Electromagnetic propagation in a curved two-dimensional waveguide

Abstract

Fields due to an electromagnetic wave propagating in a long irregular two-dimensional waveguide are calculated efficiently, using the method of left-right splitting to solve the coupled integral equations. Results are compared with those obtained from independent ray-theoretic calculations and give very close agreement. The approach has previously been applied to rough surfaces at low angles of incidence; here it is found to converge rapidly for surface slopes of 30°, and after a few iterations for incident angles up to 60° from grazing.     

Electron transport through curved two-dimensional quantum waveguide

This paper details the study of electron transport through a two-dimensional curved quantum waveguide. The curvature of the quantum waveguide is found to greatly affect the transport properties. It is shown that no evanescent mode exists when the inner radius of the curved part of the waveguide is zero. Also, this paper details how localized modes with energy below the Fermi energy can be formed in the curved part due to curvilinear effects. A series of Fano-resonance type dips of the transmission coefficient appear because of the presence of localized modes. Due to the quantum effect, the transmission coefficient and the traversal time increase nonlinearly with the curved angle θ₀${\theta }_0$. This nonlinear property is destroyed as the radius increases.     

Electromagnetic waves propagation in real multimode waveguide structures

A power flow equation describing the power flow of electromagnetic waves in a real multimode waveguide represented by a linear multichannel trasmission system exhibiting an attenuation, dispersion, and an interchannel interaction is solved in three iterative ways. In the case of constant attenuation and constant propagation velocities in all channels and for the convolution interchannel interaction, a closed analytical solution of the problem is presented. Interesting forms of the solution, transfer function, and impulse response of the system which enable us to separate and compare the attenuation, dispersion, and coupling effects independently of each other are derived. The transfer function, the impulse response, and excitation conditions for their measurements are further discussed. Relations which make it possible to compare different experimental data obtained under specific excitation conditions in various laboratories are determined. Finally, a linear system with memory in time is studied and it is shown that the real multimode waveguide as a linear multichannel transmission system can be considered as a general linear system with memory in space.     

Sound propagation in two-dimensional waveguide with circular wavefront

Sound propagation through a waveguide is generally modeled by the Webster horn equation which assumes a planar pressure wavefront. However, most of the sources are non-planar in nature. In this work, a 1-D model is derived for sound propagation through a 2-D waveguide with circular wavefront. The model is derived from the 2-D Helmholtz equation using the weighted residual method. The model assumes a uniform pressure across the angular coordinate at a given radial distance. A 2-D finite element model is used to validate the results for different waveguide geometries and it shows good agreement.     

Electromagnetic wave propagation in a rectangular waveguide partially loaded with magnetized planar ferrite

The propagation of electromagnetic waves in a rectangular waveguide containing a slab of transversely magnetized planar ferrite is investigated. Numerical results indicate a large differential phase shift on application of small magnetic fields when the easy plane is oriented normal to the waveguide axis. This suggests the possibility of application in ‘Remanence Operation’ at high frequencies. Work partially supported by CSIR (India).     

二维三角晶格光子晶体波导的出射光集束传播

为了解决光子晶体波导出射端光场控制, 同时解决二维三角晶格光子晶体波导出射光辐射困难的问题。利用二维三角晶格光子晶体设计了一种新型光子晶体波导出射口结构。在二维三角晶格光子晶体波导出射端引入两个微腔, 通过光波与微腔发生共振, 形成类似于三个点光源干涉的出射光, 同时进一步提出波导出射端喇叭口干涉出射光定向辐射的设计。通过这种微腔喇叭口设计, 利用时域有限差分法分析结果表明光波实现很好的定向辐射, 并且辐射距离显著提高。     

Conductivity of a two-dimensional curved microconstriction

The quantum conductance of a long two-dimensional curved microconstriction has been considered theoretically. It is shown that over-the-barrier-reflection of electrons at points in which the curvature of the surface is changed, results in fine structure of quantum steps of the conductance. The observation of this structure would be a demonstration of the influence of the curvature on the quantum properties of two-dimensional electrons.     

Nonlinear oscillatory waveguide propagation in a plasma

The presence of an intense Gaussian laser beam gives rise to a ponderomotive force on electrons in a collisionless plasma, leading to a redistribution of electron density along the wave-front and consequently to an intensity dependent dielectric constant which saturates with increasing intensity. The intensity dependent dielectric constant is responsible for beam propagation in an oscillatory waveguide. It is seen that (i) a beam of radiusr ₀ less thanr _0min (?c/ω _p) cannot be focused in the plasma regardless of its power, (ii) minimum dimension of oscillatory waveguide increases with increasing power of the beam. Similar results are also obtained for collisional plasma where nonlinearity arises due to nonuniform heating and consequent redistribution of carriers.     

二维平板光子晶体直波导的制备和光传输特性的测量

利用聚焦离子束刻蚀的方法在SOI(silicon on insulator)基片上制备了W3型二维光子晶体直波导.观察并测量了近红外激光通过光子晶体波导的散射图形和透过谱.实验结果说明，激光在有引入引出脊形波导的光子晶体直波导中具有很好的传输特性. 关键词： 光子晶体波导 光子带隙 脊型波导     

Pulse propagation in a nonlinear dielectric slab waveguide

The evolution of an optical pulse in a single-mode, step index dielectric slab waveguide which is characterized by an intensity dependent dielectric function in the core and cladding regions is treated by means of differential equation techniques. A cubic order non-linearity is considered. The electromagnetic field distribution in the slab waveguide region satisfies a non-linear wave equation. This field can be represented in terms of even TE guided modes with a slowly varying envelope amplitude function.Then using the well known approximation, based on the slowly varying character of the amplitude function, a non linear partial differential equation is obtained for the amplitude function. As the coefficients of this equation depend on the distance across the transverse direction X, an averaging technique over x is applied to reduce the nonlinear partial differential equation into a form that is easily transformed to the so-called non-linear Scroedinger differential equation.This equation is then attacked by means of the well known Inverse Scattering method in the case of reflection less potentials. The single and double soliton solutions are obtained explicitly for a single-mode slab waveguide. Finally numerical results are presented in the time domain.     

Logical element NOT in a two-dimensional electron waveguide

A theoretical model of logical element NOT based on a two-dimensional electron waveguide is proposed. The results of optimization of the parameters of geometry and the external electric field to accomplish the maximal efficiency of operation of the device are considered.     

Electromagnetic behavior of a FIR waveguide laser

We consider the electromagnetic behaviorof a FIR (far infrared) waveguide laser. In a first step, we deal with the different modes which can propagate in the waveguide. Then, we compute the reflection and transmission coefficients of the coupling holes. Finally, we determine the oscillation conditions for each mode.     

Intertwined Hamiltonians in two-dimensional curved spaces

The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincaré half plane (AdS₂), de Sitter plane (dS₂), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle.     

Kinetics of two-dimensional electrons on a curved surface

A number of effects associated with the curvature of the surface on which a two-dimensional (2D) electron gas is placed are studied. The most significant effect in an external magnetic field (which for 2D electrons becomes effectively nonuniform) is the lifting of the degeneracy of the Landau levels. The intensity and shape of the cyclotron resonance line (inhomogeneously broadened) for different polarizations and the corrections to the Hall constant are found for the example of a circular cylinder. A picture of the quantization of the conductance that is qualitatively different from the case of a flat strip is obtained for a quasi-one-dimensional quantum wire in the form of a hollow cylinder. It is shown that in contradistinction to the planar case the spectrum of 2D electrons on the curved surface is sensitive to the sign of the spin-orbit coupling constant (for a fixed sign of the curvature). For hetero-junctions, for example, this opens up new possibilities for extracting information about their “hidden parameters.” Pis’ma Zh. éksp. Teor. Fiz. 64, No. 6, 421–426 (25 September 1996)     

Propagation loss in a two-dimensional triangular photonic crystal waveguide

By means of a plane-wave-based transfer-matrix method, we present an extensive study of propagation loss in two-dimensional (2D) photonic crystal waveguides with limited cladding wall thickness. We examine the dependence of propagation loss on both the propagation direction and the waveguide wall thickness. It is shown that the propagation loss is a function of excitation frequency, wall thickness and waveguide outermost surface morphology. The conclusion that the propagation loss essentially decays exponentially with respect to the cladding wall thickness of a waveguide is valid only to a certain degree. In addition, we find that the propagation loss exhibit very complex behavior with respect to the excitation frequency.     

非截面二维光子晶体排列矩形波导的全模式分析

在对周期性结构进行谐波分析的基础上，导出了非截面二维光子晶体排列矩形波导的本征值方程. 基于此方程，可以对该类光子晶体波导的所有可能模式进行分析. 分析认为，非截面二维光子晶体排列矩形波导内能存在的模式包括E_(y)，TE_y，H_(y)和TM_y模式；改变波导高度，可以实现E_(y)模式和H_(y)模式与其他模式通带的完全分离. 然而改变任一结构参数，都不能使E_(y)和H_(y)的各个模式通带，以及E_(y)1模式和H_(y)1模式的通带完全隔离. 波导单模工作的带宽由E_(y)1和E_(y)2模式的低端截止频率决定. 关键词： 波导 光子晶体 本征值方程 模式     

Electromagnetic wave propagation in a medium with defects

The equations of the electromagnetic field in a solid with defects were obtained and an approximate wave solution was found by the Debye–Rytov method.     

Waves trapped by a thin curved screen in a waveguide with rigid walls

The conditions are derived for the existence of waves trapped by a symmetrical thin rigid screen in a two-dimensional waveguide with rigid walls. Asymptomatic formulas are found for the corresponding eigenvalues, while the asymptomatic structures differ from those pertaining to the eigenvalues of problems in bounded domains. Various generalizations of the results are discussed, and open questions are formulated.