Trapped modes in finite quantum waveguides

The eigenstates of an electron in an infinite quantum waveguide (e.g., a bent strip or a twisted tube) are often trapped or localized in a bounded region that prohibits the electron transmission through the waveguide at the corresponding energies. We revisit this statement for resonators with long but finite branches that we call ??finite waveguides??. Although the Laplace operator in bounded domains has no continuous spectrum and all eigenfunctions have finite L ₂ norm, the trapping of an eigenfunction can be understood as its exponential decay inside the branches. We describe a general variational formalism for detecting trapped modes in such resonators. For finite waveguides with general cylindrical branches, we obtain a sufficient condition which determines the minimal length of branches for getting a trapped eigenmode. Varying the branch lengths may switch certain eigenmodes from non-trapped to trapped or, equivalently, the waveguide state from conducting to insulating. These concepts are illustrated for several typical waveguides (L-shape, bent strip, crossing of two strips, etc.). We conclude that the well-established theory of trapping in infinite waveguides may be incomplete and require further development for applications to finite-size microscopic quantum devices.     

Polariton propagation in coupled quantum wire waveguides

The propagation of the excitonic polariton along the directional coupler consisting of adjacent parallel GaAs quantum-wire waveguides is simulated by using a finite element method. It is found that the coupling length is as short as 2.5-4 μm, which is three orders of magnitude shorter than the conventional optical directional coupler made of bulk GaAs. Such short coupling length will make it possible to fabricate extremely small optoelectronic devices such as directional-coupler-type switches.     

Guided modes in chiroplasma-filled perfect electromagnetic conductor parallel-plate waveguides

Theoretical analysis of electromagnetic wave propagation in a perfect electromagnetic conductor (PEMC) parallel-plate waveguide filled with a chiroplasma material is presented in this article. The derived formulations are general and can analyze perfect electric, perfect magnetic, or PEMC waveguides filled with any general isotropic/anisotropic material including plasma and metamaterials. The characteristic equation for the modes in this waveguide is obtained, and the behavior of the dispersion curves and the energy flux are examined and evaluated numerically. The results demonstrate that the chirality parameter, the plasma frequency, and the cyclotron frequency influence the behavior of the energy flux transported in the guide, in magnitude and orientation. The bifurcated mode cutoff frequencies are sensitive to the variations in the filling material parameters and likewise effected by the variations in the PEMC walls admittance parameter.     

任意截面介质波导导模的叠代矩量法分析

本文提出用以计算任意截面介质波导色散关系的叠代矩量法,并给出用叠代矩量法计算椭圆介质波导、三角形波导、平切圆波导、蛋形截面波导等的传播特性的实例.计算结果与有限元法、点匹配法等精确数值计算结果符合很好.本方法简便易行,计算工作量较小.     

Transverse electromagnetic modes in aperture waveguides containing a metamaterial with extreme anisotropy

We use metamaterials with extreme anisotropy to solve the fundamental problem of light transport in deep subwavelength apertures. By filling a simply connected aperture with an anisotropic medium, we decouple the cutoff frequency and the group velocity of modes inside apertures. In the limit of extreme anisotropy, all modes become purely transverse electromagnetic modes, free from geometrical dispersion, propagate with a velocity controlled by the transverse permittivity and permeability, and have zero cutoff frequency. We analyze physically realizable cases for a circular aperture and show a metamaterial design using existing materials.     

Excitons in quantum well wires: V-shaped wire,T-shaped wire and strain-induced lateral confinement

Il Nuovo Cimento D - We calculated the energy and the wave function of the exciton for i) a V-shaped quantum wire, ii) a T-shaped quantum wire and iii) a quantum wire resulting from strain-induced...     

Optical phonon modes in a free-standing quantum wire with ring geometry

The confined longitudinal-optical (LO) phonon and surface-optical (SO) phonon modes of a free-standing quantum wire with ring geometry are discussed within the dielectric continuum (DC) approximation. Two branches of SO phonon modes have been investigated. The frequencies of the SO phonons are found to be dispersed and radius dependent for small size systems. When the wave vector qz→∞, the frequencies of each SO modes converge to the frequency values of the single planar heterostructure.     

Dispersion and lifetimes of electromagnetic modes attached to strongly textured slab waveguides

The influence of strong, two-dimensional (2D) periodic texture on the dispersion and lifetimes of resonant electromagnetic modes localized in the vicinity of thin (80 to 155 nm) GaAs membranes supported on thick (1 to 2 m) wet-oxidized AlAs cladding layers is reported. A method of extracting this information by fitting Fano-like features in broadband specular reflectivity spectra is described in detail, and applied to samples containing both triangular and square 2D lattices. A new and easier method of probing the properties of these modes is also demonstrated. It involves incorporating a superlattice of defects in the principal crystal lattice, and monitoring the defect diffraction spectrum, rather than the specular reflectivity.     

Group velocity of modes and pulse distortion in dielectric optical waveguides

After a brief summary of the main factors causing pulse distortion in optical fibres, expressions are derived for phase velocity, group velocity and dispersion, that is velocity variation with frequency, of each mode. The analysis is carried out by making extensive use of the functiony(x) (y andx being the arguments of the first and second kind Bessel functions that appear in the solutions of Maxwell equations), that we call characteristic function. By using this function we obtain particularly simple and compact formulas that make easier the analysis of the behaviour of velocity and dispersion near and far from cut-off. It will also be seen that the ratio between the power propagating in the core,W ₁, and the power in the cladding,W ₂, for each mode takes a very simple form if expressed by means of the characteristic function: this fact permits a direct relation to be found between group velocity and power flow in an optical fibre. The study of the ratioW ₁/W ₂ will show that, contrary to expectation, for some modes, a substantial fraction of energy travels inside the core, even near cut-off. Expressions are given forW ₁/W ₂ at cut-off, and far from cut-off. Plots of velocity and dispersion are shown. On the grounds of the obtained results pulse distortion in optical fibres is discussed.     

Thermal conductance associated with six types of vibration modes in quantum wire modulated with quantum dot

We study the ballistic phonon transport and thermal conductance of six low-lying vibration modes in quantum wire modulated with quantum dot at low temperatures. A comparative analysis is made among the six vibrational modes. The results show that the transmission rates of the six vibrational modes relative to reduced frequency display periodic or quasi-periodic oscillatory behavior. Among the four acoustic modes, the thermal conductance contributed by the torsional mode is the smallest, and the thermal conductances of other acoustic modes have adjacent values. It is also found that the thermal conductance of the optical mode increases from zero monotonously. Moreover, the total thermal conductance in concavity-shaped quantum structure is lower than that in convexity-shaped quantum structure. These thermal conductance values can be adjusted by changing the structural parameters of the quantum dot.     

Exact transcendental equation for scalar modes of rectangular dielectric waveguides

Conclusion A Fourier operator method has been used to derive for the first time an exact closed-form eigenvalue equation for the scalar mode propagation constants of a buried rectangular dielectric waveguide. The new method has been implemented and the results used to determine the accuracy of the scalar finite-difference approach. It is hoped that the exact results obtained here may assist in the validation of the accuracy of the other numerical and semi-analytical methods.     

Coupled surface polariton with guided wave polariton modes in asymmetric metal clad dielectric waveguides

It is emphasized that in metal-dielectric layered systems with a thin metallic layer, surface plasmon-polaritons (SP) can couple with guided wave polaritons (GWP) and form new hybrid modes with properties of both SP and GWP. This is illustrated by analyzing the properties of electromagnetic modes in an asymmetric metal-clad-dielectric-slab waveguide and their dependence on the thickness of metal cladding.     

Natural electromagnetic modes of a resonator formed by cutoff waveguides

A spectral three-dimensional problem is solved to determine the resonant frequencies of a branch formed by the orthogonal intersection of cutoff rectangular waveguides. Expressions for the H _mng and E _mng modes are derived and analyzed. Two classes of free nonradiating modes typical of this structure are identified and analyzed. Numerical calculations are made of the dispersion relations obtained for the different modes. Zh. Tekh. Fiz. 69, 84–88 (April 1999)     

Some characteristics of resonant electromagnetic modes in a dielectric sphere

A set of formulae have been developed for calculations of the optical characteristics of droplets under conditions of whispering gallery mode (WGM) excitation. The WGM excitation is shown to cause the ripple structure in the Mie extinction cross section. The Chýlek equation for the distance between two neighboring morphology-dependent resonances (MDRs) in a spectrum has been revised. The equation is presented for the spherical-resonator finesse allowing for light scattering on inhomogeneities of the resonator surface, etc. A comparison of the theory and data in the literature is made and some peculiarities of spectra are explained.     

Vector modes of rectangular-core dielectric waveguides: An improved perturbation approach

We present an improved analysis to obtain vector modes of a rectangular-core waveguide (RCW) structure whose dielectric constant profile is separable in x and y coordinates. Using this analysis, a perturbation method is then developed to obtain vector modes of a practical RCW. The propagation constants so obtained for a fully-buried and a ridge RCW structure using the present analysis are found to be in better agreement with reported numerical values than the ones obtained with an earlier reported perturbation approach [Kumar et al., Opt. Lett. 8 (1983) 63].     

利用电介质柱共振器实现电磁响应模式可转变的电磁超介质

本文利用电磁场数值计算方法研究了横截面具有不同长宽比例的电介质柱的电磁共振模式,发现横截面长宽比例影响电介质柱共振模式的激发顺序.截面长宽比小于2.2时,首先激发磁共振模式;而长宽比大于2.2时,磁共振模式在第二个共振被激发;作为转折点,截面长宽比例约为2.2的电介质柱不能激发磁共振模式.结果还表明改变电磁波入射方向可以调节长方形截面的电介质柱的磁共振发生的频率位置,实现偏振可控的电磁响应,这为新颖的电介质电磁超介质的设计与研究提供有价值的信息. 关键词： 电介质 电磁超介质 共振     

太赫兹电磁场照射下量子线中的纳米电子力

研究两端连接电子库的量子线在太赫兹(THz)电磁场横向辐射下的电子力学问题. 在自由电子近似下求得了弹道区二能级电子波函数解析表达式,发现电子概率在两个能态间随线轴坐标作Rabi振荡, 其幅度与外场强度和频率有关. 利用热力学统计算符方法并利用波函数计算出了传导电子对量子线中张力贡献的大小. 其计算结果可表示成与外场无关和与外场有关的两部分之和,前者与已有的实验观测和理论计算结果一致, 而与外场参量有关的部分可用量子相干理论解释. 关键词： 量子线 THz电磁场 纳米电子力