Propagation of p-polarized waves in a linearly graded index film surrounded by negative index materials

The theory of step-index waveguides is well-established. Most practical slab waveguide structures have a graded-index profile. The basic properties of graded-index planar waveguide structures are similar to those of step-index waveguides with subtle differences. The most common types of graded-index slab waveguides are linearly and exponentially graded-index profiles. We here treat linearly graded-index slab waveguide. In this work, a three-layer waveguide structure with linearly graded-index film is considered. We assume three structures: the first structure comprises a left-handed material (LHM) cladding, the second structure contains a LHM substrate layer and the third has a LHM cladding and substrate. Closed-form expressions for electric and magnetic fields and the characteristic equation are derived. The three normalized parameters: the asymmetry coefficient (a), the normalized film thickness (V) and the normalized guide index (b) are used to study the dispersion properties of the proposed slab waveguide structure.     

Guided modes in slab waveguides with a left handed material cover or substrate

We study guided modes propagating along a dielectric slab waveguide with a left handed material (LHM) cover or substrate. The dispersion relation is derived by using normalized waveguide parameters. An analytical method is then proposed to calculate the universal dispersion curves. Different from a slab waveguide with a LHM core, we find that guidance properties are strongly dependent on dielectric permittivity ε and magnetic permeability μ of the substrate and cover layers. For oscillating guided modes, fundamental zero order mode is not always absence, sometimes it exists in a restricted range of normalized propagation constant. First order mode behaves as other higher order modes and exists up to infinite high frequency. Higher order modes have no double degeneracy in the case of LHM cover layer. For surface guided modes, the existence and the type of the mode solutions with respect to different parameters are classified systematically and discussed in detail. Unlike a slab waveguide with a LHM core where the dispersion curve of TE₁ surface mode continues with that of oscillating TE₁ mode, the dispersion curve of TE₁ surface mode continues with that of oscillating TE₀ mode. It seems that the two different kinds of modes compensate each other to form one whole mode. Both TE and TM guided modes are discussed.     

不对称左手介质平板波导模式特性分析

对不对称左手介质平板波导的几个低阶的TE模和TM模进行了数值计算,得到了模式特征方程,分析了归一化传播常数β/k_0随平板厚度d变化的色散关系,作出了模式的电场E_y(x)分布．在左手介质平板波导中,每一模式都有截止点, TE_0模和TM_0模不出现,在我们给出的特定的介质参数下,TE_1模和TM_1模不能和其他高阶模式共存,其归一化传播常数β/ k_0随k_0d的增加而减小．给出的结果对左手介质元器件的研究有实际的参考意义．     

包含左手材料的四层平板波导中的光导模

研究一个芯子层是左手材料,其他三层由传统材料构成的四层平板光波导系统,利用图解法对各种TE偏振的导波模式的解进行详细分析.研究表明,四层左手材料光波导既能支持振荡导模,也能支持表面导模,与三层左手材料光波导相比较,此四层波导的导波模式呈现一些新的特性.对于中间传统材料层存在振荡场的情形:芯子层支持振荡导模的光波导中存在基模,并且高阶振荡导模出现模式缺失的性质;芯子层支持表面导模的光波导可以支持基模和多个高阶模式,并且存在模式兼并的性质.对于中间传统材料层存在衰减场的情形,此四层波导结构可等效为三层左手材料光波导.这些新的光波导传输性质对各种光波导器件的制作有潜在的应用价值.     

Cu2+离子注入的石英光波导的特性研究

利用Cu2+离子注入的方式在熔融石英和石英晶体上分别制备了平面光波导结构.通过棱镜耦合实验测试了两种光波导的导模特性,结果表明:在同样的注入条件下熔融石英上形成了增加型的光波导结构,而石英晶体上形成了位垒型的光波导结构.研究了退火温度对两种光波导导模折射率的影响,熔融石英光波导中导模的折射率随着退火温度的升高而降低,而石英晶体光波导中导模的折射率随着退火温度的升高先增加后降低.为了进一步分析离子注入两种材料形成光波导的微观机理,利用SRIM模拟了Cu2+离子注入两种材料的电子能量损失和核能量损失,并且模拟了两种光波导结构的折射率分布.模拟结果表明:熔融石英光波导的主要形成原因是离子注入表面的折射率大于其体材料的折射率,而石英晶体光波导的主要形成原因是离子射程末端的折射率小于其体材料的折射率.因此,在熔融石英光波导的形成中电子能量损失起主要作用,而在石英晶体光波导的形成中核能量损失起主要作用.     

Composite optical fibre–slab waveguides: a scalar,coupled-mode analysis with vector corrections

Analytically-derived vector corrections are included as additional coupling coefficients in numerical calculations of scalar coupled-mode and compound-mode theory (SCMT) of composite fibre–slab waveguides. The slab waveguide is asymmetric, with moderate light-wave guiding and coupling assumed and the resultant polarization effects are of interest. It is found that the modifications to light propagation and coupling coefficients determined previously by first-order SCMT are dependent mainly on the strength of coupled fibre and slab modes, the thickness of the guiding layers and the ratio of refractive indices of guiding to cladding layer (asymmetry of the slab waveguide). The vector corrections observed are not significant compared with our previous SCMT results, as the optical constants defined appear to satisfy the approximations necessary for the scalar analysis. This revised version was published online in June 2006 with corrections to the Cover Date.     

Numerical investigation of characteristics of laser radiation scattered in an integrated optical waveguide with three-dimensional inhomogeneities

Specifics of theoretical analysis of wave phenomena in irregular integrated optical waveguides are investigated. The object of the investigation and the main types of irregularities (smooth, statistical, and sharp) are described. The goals of the numerical modeling are formulated. The structure of the program and the general structure of the algorithm allowing numerical investigation of guided modes’ scattering from 3D-irregularities of an integrated optical waveguide are described. The dispersion relations of the TE and TM modes of the integrated optical waveguide under investigation, as well as field patterns of the radiating TE modes of the substrate and the laser radiation scattered from the three-dimensional guiding-layer inhomogeneities of an integrated optical waveguide, are presented. The results are analyzed in detail. The methods developed can be used for numerical investigation of the characteristics of laser radiation scattered in various optical waveguides with three-dimensional irregularities.     

Special features of electromagnetic wave propagation in a two-layered cylindric waveguide with right- and left-handed media

Results of modeling of the coefficients of waveguide mode propagation in a two-layered circular waveguide filled with media having positive and negative refractive indices called Right- and Left-Handed Media (LHM and RHM, respectively) are presented that allow us to conclude that complex waves and waves with significant slowing down of the phase velocity exist in these waveguides.     

Parameter optimization and structural design of polymer arrayed waveguide grating multiplexer

First some important parameters are optimized for the structural design of a polymer arrayed waveguide grating (AWG) multiplexer around the central wavelength of 1.55 μm with the wavelength spacing of 1.6 nm. These parameters include the thickness and width of the guide core, mode effective refractive indices and group refractive index, diffraction order, pitch of adjacent waveguides, length difference of adjacent arrayed waveguides, focal length of slab waveguides, free spectral range (FSR), the number of input/output (I/O) channels, and that of arrayed waveguides. Then the bent angles, radii and lengths of all the input/output channels and arrayed waveguides are determined. Finally, a schematic waveguide layout of this device is presented, which contains 2 slabs, 11 input channels, 11 output channels, and 91 arrayed waveguides.     

TE modes in a slab waveguide bounded by nonlinear media

A theory is presented of guided TE modes in a one-dimensional slabe waveguide bounded by nonlinear media with intensity dependent refractive indices. It is shown that this is a straightforward generalisation of linear slab waveguide theory with the modes parametrised by the power flow down the guide. Illustrative dispersion curves and mode shapes are discussed.     

Dielectric waveguide model for guided surface polaritons

Although surface polariton modes supported by finite-width interfaces can guide electromagnetic energy in three dimensions, we demonstrate for the first time to our knowledge that such modes can be modeled by the solutions of two-dimensional dielectric slab waveguides. An approximate model is derived by a ray-optics interpretation that is consistent with previous investigations of the Fresnel relations for surface polariton reflection. This model is compared with modal solutions for metal stripe waveguides obtained by full vectorial magnetic-field finite-difference methods. The field-symmetric modes of such waveguides are shown to be in agreement with the normalized dispersion relationship for analogous TE modes of dielectric slab waveguides. Lateral confinement is investigated by comparison of power-density profiles, and implications for the diffraction limit of guided polariton modes are discussed.     

K-Na离子交换单模平面波导的制备及其表征

通过K-Na离子交换技术制备了多模玻璃平面波导.采用棱镜耦合技术测量了波导的有效折射率,用IWKB方法拟合得到K-Na离子交换波导的折射率分布符合高斯分布,由色散曲线得到单模波导的制备条件(即扩散深度范围),从而得出单模波导的离子交换时间范围,制备出单模波导,并通过求解WKB色散方程得出单模波导的表面折射率.用普通数码相机,通过对离子交换平面玻璃光波导传输线进行数字成像,根据传输线上的光强分布拟合出光强传输衰减曲线,计算出单模波导的传输损耗大约为0.4 dB/cm.     

Cutoff behaviour of graded-index slab waveguides

The cutoff behaviour of graded-index planar waveguides is analysed in terms of the normalized waveguide parameters by using the multilayer technique and the WKB approach. The results show a very high degree of accuracy when checked against exact known values for exponential and hyperbolic index profiles. A set of universal plots showing the general features is given for the cutoff values of both fundamental and first-order modes. The TM polarization is also studied by comparison with the TE one.     

Coupled mode analysis of light modulation in dielectric waveguides

A detailed analysis of electrooptic light modulation in optical waveguides is presented. Several important problems of a waveguide modulator, such as the difference of waveguide axes from crystalline electrooptic ones, the distribution of transverse and longitudinal field components of light modes, and the traveling-wave property of the modulating field, are discussed. The analysis is based on the coupled mode theory, regarding the modulation as the coupling among sidebands of unperturbed waveguide modes. The coupled mode equation is derived for the modulation in optical waveguides. It can be solved if the normal modes of the waveguide are given. Actually the equation is solved for the modulation in dielectric slab waveguides and the mechanism of modulation is discussed. The results of the analysis are applied to designing two types of waveguide modulators. In an example (10.6 μm modulator with a GaAs slab waveguide) a new efficient crystal orientation is found. The calculated phase retardation with this orientation is 0.13 rad/(V·cm) with a 1 μm thick slab. Another example of a 0.633 μm modulator using a LiTaO₃ crystal as a substrate is also described.     

Guided modes in asymmetric metal-cladding left-handed material waveguides

We investigate guided modes in the asymmetric waveguide structure with a left-handed material (LHM) layer surrounded by air and metal. A graphical method is proposed to determine the guided modes. New properties of the oscillating and surface guided modes, such as absence of the fundamental mode, coexistence of the oscillating and surface guided modes, fast attenuation of the surface guided modes, and mode degeneracy, are analyzed in detail. We also investigate dispersive characteristics of the metal-LHM- air optical waveguide. The propagation constant increases with decreasing slab thickness for the first-order oscillating mode, which is different from that in traditional metal-cladding waveguides.     

Guided surface modes in a hollow slab waveguide with a left-handed material substrate or cover

The structural dispersion characteristics of guided surface modes in a hollow slab waveguide with a left-handed material substrate or cover are investigated. Dispersion relation is derived by using normalized parameters, and universal dispersion curves have been obtained analytically, by solving transcendental dispersion equations in a reverse way. Existence condition, mode degeneracy and other dispersion properties of guided surface modes have been discussed for different ? or μ of three layers for this substrate or cover layer.     

梯形截面硅脊形波导的模式特性及其等离子体色散效应

本文运用有效折射率法和WKB法对具有梯形状截面的硅脊形波导的模式特性作了分析,导出了TE模和TM模的模方程以及截止方程,并运用一阶微扰法对因波导顶部注入载流子而引起的模式调制的大小作了数值估计。其结果可为全硅光波导器件的研制提供指导。     

Four-layer metal-clad thin film optical waveguides

An investigation of the low order modes supported by an asymmetrical four-layered metal-clad optical waveguide is presented showing the attenuation characteristics and the field profiles. The attenuation and phase constants are examined as functions of both the thickness and refractive index of the buffer layer as well as the mode order. The results for small and large buffer layer thicknesses are discussed in terms of the modes supported by simpler asymmetrical three-layered metal-clad and dielectric-clad waveguides respectively. It is shown that the coupling of the TM polarized modes to the lossy surface plasma wave depends upon the buffer layer thickness, the refractive indices of the buffer layer and dielectric cladding and the mode order. This coupling is very dependent upon the mode order with the TM₀ mode exhibiting far weaker coupling than the higher order TM modes. Methods of controlling the amount of coupling and hence the attenuation of the TM modes are discussed.This work was performed while the author was with the Department of Electrical Engineering, University of Queensland, Brisbane, Australia, 4067.     

非对称金属包覆左手介质平板波导的微扰分析

基于微扰方法分析非对称金属包覆左手介质平板波导的特性,给出了该波导的复有效折射率的一级近似解,并对波导的传输特性和损耗特性进行了数值模拟.结果表明：非对称金属包覆左手介质平板波导没有零阶模式|TE1模传播系数随波导厚度的增加迅速减小,损耗系数随波导厚度的增加快速增加,达到最大值后又迅速减小|非对称金属包覆左手介质平板波导传输特性相对于左手介质三层平板波导传输特性发生了很大改变,TM1模,TM2和 TE2模式以及更高阶模式在截止厚度附近出现双值现象|特别在二阶及高阶模式中,TE模式相对于TM模式具有高传输低损耗的特性,而以右手介质为芯层的金属包覆波导不具有这一特性.     

电磁波在负折射材料填充的3层平板波导中的传播特性

从电磁场理论出发对负折射材料填充的3层平板波导的传播特性进行研究,并进行了数值计算,分析TE和TM波在平板中传播的性质,得到了电磁波的模式方程,与电磁波在右手材料填充的平板波导中的传播特性做了对比,考察了TE模式的能流密度,进行了归一化计算。结果分析表明：基模、一阶模不存在,且任何模式都存在一个截止厚度,随着厚度的增大,模式数量也增多;在一定的入射频率下,平板薄膜厚度趋向一定数值时,可以同时传播多种模式的波,并且入射波频率越高,波导同时存在多种模式的可能性越大;与右手材料相比,左手材料填充相同尺寸的3层平板波导可以传播更高能量的电磁波,导波效果更好。