric, exponential, and hyperbolic functions, they are suitable for straightforward numerical computation as well as theoretical analysis. The variation of computed β-cutoff parameters as a function of impurity concentration is illustrated graphically and shown to be in good agreement with an approximate relation between the β-cutoff frequency and transit time due to Moll and Ross.     

Widely-linear selected mapping for peakto-average power ratio reduction in OFDM

Peak-to-average power ratio reduction in OFDM using selected mapping (SLM) is considered. A new low-complexity version of SLM is introduced which employs the principle of widely-linear signal processing, i.e. real and imaginary parts of the candidate OFDM frames are treated separately. Thereby, investing the numerical complexity of conventional SLM with U candidates, a performance almost equal to U candidates can be obtained with widely-linear SLM. Numerical simulations cover this performance.     

On the application of complex resistive boundary conditions tomodel transmission lines consisting of very thin superconductors

A resistive boundary condition for the case where the resistivity is assumed to be a complex quantity is shown to be an accurate model for a superconducting film which is thin compared to the super-conducting penetration depth. The imaginary part of the conductivity is the dominant terms and is a measure of the inductive energy stored in the superconductor. Numerical solutions of superconducting microstrip are obtained and compared to experimental results and to analytic solutions for superconducting parallel-plate waveguides. Excellent agreement is found between experimental, analytical, and numerical results     

Band-Limited Deconvolution of Locating Reflectometer Results

The locating reftectometer is a frequency-swept microwave instrument which, by analog Fourier transformation, converts the reflection coefficient, a function of frequency Gamma(s), into the spatial distribution of the reflection coefficient Gamma(x). It will be shown that by the method of deconvolution an increase in axial resolution may result. By making use of the fact that the real and imaginary parts of the "locating plot" Gamma(x) are a Hilbert transform pair, a signal-to-noise ratio improvement is achieved by averaging the results of complex deconvolution using only the real and then only the imaginary parts of the locating plots. A number of experimental results are given, illustrating the increase in axial resolution when the method of band-limited deconvolution is applied to some typical waveguide components and obstacles.     

Scattering of electromagnetic waves by rough perfectly conducting circular cylinders

A numerical method is proposed for computing the normalized correlation functions of the real and imaginary parts of the field scattered from a statistically rough perfectly conducting circular cylinder. The deviation of the surface from its mean radius is assumed to be small. The correlation function of the far-field is related to the correlation function of the scattering object by an integral equation. Far-field correlation functions are found for two types of surface correlation functions: the delta function and a periodic exponential function.     

A computational Fourier series solution of the BenDaniel-DukeHamiltonian for arbitrary shaped quantum wells

A new technique for solving the BenDaniel-Duke Hamiltonian using a Fourier series method is discussed. This method Fourier transforms the effective mass and potential profiles to calculate the eigenenergies and probability densities in transform space. Numerical solutions of the eigenenergies of a rectangular quantum well are compared to the finite difference, finite element, and transfer matrix methods. The eigenenergies of the envelope functions are computed and compared to the exact case made under a constant effective mass approximation for an asymmetric triangular and parabolic shaped quantum well. The necessity of using a variable effective mass in the BenDaniel-Duke Hamiltonian is shown by a comparison of the eigenenergies in the constant and variable effective mass cases. The Fourier series method is then used to analyze the effects of compositional gradients and electric fields on the eigenenergies and envelope functions for asymmetric coupled asymmetric triangular quantum wells     

Calculated fiber attenuation: a general method yielding stationaryvalues

A method of calculating the attenuation constant of an optical fiber under very general but weakly guiding conditions is derived. The method, based on Galerkin's formalism, allows a nonuniform and complex refractive-index profile. The real and imaginary parts of the refractive index are allowed to vary independently and arbitrarily as a function of radius. The result is the predicted complex propagation constant. The results are inherently stationary     

Debye Function Expansions of Complex Permittivity Using a Hybrid Particle Swarm-Least Squares Optimization Approach

With appropriate modifications, the finite-difference time-domain (FDTD) method can be used to analyze propagation through linear isotropic dispersive media. Although materials characterized by the Debye permittivity model can be analyzed accurately and efficiently using well established methods, the treatment of other types of frequency dependence is more difficult. This paper proposes the use of a weighted sum of Debye functions to approximate more general complex permittivity functions. A combination of the particle swarm optimization method and linear least squares optimization is used to find the relaxation frequencies and weights in the expansion, which can then be accommodated in the FDTD method using one of the established methods. Two key advantages of the proposed approach are that the relaxation frequencies are bandlimited and the weights are always positive. These two characteristics help to maintain the accuracy and stability of the FDTD solution. It is also shown that the correlation between the imaginary parts of two Debye functions is the same as that between the real parts.     

Studies of mixing formulae in the complex plane

Remote sensing signal monitoring is considered. Mixing rules that have been introduced to explain the permittivity of mixtures by analytically continuing these to the whole complex plane are discussed. Equipermittivity curves for both the real and imaginary parts of the mixture dielectric constant (the imaginary part of the permittivity is a measure for the dielectric losses) are studied. These form a map on the complex plant, illustrating the nature of a mixing rule better than the classical way of presenting the mixture permittivity as a function of the volume fraction of a component in the mixture. These maps naturally vary for a given mixing rule as the volume fraction is changed, but, in principle, the structure is the same. The resulting illustrations show that certain mixing formulae can be conceived as a continuum that gradually changes from the Maxwell-Garnett formula through Polder-van Santen and coherent potential formulas to the so-called exponential formulas     

一种基于复数相位屏的强激光大气传输仿真方案

针对传统实数相位屏法中只能表征湍流扰动而不能综合表征强激光在大气传输时导致的能量衰减、湍流扰动和非线性热晕效应等困难,提出一种基于复数相位屏表征的强激光大气传输仿真方案.该方案采用复数相位屏的实部和虚部分别表征衰减和湍流、热晕作用,其中基于能见度特征综合描述大气吸收和散射的衰减作用(复数相位屏的虚部),基于流体力学的密...     

基于复数网络与注意力机制的信号调制识别

通信信号调制识别作为管理、监测电磁频谱的重要手段,具有重要的研究价值和应用前景。本文利用调制信号的频域信息,提出一种基于复数神经网络的信号调制识别方法。首先将I、Q两路信号组合成复信号,经过快速傅里叶变换(FFT)后把得到的实部和虚部组合起来作为输入网络的数据集。其次,设计了一种复数神经网络结构,并引入了注意力机制对网络结构进行改良。仿真结果表明,本文提出的方法可以有效识别9种调制方式,在信噪比为6 dB时,平均正确识别率达到96.33%。     

Quantum Bayes estimation of the amplitude of a coherent signal (Corresp.)

The complex amplitude of a coherent quantum signal in the presence of thermal noise is to be estimated when its real and imaginary parts have a Gaussian prior distribution. Cost functions of Gaussian, power-law, and delta-function forms are shown all to lead to the same optimum estimator.     

Complex-correlation radiometer

The correlation between the signals from the two antennas in a radio interferometer can be described by a complex correlation function. The real and imaginary parts of this function can be measured by a radiometer using two feedback loops to control four noise sources,B_{pr}(positive, real),B_{nr}(negative, real),B_{pi}(positive, imaginary), andB_{ni}(negative, imaginary). Theoretical analysis shows the system to be stable against amplifier gain fluctuations, and against moderate fluctuations in the phase shifts of the two amplification channels which are included in the system. Experimental verification is described in a following paper by Hubbard and Erickson [2].     

矩形波导中径向线阻抗变换器的严格场分析

由于径向线阻抗变换器(RLT)具有宽频带高变比特性,在毫米波振荡器中经常被用作有源器件和外电路之间的匹配器.本文将模式展开、Galerkin和配置法相结合给出了一种分析RLT的混合方法,并首次给出了阻抗虚部的准确收敛结果和Q波段及W波段的阻抗特性曲线。