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.     

包层为负折射率介质的抛物型渐变光纤色散特性分析

研究了纤芯为各向同性非均匀材料,而包层为负折射率均匀介质光纤的色散特性.在纤芯满足弱渐变条件的假定下,按矢量场分析法,通过芯层与包层的介电常数比ξ和磁导率比η,讨论了导波模式色散特性对左手介质包层材料的依赖性.分析表明,ξ和 η对轴对称模色散曲线的低频段影响较大,但对非轴对称模影响不大.ξ和 η对导波模式的截止频率没有影响.由于该光纤中的HEm1模的截止频率都等于0,所以不存在理论上的单模区,但仍可近似实现无色散传输.     

Study of a slab waveguide loaded with dispersive anisotropic metamaterials

We have numerically studied the characteristics of a slab waveguide loaded with dispersive anisotropic metamaterials. For two typical-structured metamaterials, we have analyzed the tensor expressions of frequency-dependent permittivity and permeability and discussed influences of the resonant cell structures on waveguiding characteristics. Numerical results show that the slab waveguide loaded with anisotropic metamaterials may, to some extent, behave as the slab waveguides of isotropic left-handed metamaterials (LHMs) core and conventional right-handed materials core. To one’s interest, some unusual properties are revealed in this paper, such as the coexistence of the fundamental guided mode and negative group velocity, and extraordinarily large normal or anomalous group velocity dispersion. Our results may find some potential applications in both linear and nonlinear optical technology.     

Guided modes in left-handed waveguides

We investigate basic properties of linear guided modes in a waveguide slab with the core of a material with simultaneously negative effective permittivity and permeability surrounded by a normal dielectric cladding. The existence and dispersion of all possible types of guided modes have been studied in detail. We demonstrate that the two orthogonally polarized, TE and TM slow guided modes, with the same frequency and the same wave number can exist simultaneously. Their group velocities, however, can be parallel or anti-parallel.     

单轴各向异性异向介质平板波导中的导模特性

 推导了介电常数张量和磁导率张量中各分量带有不同符号的单轴各向异性异向介质平板波导的导行条件。根据分量符号的正负组合,分情况讨论了导行TE波的偶模特性,画出了平板波导中为实横波数时的布里渊图。结果表明,在特定条件下此平板波导中有无穷多导模,这与传统介质波导及各向同性异向介质平板中只有有限数量模式存在有很大不同。此外,还发现当分量参数满足一定条件时,出现了多个虚横波数的传输模式解,并且该模式存在高频截止。     

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.     

Waveguide regimes of a graded-index planar waveguide with cladding

An exact dispersion relation for the guided modes of a four-layer planar structure with an exponential permittivity profile in the main waveguide layer (slab) is derived for the first time on the basis of the wave approach. Periodicity of the mode characteristics as functions of the cladding thickness is established. The dependence of the energy flux distributions of various modes in the waveguide structure on the thicknesses of the cladding and slab layers is investigated. Zh. Tekh. Fiz. 69, 74–79 (November 1999)     

由同时具有磁谐振和电谐振结构组成的左手材料

为了在同一结构中同时实现负介电常数和负磁导率(双负),采用一种“巨”字形结构,利用丝网印刷技术在氧化铝基板上进行加工制作,并通过仿真和实验测试证实了这种结构的“双负”特性. 与利用磁谐振器和电谐振器组阵实现左手材料的方法相比,这种单一结构可以同时实现负介电常数和负磁导率,制作方便,等效电路简单,双负频段较宽. 利用丝网印刷技术进行样品的制作,工艺简单,成本低廉. 关键词： 左手材料 磁谐振 电谐振     

Transmission properties of asymmetric slab waveguides with left-handed materials

A new dielectric slab waveguide with a left-handed material (LHM) cover and substrate is proposed. The dispersion relations and normalized effective thickness of the asymmetric LHM slab waveguide are investigated, in view of the normalized parameters. A number of unusual properties are found, for example, the fundamental and first-order modes do not exist and higher-order modes have double degeneracy. The propagation modes are absent at the low normalized frequency, and the cutoff frequencies of some LHM slab waveguide modes decrease with increase in the asymmetry measure. Unlike traditional slab waveguides, the V –H curves of the LHM slab waveguides are in one-to-one correspondence. Both TE and TM modes are discussed; in addition, the dispersion relations and normalized effective thicknesses of the TM modes are discussed in detail, when the difference in refractive indices of the film and the substrate is small. The results show that the region of mode coexistence taking place near the cutoff frequency becomes narrower with increase in the difference in refractive indices of the film and the substrate. The influence of this difference on the normalized effective thickness curves is different, and becomes smaller and smaller with increase in the value of the asymmetry measure, if different values of the refractive indices are employed.     

Phase constant peculiarities of cylindrical zero-index anisotropic metamaterial waveguide

Here, we present the phase constant dependencies of propagating eigenmodes of an open cylindrical anisotropic metamaterial waveguide when the metamaterial permittivity and permeability tensor components may accept values close or equal to zero. Dispersion characteristics of rod and hollow-core waveguides with the radii 0.5, 2.5, and 5 mm at the left-handed polarization of the microwave are shown here. There are unusual shapes of eigenmode dispersion characteristics and anomalous sectors of the characteristics at certain frequencies. The first eigenmode of the rod waveguide with the lowest cutoff frequency is a particularly important mode because it is a single one in the frequency range 1.0?C1.9 GHz, and some small variations on the frequency produce large changes in the phase constant. We can observe packages of dispersion characteristic branches when their cutoff frequencies closed to the metamaterial electric and magnetic plasma frequencies between 1.9 and 3.5 GHz. There are only three modes in the hollow core anisotropic metamaterial waveguide at the frequency range 1.4?C2.8 GHz.     

Light transmission along a slab waveguide with a core of anisotropic metamaterial

We investigated the dispersion property of a slab waveguide with an anisotropic metamaterial core whose permittivity tensor is partially negative. The subwavelength guidance characteristics are presented based on the boundary conditions. The results show that, at some specific frequencies, many high-order modes can exist in present waveguide even with the thickness of the guiding core 10 times smaller than the working wavelength. It is also found that different orientations of the optical axis of the anisotropic core will lead to different dispersion of the guided modes. If the orientation of the optical axis is properly chosen, the guided modes show a transition from backward wave to a forward wave as the frequency increases. During this transition, the group velocity of some guided modes can approach zero. Since the anisotropic metamaterial we discuss here can be fabricated in GHz, near- and mid-infra-red frequencies, our result may find some applications in wave trapper, integrated optical and nanophotonic devices.     

Dispersion Properties of Photonic Crystal Fiber: Comparison by Scalar and Fully Vectorial Effective Index Methods

The development of analysis and simulation of propagation characteristics of photonic crystal fiber (PCF) using scalar and fully vectorial effective index methods are described. As a result, we report how the fundamental space filling mode, guided mode and dispersion of the PCF depends on its structural parameters like its normalized air hole spacing, center-to-center spacing of the air holes in the photonic crystal or pitch and radius of the unit cell. Normalized frequency parameter V_eff as a function of normalized wavelength for various relative air hole sizes is obtained to estimate the dispersion characteristics of PCF. It is observed that wavelength of zero dispersion, ultraflattened dispersion response and high negative dispersion remarkably differ from two different effective index methods.     

色散负折射特异介质的1维光子晶体缺陷态

在1维光子晶体中引入色散负折射特异介质,分析了其介电常数和磁导率在微波区（1～10 GHz）与频率的关系。分别对以色散负折射介质为缺陷的正折射率介质光子晶体及以正折射率介质为缺陷的正负折射率介质光子晶体进行了数值仿真,得出了均匀平面电磁波在正入射和斜入射时的透射谱。结果表明:在介电常数和磁导率均为负值的不同禁带中,分别出现了单、双缺陷模。利用透射谱的这一特点,可实现单、双通道滤波。     

Propagation Characteristics of a Novel NRD Guide with Double-Layer LHM Slab

A new waveguiding structure based on NRD (Nonradiative Dielectric) guide with a double-layer LHM (Left Hand Material) slab is carefully investigated. Rigorous multi-mode network treatment combining with mode matching method is carried out to analyze the propagation characteristics of the structure. Theoretical analysis results reveal that depending on the choice of permittivity and permeability of the two dielectric slabs, the guiding structure is of series distinct and interesting properties, such as anomalous dispersion, opposite polarization modes coupling, and the existence of complex mode. Besides, the new configuration can also be used as a leaky wave antenna working in the dominant or the first higher order mode. All these particular features create various applications in electromagnetic engineering.     

转移矩阵法在负折射率介质材料平板波导中的应用研究

利用严格电磁理论,推导出了适用于负折射率介质材料光波导的转移矩阵,分析讨论了转移矩阵的性质和应用.利用转移矩阵方法,推导出导波层为负折射率介质材料、覆盖层和衬底为右手材料的三层对称介质光波导的本征色散方程.用图解法研究了负折射率介质波导中TE波的异常色散特性.在负折射材料介质波导中没有零阶模,最低阶为1阶模,并且有截止频率,只有波导参量满足一定条件的时候才会存在,导模的横向波数可以为实数和纯虚数,而正折射率介质波导导模的横向波数只能为实数.     

含左手材料对称五层平面波导模场特性

对芯层为左手材料而内外包层都是普通材料的对称五层平面波导进行了探讨.得到了两类TE振荡模的色散方程,且在考虑材料色散的条件下,画出了相关模式的色散曲线.随着模阶数的增加,模色散曲线左移,它们的截止频率变小.其次,发现零阶TE振荡模的存在.除此以外,TE振荡模有三类色散特性：正常色散;反常色散;双模简并.     

含左手材料对称五层平面波导模场特性(英文)

对芯层为左手材料而内外包层都是普通材料的对称五层平面波导进行了探讨.得到了两类TE振荡模的色散方程,且在考虑材料色散的条件下,画出了相关模式的色散曲线.随着模阶数的增加,模色散曲线左移,它们的截止频率变小.其次,发现零阶TE振荡模的存在.除此以外,TE振荡模有三类色散特性:正常色散;反常色散;双模简并.     

负折射率介质光纤的导模异常特性分析

对芯层为负折射率介质,敷层为普通介质的光纤的导模进行了研究,并对芯层与敷层介电常数比值（ξ）和磁导率比值（η）变化对导模色散特征的影响进行分析.分析表明负折射率光纤具有许多不同于常规光纤的反常特征,如存在表面波模,存在TM00模和TE00模以及存在多个单模传输模式和单模传输区间等.同时对负折射率介质光纤的单模传输条件进行了分析,发现单模传输模式和传输区间随ξ和η的不同而改变.     

Electromagnetic wave propagation through frequency-dispersive and lossy double-negative slab

This study presents the electromagnetic wave propagation through the frequency-dispersive and lossy double-negative slab embedded between two different semi-infinite media. The double-negative slab is realized by using two models, the Lorentz and Drude medium models. The properties and the required equations for the frequency-dispersive and lossy double-negative slab, the Lorentz medium and Drude medium are given in detail. After the construction of the problem, the reflection and transmission coefficients are derived for both TE and TM waves. Then, the reflected, transmitted and loss powers are determined using these coefficients. Finally, in the numerical results, the mentioned powers for TE and TM waves are computed and illustrated as a function of the incidence angle, the frequency and the slab thickness when the damping frequency changes.     

Nonlinear dispersion equation and guided modes in a slab waveguide composed of a negative-index medium

We consider a slab waveguide made of a material with negative permeability and negative permittivity, the surrounding medium is conventional. By using the dispersion relation, we show the dispersion curves from the variation of the core width and other physical parameters. The associated energy flow for several thicknesses of the nonlinear layer waveguide is presented. We discuss possible new types of modes that can occur. It is found that the dispersion curves and the energy flow can be controlled by varying the thickness of the guide, the filling factor and the effective plasma frequency. A numerical simulation is done to well illustrate.