Frequency Selective Characteristics of Dielectric Periodic Structures for Millimeter Wave Application

In this paper, the frequency selective reflection characteristics of dielectric periodic structures for the oblique incidence of a plane wave are analyzed by a method which combines the multimode network theory with the rigorous mode matching method. The variations of the total reflection characteristics with the geometric dimensions of the dielectric periodic structures are systematically investigated to develop useful guidelines for the design of the dielectric frequency selective surface. Moreover, the relationship between the related wave phenomenon and the dispersion characteristics of multilayer plane dielectric structure is explained with the theory of plane dielectric waveguide.     

Analysis of FSS with Dielectric Losses at Millimeter Wave Band Using the Transverse Transmission Line Method

The analysis of periodic structures on isotropic substrates with dielectric losses is presented. Frequency selective surface structures composed by an array of conducting patch elements are considered. This analysis uses the Galerkin method in combination with the transverse transmission line method, in the Fourier domain, to determine the reflection and transmission characteristics of the considered structures. The analysis provides very accurate results compared to those presented by other authors.     

A periodic FMM for Maxwell’s equations in 3D and its applications to problems related to photonic crystals

This paper presents an FMM (Fast Multipole Method) for periodic boundary value problems for Maxwell’s equations in 3D. The effect of periodicity is taken into account with the help of the periodised moment to local expansion (M2L) transformation formula, which includes lattice sums. We verify the proposed method by comparing the obtained numerical results with analytic solutions for models of the multi-layered dielectric slab. We then apply the proposed method to scattering problems for periodic two-dimensional arrays of dielectric spheres and compare the obtained energy transmittances with those from the previous studies. We also consider scattering problems for woodpile crystals, where we find a passband related to a localised mode. Through these numerical tests we conclude that the proposed method is efficient and accurate.     

Radiation characteristics of multilayer periodic dielectric structures

Radiation characteristics of multilayer periodic dielectric structures are investigated by the method which combines the building block approach of multimode network theory with the rigorous mode matching procedure. The multilayer periodic structure is composed of uniform dielectric layers and single periodic layers. Two examples are given in this paper; first, radiation property of the double dielectric grating antenna is analyzed. The results indicate that the double dielectric grating antenna has relatively smaller dimensions than that of the single one. It is undoubtly of great importance in the case that the limitation of the weight and the volume of the system is strictly required. Secondly, some curved profile grating antennas are analyzed by combining the present method with the staircase approximation. In such a way, the effects of groove profile on the performance of the grating antennas are systemetically studied and some useful guidelines for the design of the dielectric grating antennas are thereby suggested.     

INVESTIGATION ON EFFECTS OF LEFT-HANDED MATERIALS ON FREQUENCY SELECTIVE CHARACTERISTICS OF DIELECTRIC PERIODIC STRUCTURES

The effects of left-handed materials (LHM) on frequency selective reflection and transmission characteristics of dielectric periodic structures are carefully investigated using a method which combines the multimode network theory with the rigorous mode matching method. In addition, the effects of LHM dielectric loss on the selective properties are also given. It has been shown that the selective behavior of periodic structures can be modified by adding LHM layers above and below the periodic layer. Supported by the National Natural Science Foundation of China (No. 60171037) (No. 60371010) and (No. 63531020)     

Analysis of Dielectric Periodic Structures with Multi-Mode Network Method

The transmission characteristics of several dielectric periodic guiding structures are analyzed in this paper with a method, which the rigorous mode matching method is combined with the multimode network theory. The precision and effectiveness of the present method are verified by experimental data.     

电磁波在周期介质中的传播及二维光子晶体的光子带结构

光子晶体是光学与凝聚态物理交叉的新领域,也是近年来应用物理学的一个重要研究领域,它是一种由介电常数高的(低的)介质在另一种介电常数低的(高的)背景介质中周期排列所组成的人造多维周期结构材料,能够产生光子带隙。频率落在带隙内的光在晶体里沿任何方向都不能传播,因而具有能够抑制原子、分子的自发辐射等诱人的光电子学特性,在基础研究和实际应用上都有着巨大的潜力。本文在这一领域里进行了富有成效的研究,获得了很好的结果。主要有:(1)利用平面波展开方法来计算二维光子晶体的带隙结构。首先,我们设计正方晶胞的二维光子晶体模型。设x₃方向为介质柱的轴方向,二维周期结构在x₁-x₂平面上。晶胞的晶格常数为a,半径为r,介质柱和空气柱的介电常数分别为ε_a=17和ε_b=1,a>2r。设计的核心思想是通过降低光子晶体结构的对称性,消除光子能带在晶体的布里渊区高对称点上的本征简并。(2)对于二维光子晶体的电磁波理论及周期介质中的Bloch波解做了详细的推导,给出了光子晶体中禁带存在的理论依据。同时以正方格子晶格的二维光子晶体为例,验证了电介质在空气圆孔中的排列存在E偏振和H偏振的光子带隙重叠区,称为绝对光子带隙。对于二维的光子晶体,两种本征偏振模式的光子能带结构可以独立地调节,以实现两者的光子带隙的最优重叠, 从而大大提高了二维光子晶体的完全带隙宽度。     

A NEW FREQUENCY SELECTIVE SURFACE COMPOSED OF LEFT-HANDED MATERIALS

The frequency selective characteristics of a new dielectric periodic structure composed of left-handed materials (LHM) are carefully studied by a method which combines the multimode network theory with the rigorous mode matching method. The variations of the frequency selective characteristics with structure parameters and dielectric loss are presented and comparisons for the frequency selective properties between RHM and LHM gratings are also shown with some explanations. Guidelines for accurate design of the LHM dielectric frequency selective surface are given. Supported by the National Natural Science Foundation of China (No. 60171037) (No. 60371010) and (No. 63531020)     

Scattering Analysis of Dielectric Periodic Structures by an Oblique Incidence

The scattering of dielectric periodic structures by a plane wave incident in the direction oblique to the periodic grooves is analyzed by a method which combines the multimode network theory with the rigorous mode matching method. Combining the TE and TM characteristic mode functions determined in the corresponding 2-D scattering problem resulting from a TE or TM wave incident along the principal-plane of the same structure, and using a simple mathematical transformation, the 3-D scattering problem by an oblique incidence is rigorously solved.     

A Simple Bi-directional Mode Expansion Propagation Algorithm Based on Modes of a Parallel-plate Waveguide

The bi-directional mode expansion propagation algorithm (BEP) is known to be an accurate and efficient method for modelling field distribution in high-index contrast waveguide structures with strong back-reflections like Bragg gratings and photonic crystals. The main difficulty of this method is that for lossy structures, the propagation constants of modes are to be searched in the complex plane. To speed-up this procedure, a two-step algorithm for eigenmode calculation based on the expansion into the modes of an empty metallic waveguide has recently been proposed. Proper truncation rules possessing good convergence of the expansion method for both TE and TM modes have also been recently published. In this contribution, both these approaches are combined in the development of an extremely simple version of the two-dimensional BEP method that makes use of the field expansion into the eigenmodes of a parallel-plate waveguide. The method is strictly reciprocal and appeared to be computationally reliable also for strongly lossy structures. High numerical stability is ensured using the scattering matrix formalism, and an efficient method of calculating Bloch modes for symmetric as well as asymmetric periodic waveguide structures is adopted. A wide range of applicability of the method is demonstrated by a few examples.     

用转移矩阵法数值研究二维正方介质柱光子晶体的传输特性

利用转移矩阵方法对二维正方介质柱光子晶体的传输特性进行了研究,数值计算研究了不同晶格、同一晶格柱体截面面积不同、放置方位角不同时光子晶体的传输特性。数值结果表明光子禁带的宽度与中心频率和晶格结构有很大关系,正方晶格更易形成平坦光子禁带,柱体截面面积大,则形成的禁带较宽,在其他因素相同的条件下柱体放置的方位角对光子禁带有重要影响。数值研究表明在正方介质柱下设计宽平坦光子禁带时,可以首先考虑正方晶格结构,其次设法使柱体截面尽量大一些,最后可通过柱体放置方位角来微调光子禁带的宽度与中心频率以达到设计要求。     

Volume integral equation for analysis of three-dimensional scattering from dielectric frequency-selective structures

The space-domain volume integral equation method is presented for the analysis of three-dimension scattering from dielectric frequency-selective structures involving homogeneous and inhomogeneous lossy materials. The method directly solves for the electric field in order to easily enable the periodic boundary conditions in the spatial domain. The special basis and test functions are introduced to deal with the current continuity in periodic boundaries. The computation of the spatial domain periodic Green’s function (PGF) is accelerated by the modified Ewald transformation, so that a very thick periodic structure can also be analyzed efficiently and accurately. The PGF mentioned above is of free-space type and very smooth and amenable to interpolation. Thus, optimized interpolation procedures for the PGFs can be applied, resulting in a considerable reduction of matrix-filling time without any significant influence on the accuracy. A study of the scattering parameters of a multilayered dielectric periodic structure is accomplished by imposing the boundary conditions in terms of the multimode scattering matrix. Numerical examples show the reliability and accuracy of the proposed method.     

A full-wave three-dimensional analysis of open dielectric waveguides and periodic structures using an equivalent network model

An accurate fully vectorial wave analysis to calculate the propagation characteristics and field distribution of open dielectric waveguides and optical integrated circuits is presented. Based on the periodic repetition concept and using an equivalent network model, a method to analyze wave propagation in these guides is developed, which is able to take the simultaneous presence of mixed polarizations into account. Compared with conventional approaches like mode matching as well as with other numerical methods, the presented three-dimensional (3D) method shows individual advantages like accuracy, simplicity, and numerical efficiency. To show both validity and usefulness of this approach, some fundamental structures are investigated and the obtained numerical results are presented.     

Scattering Characteristics of Dielectric Periodic Structure Composed of Left-handed Materials with Arbitrary Oblique Incidence

Scattering characteristics of monolayer and multilayer dielectric periodic structure composed of left-handed materials (LH-DPS) with plane wave arbitrary oblique incidence are carefully analyzed using a method which combines multimode network theory with the rigorous mode matching method. Our analysis results reveal that the arbitrary oblique incident angles and relative position between different LH-DPS have great effects to the scattering characteristics of LH-DPS which different from the situation of dielectric periodic structure composed of right-handed materials (RH-DPS). The reasons why the reflection characteristics of the LH-DPS are totally different from those of the RH-DPS with arbitrary oblique incidence are also given. The present quantitive investigation provides guidelines for the design of the monolayer and multilayer dielectric frequency selective surfaces for millimeter wave applications.     

Effect of Dielectric Groove Profiles on Reflection Characteristics of Millimeter Wave Frequency Selective Surface

In this paper, the frequency selective reflection characteristics of dielectric periodic structures with arbitrary groove profiles are analyzed by a method which combines the multimode network theory with the rigorous mode matching procedure. Emphasis is placed on the discussion about the effect of the different groove profiles, such as rectangle, trapezoid, increasing cosine and triangle, on the reflection characteristics of the millimeter wave (MMW) frequency selective surface (FSS). Some useful guidelines for the design of the MMW dielectric FSS are thus suggested. Moreover, the physical explanation of the related wave phenomenon is given.     

Multimode network analysis for dielectric leaky-wave antennas consisting of multilayer periodic structure with arbitrary dielectric distributions

The multimode network method is used to analyze the radiation characteristics of the leaky-wave antenna consisting of multilayer dielectric periodic structure with arbitrary dielectric distributions in each layer. The eigenfunction of each periodic layer is determined by Floquet theorem; and the mode matching combining with generalized transverse resonant method are used to derive the dispersion equation of the leaky-wave antenna. The complex transmission constant is calculated by Newton iterative method and the radiation characteristics of the antenna are obtained. Some antenna structures are analyzed and useful guidelines for design of the leaky-wave antennas are suggested.     

Vector coupled-wave method for analyzing diffraction by multilayer gratings

In the framework of the matrix formulation of the coupled plane wave approach, a method is proposed for increasing the stability of the numerical analysis of vector electromagnetic fields in periodic structures, including dielectric and metallic anisotropic layers and relief boundaries.     

Complete Polarization Conversion Characteristics of Dielectric Grating Composed of Left-Handed Materials

The TE/TM polarization conversion characteristics of dielectric grating composed of left-handed materials for the case of plane wave oblique incidence are carefully investigated by a method which combines the multimode network theory with the rigorous mode matching method. It is indicated that complete polarization conversion between TE and TM modes can be realized using left-handed gratings. This can hardly achieve in the conventional right-handed gratings. Comparisons of polarization conversion properties between right-handed gratings and left-handed gratings are given with physical explanations. This unique merit of left-handed periodic structure is of important significance for accurate design of new millimeter wave TE/TM polarization converters.     

Scattering Parameters of FSS on Anisotropic Layers at Millimeter Wave Frequencies

The analysis of periodic structures on anisotropic substrates is presented for incident millimeter waves. Frequency selective surface structures composed by a periodic array of conducting crossed dipoles on anisotropic layers are analyzed. A full-wave analysis for the problem of scattering is performed. The formulation uses the moment method in combination with the immitance approach, in the Fourier domain, to determine the scattering parameters of the considered structures. A set of entire-domain type basis functions is used in the expansion for the unknown induced current. This analysis is computationally efficient, and its accuracy is verified by the agreement between results obtained in this work and those available in the literature, for particular cases.     

A new approach for analysis of closed dielectric waveguides

The dispersion characteristics of a class of closed dielectric waveguides are investigated by the method which combines the building-block approach of mul timode network theory with rigorous mode matching procedure. Several numerical examples for different guiding structures have been given by the approach. The same structures are also analyzed with the finite element method and the EDC method for comparison. The calculations show that the present approach yields as highly accurate results as the finite element method while almost retaining the simplicity of the EDC method, and justify the utility of the present method