Analysis of Truncated Gratings and a Novel Technique for Extrapolating their Characteristics to those of Infinite Gratings
Keywords:
Current density, electromagnetic scattering, extrapolation algorithms, frequency selective surfaces, periodic strip gratingsAbstract
Periodic gratings, such as Frequency Selective Surfaces (FSSs) and EBG (electromagnetic band gap) structures, are used in a wide variety of electromagnetic applications and are typically analyzed under the assumption that they are infinite periodic. Since the real-word structures are necessarily finite, and are derived by truncating the corresponding infinite structures, it is of interest to determine how large the finite structure needs to be so that it mimics its infinite counterpart. A related question is how to extrapolate the simulation results of a finite structure to predict the performance of the corresponding infinite structure in a computationally efficient manner. The objectives of this work are to address both of these questions and to present a novel computational technique which hybridizes analytical and numerical techniques to provide the answers. We illustrate the application of the proposed technique by considering the test case of plane wave scattering by a strip grating and investigate the asymptotic behavior of the solution for the current on a truncated periodic grating as we increase its size. The proportionality constant, relating the current distribution on the unit cell of the infinite grating to the corresponding distribution in the truncated grating, is computed, and its asymptotic value is accurately predicted by using an extrapolation algorithm presented in the paper. The required number of strips is estimated such that the current on the finite structure is sufficiently close to that on the infinite one. The results obtained for the current are found to be in excellent agreement with those derived from full-wave simulations.
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References
B. Munk, Frequency Selective Surfaces: Theory and Design. John Wiley, 2000.
Y. Rahmat-Samii, “The marvels of electromagnetic band gap (EBG) structures,” ACES Journal, vol. 18, pp. 1-10, 2003.
A. Mackay, B. Sanz-Izquierdo, and E. A. Parker, “Evolution of frequency selective surfaces,” Forum for Electromagnetic Research Methods and Application Technologies (FERMAT), vol. 2, 2014.
R. Mittra, C. H. Chan, and T. Cwik, “Techniques for analyzing frequency selective surfaces-A review,” Proceedings of the IEEE, vol. 76, pp. 1593-1615, 1988.
C. H. Chan and R. Mittra, “On the analysis of frequency-selective surfaces using subdomain basis functions,” IEEE Transactions on Antennas and Propagation, vol. 38, pp. 40-50, 1990.
Y. Hao and R. Mittra, FDTD Modeling of Metamaterials: Theory and Applications. Artech House, 2009.
I. Bardi, R. Remski, D. Perry, and Z. Cendes, “Plane wave scattering from frequency-selective surfaces by the finite-element method,” IEEE Transactions on Magnetics, vol. 38, pp. 641-644, 2002.
F. Costa, A. Monorchio, and G. Manara, “An overview of equivalent circuit modeling techniques of frequency selective surfaces and metasurfaces,” ACES Journal, vol. 29, pp. 960-976, 2014.
J. Blackburn and L. R. Arnaut, “Numerical convergence in periodic method of moments analysis of frequency-selective surfaces based on wire elements,” IEEE Transactions on Antennas and Propagation, vol. 53, pp. 3308-3315, 2005.
G. L. Baldwin and A. E. Heins, “On the diffraction of a plane wave by an infinite plane grating,” Mathematica Scandinavica, vol. 2, pp. 103-118, 1954.
E. Luneburg and K. Westpfahl, “Diffraction of plane waves by an infinite strip grating,” Annalen der Physik, vol. 7, pp. 257-288, 1971.
J. H. Richmond, “On the edge mode in the theory of TM scattering by a strip or strip grating,” IEEE Transactions on Antennas and Propagation, vol. AP-28, pp. 883-887, 1980.
W. A. Walker and C. M. Butler, “A method for computing scattering by large arrays of narrow strips,” IEEE Transactions on Antennas and Propagation, vol. AP-32, pp. 1327-1334, 1984.
K. Uchida, T. Noda, and T. Matsunaga, “Spectral domain analysis of electromagnetic wave scattering by an infinite plane metallic grating,” IEEE Transactions on Antennas and Propagation, vol. AP-35, pp. 46-52, 1987.
M. Ando and K. Takei, “Reflection and transmission coefficients of a thin strip grating for antenna application,” IEEE Transactions on Antennas and Propagation, vol. AP-35, pp. 367- 371, 1987.
A. Matsushima and T. Itakura, “Singular integral equation approach to plane wave diffraction by an infinite strip grating at oblique incidence,” Journal of Electromagnetic Waves and Applications, vol. 4, pp. 505-519, 1990.
F. B. Gross and W. J. Brown, “New frequencydependent edge mode current density approx.- imations for TM scattering from a conducting strip grating,” IEEE Transactions on Antennas and Propagation, vol. 41, pp. 1302-1307, 1993.
E. Danicki, B. Langli, and K. Blotekjaer, “Spectral theory of EM wave scattering by periodic strips,” IEEE Transactions on Antennas and Propagation, vol. 43, pp. 97-104, 1995.
R. Mittra, C. Pelletti, N. L. Tsitsas, and G. Bianconi, “A new technique for efficient and accurate analysis of FSSs, EBGs and metamaterials,” Microwave and Optical Technology Letters, vol. 54, pp. 1108-1116, 2012.
C. Pelletti, R. K. Arya, A. Rashidi, H. Mosallaei, and R. Mittra, “Numerical techniques for efficient analysis of FSSs, EBGs and metamaterials,” Chapter 11, Computational Electromagnetics: Recent Advances and Engineering Applications, R. Mittra (Ed.), Springer, 2014.
N. L. Tsitsas, C. Pelletti, and R. Mittra, “Efficient analysis of scattering by strip gratings,” Proceedings of the 2016 USNC-URSI Radio Science Meeting, pp. 61-62, 2016.
T. Cwik and R. Mittra, “The effects of the truncation and curvature of periodic surfaces: A strip grating,” IEEE Transactions on Antennas and Propagation, vol. 36, pp. 612-622, 1988.
L. Gurel and W. Chew, “Recursive algorithms for calculating the scattering from N strips or patches,” IEEE Transactions on Antennas and Propagation, vol. 38, pp. 507-515, 1990.
E. G. Johnson and C. G. Christodoulou, “Electromagnetic scattering from aperiodic strip gratings,” Journal of Electromagnetic Waves and Applications, vol. 6, pp. 219-234, 1992.
H. Shigesawa and M. Tsuji, “A new equivalent network approach to electromagnetic wave problems,” Progress in Electromagnetics Research, vol. PIER 13, pp. 243-291, 1996.
Y. Shifman, Z. Baharav, and Y. Leviatan, “Analysis of truncated periodic array using twostage wavelet-packet transformations for impedance matrix compression,” IEEE Transactions on Antennas and Propagation, vol. 47, pp. 630-636, 1999.
HFSS,ANSYS:www.ansys.com/Products/Electronics/ ANSYS-HFSS
K. Chen, J. Song, and T. Kamgaing, “Metal strip grating on grounded dielectric slab and PEC/PMC shielded interconnect: Modal relationships,” ACES Journal, vol. 29, pp. 828-836, 2014.
N. Farahat, R. Mittra, and N.-T. Huang, “Modeling large phased array antennas using the finite difference time domain method and the characteristic basis function approach,” ACES Journal, vol. 21, pp. 218-225, 2006.
