Mode content analysis from intensity measurements in a few cross sections of oversized waveguides

A method of mode content analysis in oversized waveguides basing on intensity measurements in a few cross sections is suggested. The method is based on iterative synthesis of phase fronts of the radiation measured in a few cross sections of an oversized waveguide. The phase reconstruction makes it possible to calculate field distribution as well as the mode content at any place of the waveguide. The method was tested in experiments with circular and rectangular waveguides with impedance corrugation of the walls [8].     

Mode content analysis from intensity measurements in a few cross sections of oversized waveguides

A method of mode content analysis in oversized waveguides basing on intensity measurements in a few cross sections is suggested. The method is based on iterative synthesis of phase fronts of the radiation measured in a few cross sections of an oversized waveguide. The phase reconstruction makes it possible to calculate field distribution as well as the mode content at any place of the waveguide. The method was tested in experiments with circular and rectangular waveguides with impedance corrugation of the walls [8].     

NETWORK CHARACTERIZATION OF STEP DISCONTINUITY WITH GENERALIZED CONSERVATION OF COMPLEX POWER TECHNIQUE AND ITS APPLICATION TO ANALYZING PERIODIC DIELECTRIC WAVEGUIDES

The propagation of electromagnetic waves along open periodic, dielectric waveguides is formulated in the case that surface wave is guided and propagates normally to the corrugation. Our approximate analysis with the propagation characteristics is to consider a corresponding bounded waveguide problem in which perfect electric or magnetic walls are introduced, and the periodic corrugation is regarded as consisting of step discontinuities connected by a length of uniform slab waveguide. By properly taking into account of both surface modes and only a few non-surface-modes, a novel network approach is proposed for characterizing step discontinuity based on the generalized conservation of complex power technique (GCCPT). Employing solution selection rule (SSR), we can readily derive propagation characteristics in the Bragg interaction region. A number of numerical results are shown to demonstrate the usefulness of our approach.     

Effect of diffraction on the electrodynamic characteristics of two-dimensional coaxial Bragg resonators

The electrodynamic properties of coaxial two-dimensional Bragg resonators with two-dimensional distributed feedback are analyzed. These resonators are made of coaxial waveguide sections with doubly periodic corrugation, which provides coupling and mutual scattering of four partial waves. Two of them propagate along the waveguide, while the other two propagate in the transverse (azimuthal) direction. It is shown that the high azimuthal index selectivity of two-dimensional Bragg resonators may be related to a qualitative difference in topology of the dispersion characteristics of azimuth-symmetric and asymmetric normal waves propagating in infinite waveguides of such a geometry. For the finite-length systems used as two-dimensional Bragg resonators, the eigenmode spectrum is found for two types of boundary conditions that correspond to the limiting cases of perfectly matched (open) systems and, conversely, of systems closed for the extraction of transverse electromagnetic fluxes. Perimeter-to-length ratios of the resonator at which the Q factor of the fundamental azimuth-symmetric mode is greater than those of the other modes are determined. The applicability domain of the geometrical approach, which was earlier applied to two-dimensional Bragg resonators, is discussed.     

Enhancement of single mode operation in coaxial optical waveguide using DB boundary conditions

In this study, a competent numerical strategy to compute the dispersion of optical waveguides is presented and propagation of electromagnetic waves in a coaxial optical waveguide with DB boundary conditions is instigated. For this intend, cylindrical coordinates are here being used to derive the DB boundary conditions and to obtain field components for the modes. The propagation constant for the waveguide to be studied is determined by solving the Bessel and the modified Bessel functions. The cutoff frequencies for various lower order modes have been calculated and their dispersion characteristics are plotted correspondingly. The behavior of the coaxial optical waveguide under DB boundary conditions is shown to be significantly different from that of coaxial optical waveguide and conventional optical waveguide under traditional or tangential boundary conditions. Finally, the effect of waveguide dimensions on the mode cutoff frequencies and fabrication issues are also addressed.     

左手介质矩形波导导模和表面模的场分布

从麦克斯韦方程组出发,结合电磁场的边界条件,推导出介质矩形波导导模的一般色散方程.对普通介质矩形波导和左手介质矩形波导的导模场分布分别进行了数值模拟.通过对比两种介质矩形波导的导模场分布的模拟结果,发现左手介质矩形波导Ex22模的场分布比普通介质波导Ex00模的场更集中在波导中部.同时,根据处理普通介质矩形波导的Marcatili方法.类比得到左手介质矩形波导表面模的色散方程,并数值模拟了低阶模的场分布,结果表明,能量主要集中在波导的四个角区以及波导的边缘.     

Elastic wave propagation in sinusoidally corrugated waveguides

The ultrasonic wave propagation in sinusoidally corrugated waveguides is studied in this paper. Periodically corrugated waveguides are gaining popularity in the field of vibration control and for designing structures with desired acoustic band gaps. Currently only numerical method (Boundary Element Method or Finite Element Method) based packages (e.g., PZFlex) are in principle capable of modeling ultrasonic fields in complex structures with rapid change of curvatures at the interfaces and boundaries but no analyses have been reported. However, the packages are very CPU intensive; it requires a huge amount of computation memory and time for its execution. In this paper a new semi-analytical technique called Distributed Point Source Method (DPSM) is used to model the ultrasonic field in sinusoidally corrugated waveguides immersed in water where the interface curvature changes rapidly. DPSM results are compared with analytical solutions. It is found that when a narrow ultrasonic beam hits the corrugation peaks at an angle, the wave propagates in the backward direction in waveguides with high corrugation depth. However, in waveguides with small corrugation the wave propagates in the forward direction. The forward and backward propagation phenomenon is found to be independent of the signal frequency and depends on the degree of corrugation.     

Effect of Distortions on an Annular Optical Fiber Waveguide

We present the modal analysis and dispersion curves of some asymmetric annular optical-fiber waveguides. The proposed cross-sections can be conceived as having the shape of a distorted annular circular waveguide and leads to a tolerance study of deformation in an annular optical-fiber waveguide. We obtain mathematical expressions for the modes of the proposed waveguides using boundary matching techniques under some logical assumptions. We observe that the proposed distortions are able to tune the cutoff values of annular circular waveguide at desired levels.     

Optimal designing of grating couplers for diffused waveguides in electro-optical crystals

Grating couplers for electro-optical diffused waveguides (such as Ti:LiNbO₃, Ti:LiTaO₃, etc.) are examined theoretically. A comparison of the improvements resulting from groove deepening, grating metallization, covering and multicovering of waveguide corrugation is made. Expressions for the calculation of the optimum parameters for multicovering are given and the method for optimization of the parameters is presented. It is shown that high-efficiency couplers for diffused electro-optical waveguides can be made using corrugations no longer than 1 mm and no deeper than 10 nm. A numerical illustration is presented to demonstrate the usefulness of the method for the improvement of other grating devices (distributed Bragg reflector, thin-film grating coupler).     

Analysis of non-linear multilayer waveguides with Kerr-like permittivities

This paper presents a semi-analytical method for calculating the dispersion relationships for stationary non-linear TE waves guided by general multilayer waveguides with Kerr-like permittivities. The non-linear wave equations are solved rigorously for each layer, and the mode index and field distribution are systematically determined so as to satisfy the boundary conditions at all interfaces. To verify the validity of the present method, a non-linear graded-index waveguide is approximated by a number of step layers and the resultant multilayer waveguide is analysed numerically. The convergence properties of mode index and total power flow are presented, and these are compared with direct solutions of the non-linear wave equation by the numerical integration method. The dispersion relationships for a non-linear multiple-quantum-well waveguide have also been investigated under two simple permittivity models. The present method is useful for the analysis of non-linear graded-index waveguides in addition to non-linear multilayer waveguides such as the multiple-quantum-well structure.     

初态对光波导阵列中连续量子行走影响的研究

本文使用近邻耦合模型得到的解析解,分析了周期性波导中输入态对量子行走的粒子数的概率分布函数 和二阶相干性的影响.结果表明:输入态的对称性质对量子行走过程的二阶相干度有影响, 而对粒子数的概率分布函数影响不大. 关键词： 周期性光波导阵列 量子行走 二阶相干度 纠缠态     

The sharpness-induced mode stopping and spectrum rarefication in waveguides with periodically corrugated walls

Abstract

Starting from the rigorous excitation equation, the propagation of waves through a 2D waveguide with the periodically corrugated finite-length insert is examined in detail. The corrugation profile is chosen to obey the property that its amplitude is small as compared to the waveguide width, whereas the sharpness of the asperities is arbitrarily large. With the aid of the method of mode separation, which was developed earlier for inhomogeneous-in-bulk waveguide systems [Waves Random Media 2000; 10: 395], the corrugated segment of the waveguide is shown to serve as the effective scattering barrier whose width is coincident with the length of the insert and the average height is controlled by the sharpness of boundary asperities. Due to this barrier, the mode spectrum of the waveguide can be substantially rarefied and adjusted so as to reduce the number of extended modes to the value arbitrarily less than that in the absence of corrugation (up to zero), without changing considerably the waveguide average width.     

Effect of metal boundaries on surface-wave spectrum in plasma-vacuum structures

The effect of metal on the surface-wave spectrum in cylindrical metal-plasma-vacuum-metal and metal-vacuum-plasma-metal waveguide structures and waveguides with a single metal boundary is investigated. It is shown that such boundaries can greatly affect the spectral properties of the waveguide and change the nature of surface-wave dispersion. Analytic expressions are obtained for the frequency of symmetrical surface waves in various spectrum intervals. The strong dependence of phase velocity on the size of the internal metal cylinder that is found can be convenient for beam and wave synchronization in a plasma waveguide.     

Nonlinear band gap transmission in optical waveguide arrays

The effect of nonlinear transmission in coupled optical waveguide arrays is theoretically investigated and a realistic experimental setup is suggested. The beam is injected in a single boundary waveguide, linear refractive index of which (n(0)) is larger than refractive indexes (n) of other identical waveguides in the array. Particularly, the effect holds if omega(n(0)-n)/c>2Q, where Q is a linear coupling constant between array waveguides, omega is a carrier wave frequency, and c is a light velocity. Numerical experiments show that the energy transfers from the boundary waveguide to the waveguide array above a certain threshold intensity of the injected beam. This effect is due to the creation and the propagation of gap solitons in full analogy with a similar phenomenon in sine-Gordon lattice [Phys. Rev. Lett. 89, 134102 (2002)]].     

Full-vector mode solver for bending waveguides based on the finite-difference frequency-domain method in cylindrical coordinate systems

A full-vector mode solver for bending waveguides is described based on the finite-difference frequency-domain method in a local cylindrical coordinate system in which the formulas are directly derived from Maxwell's equations with the help of Yee's mesh. The perfectly matched layer absorbing boundary conditions are incorporated into the present approach in order to effectively demonstrate the leaky nature of bending waveguides. A typical bending rib waveguide is considered as a numerical example to show the effectiveness of the established method.     

一种水平变化波导中声传播问题的耦合模态法

针对介质参数及海底边界水平变化波导中的声传播问题,本文基于多模态导纳法提出一种能量守恒且便于数值稳定求解的耦合模态方法.将声压表示为一组正交完备的本地本征函数之和,对声压满足的Helmholtz方程在本地本征函数上作投影,推导出关于声压模态系数的二阶耦合模态方程组.耦合矩阵直观描述水平变化因素对模态耦合的贡献.为避免直接求解二阶耦合模态方程组可能遇到的数值发散问题,将其重构为两个耦合的一阶演化方程组,引入导纳矩阵并使用Magnus数值积分方法获得稳定的声场解.利用该耦合模态方法数值计算水平变化波导中的声场,并与COMSOL参考解比较,结果表明该耦合模态理论能够精确求解水平变化波导中的点源及分布源传播问题.     

An azobenzene functionalized polymer for laser direct writing waveguide fabrication

We report on non-lithographic laser direct writing fabrication of optical waveguides by using a 4′-hydroxy-4-nitroazobene dye-functionalized polymer film. The polymer film reveals permanent change of refractive index at high laser illumination intensity. A focused continuous wave low power green laser beam at 532 nm wavelength is used to directly write waveguide structures on the polymer film. The magnitude of refractive index increase at film surface is about 0.006. One-step laser writing results in graded index waveguides in film depth direction under ambient conditions without pre- and post-processing. As a by-product, the laser writing also results in a very small air valley at the boundary between the laser written and non-written regions which may contribute in part although minimal to the waveguide lateral confinement and can be used for visual observation of waveguide patterns. The fabricated waveguide is found to be stable and easily reproducible.     

Applications of the finite difference mode solution method to photonic crystal structures

The finite difference waveguide mode solution method, which has been popularly employed in the study of waveguide modes on various optical and dielectric waveguides, is utilized to calculate the modal characteristics of photonic crystal fibers (PCFs) and planar photonic crystal waveguides and the band diagrams of two-dimensional photonic crystals. Vector guided modes on both PCFs based on the total internal reflection guiding mechanism ('holey fibers') and those resulting from photonic band gap effect are accurately computed, with their effective indexes and field distributions compared with other methods. Calculated dispersion of a single-core holey fiber and coupled-power behavior of a two-core holey fiber are found to agree with measured results. For applications to band diagram calculation and planar photonic crystal waveguide analysis, the finite difference scheme is modified simply by imposing suitable periodic boundary condition. Numerical results for air-column crystals and dielectric-rod crystals are both found to agree well with calculations using other methods.     

Experimental analysis of metal coated dielectric waveguides

This paper concerns the experimental characteristics of metal coated dielectric waveguides with a rectangular surface corrugation. Waveguide are designed to operate at a second Bragg frequency of 90 GHz. The period, height and the duty cycle of a rectangular grating were calculated using the chosen frequency. A metallic layer of aluminum is sputtered on one side of the slab waveguide. The purpose of the metallic layer is to simulate a layer of high density plasma on the surface of the waveguide similar to that obtained by optical excitation of semiconductor structures. Experiments were performed to examine the far field radiation pattern, attenuation constant and the dispersion relation. Due to the presence of the plasma layer there will be an angular shift in the far field radiation pattern. We have observed angular shifts of about 20 in the radiation pattern of the waveguide before and after coating. Measurements are made in the frequency range of 88–95 GHz. This waveguide structure can be used to design an electronically steerable antenna and an electronic phase shifter operating in the millimeter-wave frequency band.Supported in part by the Army Research Office.