Proper and improper modes of the left-handed material waveguides

The guided, complex, and virtual modes of the planar left-handed material waveguides are studied. The modal dispersion and field distributions are analyzed for the systems with step and parabolic profiles of dielectric permittivity and magnetic permeability. It is shown that anomalously high magnitudes of the magnetic fields may be observed in such structures. Effects of material nonlinearity and spatial dispersion are discussed.     

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.     

Scattering from an abruptly terminated planar metamaterial waveguide

We use a variational method to study the problem of reflection of a guided mode from an abruptly terminated planar dielectric waveguide made of a metamaterial. The theory is illustrated by problems of abruptly terminated three-layer waveguides with piecewise-constant and variable permittivity profiles. Differences in the scattering characteristics for systems with metamaterials and conventional media are discussed.     

Simple high-order Galerkin finite element scheme for the investigation of both guided and leaky modes in anisotropic planar waveguides

A simple high-order Galerkin finite element scheme is formulated to compute both the guided and leaky modes of anisotropic planar waveguides with a diagonal permittivity tensor. Transparent boundary conditions derived from the Sommerfield radiation conditions are used to model the fields at the computational boundaries that allow the radiation into the high index cladding/substrate and decay into the low index cladding/substrate, hence work for both guided and leaky modes. Richardson's extrapolation is employed to achieve high-order accuracy by only using simple first-order-polynomial basis functions. Schemes up to sixth-order of accuracy in the effective index are demonstrated. The resulted non-linear sparse matrix eigenvalue equation is solved using an iterative procedure. The ability of the scheme to compute leaky and guided modes of various structures with isotropic and anisotropic materials, step and graded index profiles is demonstrated; including its applications to investigate the properties of ARROW structures.     

Scaling of optical forces in dielectric waveguides: rigorous connection between radiation pressure and dispersion

We show that eigenmodes of dielectric optical waveguides exert surface dilation forces on waveguide boundaries owing to radiation pressure, and we develop an exact scaling law relating modal dispersion of an arbitrary dielectric waveguide to the magnitude of optical forces generated by radiation pressure. This result points to highly dispersive waveguides as an optimal choice for the generation of large optical forces in nano-optomechanical systems. Exact agreement with ab initio calculations is demonstrated.     

一种可用于分析任意介电常数张量的各向异性波导导模的二维时域有限差分模型

为分析具有任意介电常数张量的各向异性波导的导模,本文通过把简化的二维时域有限差分(2-DFDTD)法扩展至任意各向异性介质,提出了一种以D、E和H场为基础的统一的简化2-DFDTD模型.利用该模型,研究了简化的复数2-DFDTD方法与实变数2-DFDTD方法之间的关系.文中还讨论了复变数方法和实变数方法的激励技术.     

一种可用于分析任意介电常数张量的各向异性波导导模的二维时域有限差分模型

为分析具有任意介电常数张量的各向异性波导的导模，本文通过把简化的二维时域有限差分（２－ＤＦＤＴＤ）法扩展至任意各向异性介质，提出了一种以Ｄ、Ｅ和Ｈ场为基础的统一的简化２－ＤＦＤＴＤ模型．利用该模型，研究了简化的复数２－ＤＦＤＴＤ方法与实变数２－ＤＦＤＴＤ方法之间的关系．文中还讨论了复变数方法和实变数方法的激励技术．     

Wave-matching method for mode analysis of dielectric waveguides

Frequently the cross-section of a longitudinally homogeneous dielectric waveguide may be decomposed into rectangles with constant permittivity. For points inside these rectangles the wave equation for modal fields is solved analytically by expanding into functions with harmonic or exponential dependence on the transverse coordinates. Minimization of a least-squares expression for the remaining misfit on the boundary lines allows us to determine propagation constants and fields for guided modes. Semivectorial calculations for two sets of rib waveguides and the centre sections of a directional coupler and an MMI device show very good agreement with results found in the literature. This revised version was published online in November 2006 with corrections to the Cover Date.     

Dielectric‐loaded plasmonic waveguide components: Going practical

Surface plasmon propagating modes supported by metal/dielectric interfaces in various configurations can be used for radiation guiding similarly to conventional dielectric waveguides. Plasmonic waveguides offer two attractive features: subdiffraction mode confinement and the presence of conducting elements at the mode‐field maximum. The first feature can be exploited to realize ultrahigh density of nanophotonics components, whereas the second feature enables the development of dynamic components controlling the plasmon propagation with ultralow signals, minimizing heat dissipation in switching elements. While the first feature is yet to be brought close to the domain of practical applications because of high propagation losses, the second one is already being investigated for bringing down power requirements in optical communication systems. In this review, the latest application‐oriented research on radiation modulation and routing using thermo‐optic dielectric‐loaded plasmonic waveguide components integrated with silicon‐based photonic waveguides is overviewed. Their employment under conditions of real telecommunications is addressed, highlighting challenges and perspectives.     

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.     

Scattering matrix and radiation characteristics of the junction between two different monomode microwave or optical dielectric waveguides

The elements of the scattering matrix of the junction between two circular monomode dielectric waveguides with different diameters and/or different refractive indices are calculated using the mode matching method. The theory is evaluated numerically for a wide range of parameters and simplified considerably for two important cases of weakly guiding waveguides.The radiation pattern of the junction is calculated using the Huygens-Kirchhoff theory of diffraction and shown to be reducible to the weighted difference of the radiation patterns of the ends of the primary and secondary waveguide. Simple approximations are derived for weakly guided waves.The theory is verified experimentally by measuring the scattering parameters, the far-field radiation pattern and the near-field distribution of abrupt changes in diameter of microwave dielectric rod transmission lines.     

Compact-2D FDTD for waveguides including materials with negative dielectric permittivity, magnetic permeability and refractive index

An efficient compact-2D finite-difference time-domain method is presented for the numerical analysis of guided modes in waveguides that may include negative dielectric permittivity, negative magnetic permeability and negative refractive index materials. Both complex variable and real variable methods are given. The method is demonstrated for the analysis of channel-plasmon-polariton guided modes in triangular groves on a metal surface. The presented method can be used for a range of waveguide problems that were previously unsolvable analytically, due to complex geometries, or numerically, due to computational requirements of conventional three-dimensional finite-difference time-domain methods. A three-dimensional finite-difference time-domain algorithm that also allows analysis in the presence of bound or free electric and equivalent magnetic charges is presented and an example negative refraction demonstrates the method.     

Vectorial wave-matching mode analysis of integrated optical waveguides

For mode fields of integrated optical waveguides with piecewise constant and rectangular permittivity profile, Maxwell's equations reduce to the two-dimensional Helmholtz wave equation, supplemented by continuity requirements on the boundaries between different media. Two basic components of the mode field are expanded into factorizing harmonic or exponential functions, separately on each rectangular region. We determine approximations for guided modes and propagation constants by means of a minimization procedure based on a least squares expression for the mismatch in the continuity requirements. Results for the hybrid mode fields of typical sample waveguides classify this approach as competitive with and superior to alternative methods for vectorial mode analysis, although some open questions remain.     

Transformation of a plane wave by a periodically time modulated dielectric medium

The problem of the transformation of a plane monochromatic wave by a finite-duration sequence of periodic rectangular pulses of the dielectric permittivity and magnetic permeability is solved exactly with integral equations. The expressions for the transformed component of the electric field at any point in space at an arbitrary time are derived and analyzed.     

矩形芯介质波导色散关系及定向耦合器耦合长度的加权余量法计算

本文用加权余量法导出了用以计算各种条形介质波导色散关系,矩形芯双沟道耦合器耦合长度以及条载型波导色散关系的数学表达式,其精确度较其它近似方法高,且简便易行。     

Investigation of 2-D electromagnetic transients in a circular cylinder with time discontinuity in permittivity via the resolvent method

The resolvent method approach is proposed for analytically solving the time domain Volterra integral equation (TDVIE) which describes the electromagnetic fields in 2-D cylindrical structures with time changes in the permittivity. It is shown that the approach allows investigation of the electromagnetic field transformation due to an abrupt time change in dielectric permittivity inside a circular cylinder as well as the construction of the Green’s function for an initial-boundary value problem. Key mechanisms of electromagnetic field transformation are investigated and a qualitative distinction of the processes is shown that depends on an initial field configuration.     

Analysis of arbitrary index profile planar optical waveguides and multilayer nonlinear structures: a simple finite difference algorithm

we present here a simple numerical method to obtain the mode effective indices as well as field distributions of modes of any arbitrary profile planar optical waveguide. The method is based on the solutions of scalar and semivectorial Helmoltz’s equation by finite difference algorithm and devised with a field convergence technique. This approach is quite general and can be applied straightforwardly to calculate the guided as well as quasi- or leaky modes of any arbitrary planar structure without the need to solve any eigenvalue equation or any complex matrix formalism. Besides providing the ease of application, the algorithm is particularly useful for waveguides with any graded index profile or with irregular multilayered structure and multilayered waveguides with a localised arbitrary nonlinear film. The performance of our method is verified against typical problems with analytical solutions or having results known otherwise, and is shown to yield results with good accuracy.     

Effect of organic dyes on the dielectric properties of KH<Subscript>2</Subscript>PO<Subscript>4</Subscript> crystals

The effect of organic dyes on the dielectric properties of KH₂PO₄ (KDP) crystals is studied over a wide range of temperatures. The dielectric properties of KDP crystals doped with molecules of the Chicago Sky Blue and Amaranth organic dyes are investigated for the first time. The dye molecules can be incorporated into the crystal lattice of KDP and selectively paint the pyramidal growth sectors of the crystal. The influence of dye organic impurities on the domain contribution to the permittivity is analyzed with due regard for the sectoral crystal structure. It is demonstrated that, upon doping of KDP crystals with organic dyes, the blocking effect of background impurities on domain walls is substantially weakened in the prismatic growth sector of the crystal in the polar phase. This leads to a noticeable change in the dielectric properties, specifically to an increase in the domain contribution to the permittivity of the crystal.     

Network analysis of eigenvalue problem for multilayer dielectric waveguide consisting of arbitrary number of layers

In this paper, the eigenvalue problem of a multilayer dielectric waveguide consisting of arbitrary number of layers is solved by the microwave network method. A general program with the function of computer graphics has been developed for analyzing the dispersion characteristics and the electromagnetic field distributions of an N layer dielectric waveguide. As examples of practical applications of the program, first, the dispersions and field patterns for the planar waveguides with refractive index of parabolic and exponential profiles are analyzed. Secondly, the procedure of mode conversion and mode separation in dielectric branching waveguides is vividly demonstrated through analyzing the field distributions of asymmetric multilayer dielectric structures and the general rules of mode conversion are discussed. The examples show that the present method possesses the advantages of versatility, rapidity, simplicity and accuracy.     

Mode coupling and radiation loss of clad-type optical waveguides due to the index inhomogeneities of the core material

Closed form approximate expressions are derived for the mode-coupling, radiation loss and losses of each guided mode in multimode clad-type dielectric slab waveguides due to the index inhomogeneities of the core material. The analysis considers the inhomogeneities of the core-index in the axial and transverse directions and includes correlation lengths of any magnitude. It allows us to conclude that there will be considerable mode-dependency for the mode-coupling and radiation loss if the axial and/or transverse correlation lengths are of the order of or greater than the wavelength. It is also found that the mode-coupling and radiation loss peak at some value of the axial correlation length, and the radiation loss can be reduced by increasing the refractive-index difference of the core and cladding materials. Finally, it is shown that if the correlation lengths are shorter than, or of the order of the wavelength, the losses of each guided mode will mainly be due to the radiation process. But, in the case where the axial correlation length is much greater than the wavelength, the scattering into other guided modes is the dominant mechanism.