To study loss and dispersion characteristics of the **dielectric**-coated **hollow**-core waveguide, a full-vectorial finite element method (FEM) is considered. An accurate, versatile and numerically efficient FEM based on full-vectorial H-field formulation developed earlier [26] which has been widely used in the analyses of microwave and optical guided-wave devices including the intermediate terahertz waveguide. In this study, the H-field formulation is utilized to obtain the modal solutions of **dielectric**-coated **hollow**-core **waveguides**: rectangular, circular and elliptical **waveguides**. The cross- section of **waveguides** can be represented by using many triangles of different shapes and sizes. The flexibility of unequal size elements in the FEM is a preferable choice which can also represent the **curved** interfaces of circular and elliptical **waveguides** more accurately. Here, this method is used to find the different modes, their propagation constants and their corresponding full-vectorial field profiles.

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Slabs with more general refractive index distributions were considered by Heiblum and Harris [3] and by Kawakami, Miyagi and Nishida [4], using a WKB method [5]. These two papers consider the case when the mode on the **curved** waveguide is not a small perturbation of a mode on the straight guide, but was guided essentially by the outer boundary. The modes of this nature are known as “edge-guided” modes. The increase in radiation losses due to curvature for slightly leaky modes on **hollow** **dielectric** or imperfect metallic **waveguides**, a sort of composite of open and closed waveguide behavior, was investigated by Marcatily and Schmeltzer [6].

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Slabs with more general refractive index distributions were considered by Heiblum and Harris [7] and by Kawakami et al. [8], using a WKB method [9]. These two papers consider the case when the mode on the **curved** waveguide is not a small perturbation of a mode on the straight guide, but was guided essentially by the outer boundary. The modes of this nature are known as “edge-guided” modes. The increase in radiation losses due to curvature for slightly leaky modes on **hollow** **dielectric** or imperfect metallic **waveguides**, a sort of composite of open and closed waveguide behavior, was investigated by Marcatily and Schmeltzer [10].

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Terahertz (THz) transmission simulations play an important role in THz technology researches, especially for the structural design of a THz wave- guide. Ray model takes into account both structure parameter of waveguide and the divergence angle of beam light and could be an alternative way for THz transmission behavior simulations. In this paper, the ray model is used to calculate the transmission loss of tube waveguide, and the simulated transmission losses are presented to compare with the results calculated by COMSOL. The suitable THz frequency range of ray model is discussed by analyzing the transmission loss spectra of tube **waveguides** with various core sizes. The credibility of ray model on terahertz transmission simulations is demonstrated based on the experimental results tested by THz-TDS and cal- culated results.

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The modeling of bending loss of optical **waveguides** has been of special interest since the demonstration of the first functional laser in 1960. Many classical publications ex- ist, e.g. Marcatili (1969); Lewin et al. (1977); Marcuse (1982); Snyder and Love (2000), but the presented ap- proaches are mostly approximations for small radiation loss. Often the leaky mode ansatz is presented as exact solution of Maxwell’s equations for the cylindrical slab waveguide. This ansatz uses Hankel functions in the outer region in order to satisfy the radiation condition. But it is not the single mode that has to satisfy this condition, it is the sum of all modes. In addition the discrete and limited set of leaky modes can not build a complete set of solutions. In 1990 Morita and Yamata presented a new, initially nonrestrictive theory, but also ap- plied the radiation condition to the individual mode (Morita and Yamada, 1990). Hence it was Kerndlmaier in 1992 who first presented the theory, that is not limited to any special

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Much the same results can be obtained for several core-cladding **dielectric** **waveguides**. To show this in our study, we have reduced the required continuity and boundary conditions for core- cladding waveguide to one-side boundary conditions on the ﬁeld inside the core region. The resultant boundary conditions were found to have the same form as for circular waveguide with anisotropic surface impedance. We have determined the components of eﬀective surface impedance as functions of cladding parameters and desired eigenfrequency for step-index waveguide and perfectly conducting (PEC) waveguide with **dielectric**-lined surface. In the general case these components appear to be mode-dependent. This diﬀerentiates our results from those presented in [34], which are mainly related to several special cases of frequency-dependent surface impedance. Besides, our study diﬀers from [34] in that it concerns anisotropic cladding material [35–37].

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a DFW with those of a **hollow** waveguide assuming compactness ratio K = 2 and desired frequency f 0 = 10 GHz considering N = 5 and 11 layers. The required electrical parameters have been obtained as (µ rm = 2, ε rm = 1.35) and (µ r = 3, ε r = 1.85). Also, Fig. 5 illustrates

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Numerous designs of circularly polarized cylindrical DRAs have been reported in the literature by using the dual and single feed mechanisms. For instance, a 3-dB axial ratio bandwidth of 3.4% has been obtained when a cylindrical DRA is excited by perturbed annular slot with backing cavity [9]. A circularly polarized cylindrical **dielectric** resonator antenna using a helical exciter with a 3-dB axial ratio bandwidth of 6.4% has been reported in [10]. The **hollow** rectangular DRA with an underlaid quadrature coupler offering a 10.54% AR bandwidth has been demonstrated in [11]. An elliptical DRA with a circular polarization bandwidth of 3.5% has been investigated using a single-probe feed [7]. AR bandwidths of 3.91% and 2.2% have been achieved for cylindrical DRA excited by a cross-slot [12], and slot- coupled structure [13], respectively. A conformal square spiral strip exciting the cylindrical DRA with a 4.3% CP bandwidth has been reported in [14]. Since the traveling-wave current distribution changes slowly with frequency, a wider CP bandwidth is expected. Such a feeding method has been reported in [15], where a CP bandwidth of 7% has been achieved using a spiral strip to excite a rectangular DRA. In this paper, a square spiral microstrip line is used to achieve a left hand circularly polarization (LHCP) radiation. Potential advantages include a simpler structure, a 31.25% impedance-matching bandwidth with S 11 < −10 dB and a 15.5% bandwidth with AR less than 3 dB.

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Review of literature For several years, atmospheric non-thermal plasmas have been studied by various research groups in context with their applications of excimer synthesis in working media of rare gas and their halides. Besides the use of DBD technology for excimer formation, in the beginning of 21 st century, VUV/UV source based on excimer formation pumped by micro **hollow** cathodes discharge [Kurnczi et al., 1999; Kurnczi and Becker, 2000] were investigated. Schoenbach and his coworkers investigated MHCD technology for excimer synthesis and efforts were made towards the parallel operation of MHCD discharge and their fabrication in semiconductor [Schoenbach et al., 1997; Habachi and Schoenbach, 1997; Schoenbach and Stark, 1998; Becker et al., 2006]. A special emphasis was laid on spectroscopic studies of plasmas used as a source of noncoherent vacuum ultraviolet radiation such as rare excimer emission, and atomic and molecular emission from plasmas in admixture of rare gases and molecular gases.

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For the design of a PDWG cross connection structure, the basic construction units are single mode and multi-mode PDWGs. Therefore, dispersion and transmission properties of single mode and multi-mode PDWGs are studied ﬁrstly. The considered one-dimensional (1D) PDWG consists of circular **dielectric** pillars, as shown in the inset of Fig. 1. Lattice period of the PDWG is a . All the **dielectric** pillars have the same radius of R = 0 . 5 a . Refractive index of the **dielectric** pillar is set as 3.4, and the background material is supposed as air with an index of 1. Through a PWE method, the dispersion properties of the PDWG are calculated. As shown in Fig. 1, the PDWG is single mode in a wide frequency range. In this paper, only TE mode is considered, of which the electric ﬁeld vector is perpendicular to the propagation direction and parallel to axial direction of the **dielectric** pillars.

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Abstract—In this paper a novel approach based on Asymptotic Iteration Method (AIM) is presented to solve analytically the light propagation through one-dimensional inhomogeneous slab waveguide. Practically implemented optical slab **waveguides** based on traditional techniques are usually inhomogeneous and numerical methods are used to obtain guided wave characteristics. In this work, we develop analytical method for modal analysis includes Eigen modes (electric and magnetic ﬁelds distribution) and Eigen values (guided wave vector) using AIM. The developed method is applied to some especial examples.

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Grain moisture measurement based on **dielectric** properties data became the most prominent agricultural application. The development of this encourage to a new technique which contributed to several applications of radio frequency **dielectric** heating. For the last 15 years, the concept of permittivity measurement has been extended and applied to various cultural and food. The main purpose of this project is to study Radio Frequency method of **dielectric** properties measurement between frequency range of 2.1GHz to 3.0GHz and the procedure to get the value of **dielectric** by using the microwave reflection and transmission theory.

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On the basis of the theoretical analysis, a typical application is in progress, which is combined with the actual situation of the section in Jinhua: the setting of the speed-limit sign at the bend of the double dragon cave scenic area in Jinhua. It provides the design index and the evaluation method of the road alignment safety and the driver’s driving comfort for the traffic management and the decision makers. And it establishes the perfect setting system of the speed-limit sign. so it can compute and set the sign by alignment and road grade, it will make a contribution to decrease the traffic accident of the double-lane steep **curved** sections.

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wide bandwidth and low polarization dependence. MMI devices are based on the self-imaging property [13], where the guided modes of a multimode waveguide are excited and interfere constructively to produce single or multiple images of an input field launched usually via single mode optical **waveguides** at the one end of the structure, at periodic intervals along the direction of propagation. The number of the modes excited in each MMI structure and consequently the position of the images along the direction of propagation are dependent on the position of the input **waveguides** in the lateral x- direction, called the interference mechanism [13]. Under the symmetric interference (SI) mechanism, the first image of an input field launched via an input waveguide placed in the centre of the MMI width, is obtained at a self image length of L i =3L π /4, along the direction of propagation, where the

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black arrow direction. The mechanism of PCSBGs is displayed in Figures 4(a) and 4(b) in which the letter K stands for a cell in cylinder, and two arrows highlighting the skew grid lines connecting to the side of the K cell are used to assist in explaining PCSBGs. At a certain moment of time, all grid lines inside the rotating cylinder are half way passing the grid as in Figure 4(a). Then in Figure 4(b) it is the very instant when PCSBGs are to be maneuvered to swing back by one grid to the right of the K cell. As illustrated above, MOC solves the time-domain Maxwell equations with the rotating **hollow** cylinder in team working with PCSBG and the modiﬁed O-grid. During the process, MOC constantly and precisely updates every change in grid measurement and orientation of those dynamic grids.

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The conventional AWG Demux is shown in Fig1.The **waveguides** in the array section differs from the adjacent one by an incremental length. The incremental length is chosen in such a way that optical path length difference between the adjacent **waveguides**,equals an integer multiple of the central wavelength of the Demultiplexer[Smit (1988)].

Fig. 8 shows an optical switch which is a device that allows optical signals to be switched on and off or switched from one channel to another. An optical switch is made of two parallel **waveguides** coupled with a directional coupler [14]. A directional coupler is made of two optical **waveguides** that are brought close to each other in such a way that their respective optical modes can interact and split into even and odd symmetries that allow the transfer of power between them [15]. For an optical switch, the relative phase difference between the supermodes of the coupling system must be π and hence the value of the coupling length L c must be chosen to satisfy this condition.

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mm. (b) Theoretical results. Reflection, R, and transmission, T , coefficients, versus frequency, for the fundamental proper mode. Basic modes number: 20. Proper modes number in all **waveguides**: 20. structures. In all cases we have used a sequence of alumina-air-alumina discontinuities in the channel as periodical parameter, as shown in Figure 8. Different periodical configurations were designed and tested. As an example, Figure 10(a) shows a periodic structure and the cross section dimensions. In this case, the physical parameters were as follows: 23 inverted Π **dielectric** **waveguides**; conducting walls cross section dimensions (mm); a = 22.86, b = 10.16; basic modes number: 20; proper modes number: M = N = P = . . . = 20; ε r1 = 2.1 (teflon), ε r2 = 10 (alumina) in odd order inverted Π **dielectric** **waveguides** and ε r2 = 1 (air) in even order inverted Π **dielectric** **waveguides**.

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Chambers, “Measurement of the complex permittivity of curved dielectric radome specimens using an open resonator,” in Proc.. 16th European Microwave Conf., Dublin, Ireland, Sept.[r]