Calculation and Optimization of 3D Waveguiding System with Help of Integral Equation Method
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Calculation and Optimization of 3D Waveguiding System with Help of Integral Equation Method A. P. Gashturi & G. G. Denisov & S. V. Mishakin & S. V. Samsonov
Received: 22 October 2008 / Accepted: 2 January 2009 / Published online: 30 January 2009 # Springer Science + Business Media, LLC 2009
Abstract For 3d waveguiding system calculations we used the Electric Field Integral Equation (EFIE) model, applied to infinitely thin, perfectly conducting waveguide surfaces. The solution represents induced current, from which the field in the device is obtained. With the help of this method an asymmetric mode converter TE01-TE11 was simulated and optimized for maximum efficiency. We have also studied a helically corrugated structure, which is used in pulse compressors, and analyzed the structures dispersion curves and compared it with measurement results. Keywords Electric field integral equation . Multilevel fast multipole algorithm . Multi-mode waveguide
1 Introduction The use of Electric Field Integral Equation (EFIE) is the one of the powerful methods for solving diffraction tasks in multi-mode microwave systems [1], which are used in many kinds of microwave devices. The approach has many advantages over others, such as high accuracy and relatively moderate requirements to the computer resources. In the present work a computer code solving EFIE was realized and adapted to analysis and optimizing of waveguide mode converters. Several problems were considered with help of this program. An asymmetric mode converter TE01-TE11 was calculated and optimized for maximum efficiency. Dispersion and eigenmodes for pulse compressor oversized waveguides with multi-fold helical wall deformation were also calculated [8].
A. P. Gashturi (*) : G. G. Denisov : S. V. Mishakin : S. V. Samsonov Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod 603950, Russia e-mail: [email protected]
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J Infrared Milli Terahz Waves (2009) 30:319–327
2 Electric Field Integral Equation formulation The Electric Field Integral Equation (EFIE), which can be applied to infinitely thin, perfectly conducting waveguide surfaces (Fig. 1) is written as (see, for example [1]): Z 4p ~i rr0 b E ð~ r;~ r 0 Þ~jð~ I 2 Gð~ r 0 ÞdS 0 ; ð1Þ rÞ ¼ k k S 0
eik ð~r~r Þ r~ r 0j j~
is the Green function for Helmholz equation ~jð~ r 0 Þ, is the where Gð~ r;~ r Þ¼ i ~ rÞ is the incident waveguide source field, which is calculated unknown surface current, and E ð~ mA on the surface A. as the radiation of currents ~jA ; ~ The Method of Moments (MoM, [1]) is used to transform this integral equation into an algebraic system of linear equations. A finite set of N basis functions ~ wl should be defined on the surface S to represent ~jð~ r 0Þ n X ~j ¼ xl ~ wl ; ð2Þ 0
l¼1
and the result of expansion of the EFIE is the matrix equation: b x ¼ b; Z
ð3Þ
where vector x contains unknown coefficients xl. Vector b1 and elements Zlp of matrix Z are defined as: Z E i ð~ bl ¼ ~ rÞ~ wl ð~ rÞdS; ð4Þ S
0 1 ZZ 1@ 2b 0 0 0A ~ r;~ r Þ~ Zlp ¼ wp ð~ wl ð~ rÞ k
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