Derivative free method for computing modes of multilayer planar waveguide

A technique to solve generalized dispersion equation of multilayer planar waveguide has been demonstrated to obtain all the expected guided modes. The solution is based on the derivative free method for computing the zeros of an analytical function in complex plane. The derivative free method extracts the roots which are very close to actual zeros of the function. Roots are further refined using the robust iteration method to achieve the desired accuracy. Application of the proposed method has been verified by solving the modes of a variety of structures including lossless structure, leaky structure, quantum well waveguide, active waveguide, ARROW waveguide and metal clad waveguide. The method is efficient and computes all modes of planar waveguide with high accuracy.     

Electromagnetic field and dispersion characteristic analysis of absorbing onion-like carbon tube waveguides

Here, we present our calculation results of the electromagnetic field distributions and the dispersion characteristics of open cylindrical tube waveguides. The analyzed waveguides are made of the onion-like carbon (OLC) material. The solution of the boundary problem was fulfilled by the partial area method (Nickelson et al. in electrodynamical analysis of open lossy metamaterial waveguide and scattering structures. InTech, UK, pp 27–58 [1]). We have determined the complex roots of the dispersion equation using of the Muller method. It discovered the very complicated dependencies of the phase and attenuation constants on the waveguide radii. Such dependencies arise because the OLC material is the highly dispersive and absorbing one. We have investigated the high-frequency cutoff frequency of the propagating hybrid modes HE₁₁ and HE₁₂ dependent on the tube waveguide external and internal radii. We found that it is possible to reach the one-mode regime of OLC tube waveguide.     

Sensitivity of prismatic integrated optical sensors under nearly critical conditions

The sensitivity of integrated optical sensors based on prismatic excitation of planar waveguides is analyzed. It is shown that the sensitivity peak is attained when the waveguide modes are excited under nearly critical conditions.     

Propagation characteristics of guided waves in a rod surrounded by an infinite solid medium

The dispersion and excitation characteristics of the guided waves in a rod surrounded by an infinite solid medium (cladding) are investigated. First, the bisection technique is employed to find all the roots of the dispersion function on the basis of theoretical analysis and to obtain the complex phase and group velocity dispersion curves of the guided modes. Second, according to their different dispersion characteristics, the guided modes are divided into two categories: normal modes and Stoneley modes. And it is concluded that the normal modes merely exist in the “hard cladding” model in which the cladding’s shear velocity is larger than the rod’s; while the Stoneley modes in cylindrical interface are highly dispersive and merely exist in the model whose acoustical parameters satisfied the existence condition of the Stoneley waves. Third, the seldom discussed issue, the excitation mechanisms of the guided waves, excited by three source models: symmetric point source, axial and radial force sources, are simulated respectively. Attention is paid on the dominant mode which has better excitation sensitivity and the suitable excitation frequency range. Moreover, the propagation characteristics of the Stoneley modes, ignored in previous references, are analyzed and compared with those of the normal modes.     

Numerical simulation of quasisurface magnetostatic waves in a ferrite film with two magnetic channels

Quasisurface magnetostatic waves propagating in a ferrite film along two magnetized channels are simulated numerically. It is shown that the interaction between the channels is manifested differently, depending on the wavelength. In the long-wavelength region the interaction between the channels has a distributed character; in the short-wavelength region the interaction between the channels appears as if it takes place at their boundary. The magnetized region of the ferrite film between the channels behaves both as a conductor of the alternating field and as a medium with eigenmodes, so that under certain conditions the waveguide can be transformed into a three-channel structure. The dispersion curves of the magnetostatic wave modes of a two-channel waveguide lie in zones bounded by the dispersion curves of the corresponding modes of a one-channel waveguide of double width. As the gap between the channels increases, the dispersion curves of the odd modes shift toward shorter wavelengths, and those of the even modes shift toward longer wavelengths. Zh. Tekh. Fiz. 68, 91–96 (February 1998)     

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.     

Waveguide Modes in a Planar Graphene–Dielectric Thin-Layer Structure

Particular features of waveguide propagation of modes in a planar structure that consists of alternating layers of a dielectric and graphene are investigated. Within the effective-medium approximation, dispersion relations are obtained for symmetric and antisymmetric waveguide modes. Based on their numerical analysis, the frequency dependences of the propagation and decay constants, of the group and phase velocities, and of the energy flux carried by waveguide modes are constructed. The influence of the fraction of graphene in the structure on the behavior of waveguide modes is analyzed.     

Investigation of the guided modes in anisotropic diffused slab waveguide with embedded metal layer

Abstract

The optical characteristics of the TE and TM guided modes of a multilayer anisotropic two-dimensional waveguide are investigated by using the field component transformation matrix, and also taking into account the substrate intrinsic dispersion. The embedded thin metal layer effects on the propagation constant for both lossless approximated and exact solutions are presented. The lossless approach is accurate enough for the TE waves, but it is not for the TM ones, which exhibit changes of about 10^?6 for the equivalent index. The TM modes also present attenuation constant changes between the lossy and weakly-lossy solutions of the order of 9 dB/cm. Several complex field component mappings are drawn, and the surface plasma waves are also examined.     

Study of phonon polaritons in GaAs/GaPAs superlattices using methods of IR reflection spectroscopy

We studied phonon-polariton modes in long-period GaAs/GaPAs semiconductor superlattices using the methods of frustrated total internal reflection and IR spectroscopy in the region of residual rays. The excitation of waveguide, real, and virtual surface and volume phonon polariton modes was observed experimentally. Their dispersion relations were calculated and compared with experimental data, and the excitation nature was identified with the aid of the spectra of permittivity and a normal component of the wave vector in heterostructure layers. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 4, pp. 460–466, July–August, 1999.     

Theoretical analysis of the waveguide propagation of electromagnetic waves in dielectric smoothly-irregular integrated structures

The waveguide propagation of a monochromatic electromagnetic wave in a multilayer smoothly-irregular integrated dielectric structure has been studied under natural physical and mathematical assumptions. Approximate solution of the vector electrodynamic problem satisfying the condition of smoothly varying shape of the structure is found using the Kantorovich method of the partial separation of variables, since the conventional method of separating variables, which is usually employed for regular waveguides, in the given case is inapplicable. Using the obtained solution, it is possible to describe analytically the fields of smoothly deforming modes of a dielectric waveguide, their interrelation, and the dispersion relations between the distribution of the phase slowing coefficient and the local inclination of layers in the structure under consideration. The proposed method can also be used, in a quite broad range of wavelengths, for an analysis of analogous waveguide structures made of both dielectric and magnetic materials.     

Excitation mechanisms and dispersion characteristics of guided waves in multilayered cylindrical solid media

This paper first reviews a method of simulating the propagation characteristics of guided waves in multilayered coaxial cylindrical elastic solid media. Secondly, this method is used to investigate the properties of the guided waves for the ultrasonic long-range non-destructive evaluation techniques for rockbolts. To do so, the special case of non-leaky guided modes in open waveguides is considered. The method explains how the complex dispersion function is converted into a real function: hence the bisection technique can be employed to search for all the real roots. The model is used to (i) characterize the low dispersion range and anomalous dispersion of normal and Stoneley modes and (ii) analyze the excitation mechanisms of guided waves from axisymmetric and non-axisymmetric acoustic sources. The results are used to select suitable excitation frequency ranges associated with dominant modes with large amplitudes, low dispersion, and distinguishable propagation velocities to reduce signal distortion. The results suggest the lowest order flexural mode, excited by a radial force source, has potential to be used in practice. Also, the highly dispersive Stoneley mode propagating along a cylindrical interface is defined and distinguished from the normal mode using two properties, velocity high-frequency asymptotes and amplitude distributions along the radial direction.     

Helmholtz equation solutions corresponding to multiple roots of the dispersion equation for a waveguide with impedance walls

The Helmholtz equation solutions corresponding to multiple roots of the dispersion equation are considered for a waveguide with impedance walls. It is shown that in this case the eigenfunctions are determined by expressions that cannot be obtained by the separation of variables. In addition to exponential or trigonometric factors, such functions involve factors linear in coordinates. Equations for calculating the multiple roots are obtained, and the relationships that determine the impedance values at which the multiple roots appear are presented. The Green’s function is constructed for the case of the appearance of multiple roots. A plane waveguide and a circular waveguide with axially symmetric modes are considered.     

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)     

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.     

Excitation of anti-symmetric coupled spoof SPPs in 3D SIS waveguides based on coupling

According to the electromagnetic field distributions, there exist two kinds of coupled spoof surface plasmon polaritons(SSPPs), the symmetric and anti-symmetric modes, in the three-dimensional(3D) subwavelength spoof–insulator–spoof(SIS) waveguide. We study the dispersion and excitation of the two kinds of coupled SSPPs supported by the 3D SIS waveguide. The evolution of the dispersion with the thickness and gap width of the waveguide is numerically investigated,and we give a theoretical analysis according to the coupling mechanism. Specially, based on the coupling mechanism,we design a zipper structure, through which the excitation and propagation of the anti-symmetric coupled modes can be realized effectively.     

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.     

Planar anisotropic Mikaelian lens on the basis of EBG-structure

The problem on the synthesis of a planar Mikaelian lens in the form of layered metal?dielectric waveguide with a nonuniform anisotropic dielectric layer is solved. The problem is reduced to solution of the dispersion equations for E and H modes of a homogeneous layered waveguide. As an example of implementation of the solution obtained, the synthesis and analysis of the Mikaelian lens is carried out on the basis of the EBG structure in the form of a planar corrugated open and closed layered metal?dielectric waveguide. For a special case of the closed waveguide, the solution of the problem of synthesis for both polarizations is obtained explicitly.     

线性分段折射率分布多量子阱波导色散关系的精确分析

本文从标量Helmholtz方程出发,采用转移矩阵技术,求出了线性分段折射率分布多量子阶波导TE模色散关系的精确解,数值计算结果显示出该波导的色散特性以及与波导结构的关系,为实际制作该量子阶波导进行参数选择提供了理论依据。     

沿均匀无限介质中固体杆传播的导波特性研究

针对均匀无限固体介质包围的无限长固体杆,研究了沿固体杆传播的导波的频散和激发特性。在理论分析的基础上,用二分法快速求取了导波所有模式的频散曲线,在4种介质参数下,对斯东利模式和简正模式进行了深入的分析和总结;研究了固体杆中导波的激发强度特性,分别在对称点源、轴向力源和径向力源激励下,研究了导波诸模式的激发机理及频谱特性,分析了不同频段导波的主导模式,研究了主导模式的频响特性及位移径向分布关系。      

Effect of finite V⊥ on Cerenkov FEL in adielectric loaded waveguide

Allowance for finite V_⊥ of an annular electron beam propagating through a dielectric-loaded waveguide immersed in an axial magnetic field opens up the possibility of excitation of TE modes. The interaction is observed using Cerenkov and cyclotron resonances. On approximating the field distribution at the electron orbits to some suitable form, an analytical solution to the Vlasov equation is obtained, leading to a comprehensive dispersion relation for azimuthally symmetric TE_0n modes. In the special case where all the guiding centres lie on the axis, a fluid treatment for the arbitrary azimuthal-mode number is applicable. In these cases the growth rate increases with V_⊥