The curvature induced degenerated separation in curved waveguides is stud- ied in this paper. The analysis of curved waveguides is performed by using a two dimensional (2-D) Finite Difierence Frequency Domain (FDFD) eigenvalue method employing orthogonal curvilinear coordinates. The eigenvalues frequency spectrum (propagation constants dispersion curves) of curved circular waveguides is considered. Curvature lifted degeneration is ob- served in these numerical results. The accuracy of the method is examined through comparisons with already published results. Curved waveguides have become a signiflcant key in the design of several microwave circuits and systems. A variety of applications like moving airborne platforms or modern phased arrays carrying microwave transmit-receive systems require their antennas to be made conformal to the objects surface. The recent adoption of \smart skin ideas asks for the whole RF front end to be made conformal to the host object's surface. This approach enforces printing or integrating microwave devices on curved surfaces. The curvature varies from canonical objects surfaces as cylinders, to almost arbitrary (usually aerodynamic) curvatures. In turn, a plethora of microwave devices can be considered as comprised of curved waveguiding sections. Therefore, the accurate design of conformal systems requires the knowledge of curved waveguides and particularly printed transmission lines characteristics. This paper contributes exactly to this speciflc research fleld. Despite its apparent simplicity, the analysis of propagation in a curved waveguide continues to be a challenging electromagnetic problem. Since the publication of Lewin et al book in 1977, (1), an extensive research on curved waveguides has been carried out, e.g., (2{4). However, these works were mainly restricted to the study of canonical geometries. In Particular, Lewin etal., (1), investigated E- and H- plane bends of rectangular or circular waveguides with a perturbation method. Besides, other perturbation methods were employed for the analysis of curved waveguides mainly in the optical spectrum, for example Xi Sheng Fang, (2). Within this efiort the \expansion of the bend into straight waveguide modes was also employed by many researchers, e.g., (3). Experiments with bends in nonradiative dielectric waveguides were also performed, (4). Concerning the analysis of practical devices, numerical methods like the two dimensional Finite Element Method (FEM) or the Method of Moments (MoM) are in principle capable of handling curved geometries e.g., (5{6). Yet, FEM is unable to handle waveguide curvatures in the propagation direction and MoM involves the Green's functions of the structure which are not usually available for arbitrary shaped curved geometries. Hence, these methods by no means can serve as a general tool for the analysis of arbitrary curved waveguides. Our research efiort is based on a two-dimensional Finite Difierence Frequency Domain (2-D FDFD) eigenvalue method formulated in orthogonal curvilinear coordinates. The theoretical ba- sics have been presented in our previous works, (7{8). This analysis is formulated as an eigenvalue problem for the complex propagation constants. It is restricted to structures uniform along the propagation direction. The waveguiding structure can be curved in all directions and this consti- tutes its main advantage. Besides that, it retains the classical FDFD method capability of handling arbitrary shaped geometries loaded with either isotropic or anisotropic materials. The present work mainly focuses on the degenerated separation. For instance, in straight circular waveguides the TE01 and TM11 are degenerative, namely they present the same dispersion curves. Besides that, all right and left hand circularly polarized are also degener- ative. When the waveguide is curved - bend the degeneration is lifted and the dispersion curves are separated. This phenomenon must be distinguished from the \birefringence, where a new mode (not existed before) is generated due to some perturbation, for example a material anisotropy. In the following sections this phenomenon will be studied for a curved circular waveguide.
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Jan 1, 2017
Peng Fei Kou + 1
Open Access