An Overview of Equivalent Circuit Modeling Techniques of Frequency Selective Surfaces and Metasurfaces
关键词:
Equivalent circuit model, frequency selective surfaces, periodic gratings摘要
Circuit analysis of frequency selective surfaces is reviewed with the aim to underline range of validity of different models and their advantages in terms of simplicity and physical insight. The circuit approach is based on an equivalent representation of the FSSs with series or shunt connections of inductances and capacitances. Dense non-resonant periodic surfaces (i.e.: grid or patch arrays) can be analyzed analytically by computing the values of inductors or capacitors via the homogenization theory. As the lattice period increases with respect to the operating wavelength or the element shape becomes resonant, a fully analytical circuital approach fails, in particular, in the presence of thin substrates. However, simple circuit approaches can still be employed by deriving lumped parameters values via a quick pre-processing and then generalizing them. The results are accurate up to the resonant frequency region of the element. By including an additional lumped element it is possible, taking into account the effect of the first high order Floquet harmonic. The multi-mode formulation is also able to catch the highly nonlinear response of FSS screens in the grating lobe region provided that the current profile of the element does not change significantly.
##plugins.generic.usageStats.downloads##
参考
D. Rittenhouse, “An optical problem, proposed by mr. hopkinson, and solved by mr. Rittenhouse,” Trans. Amer. Phil. SOC., vol. 2, pp. 201-206, 1786.
E. G. Loewen and E. Popov, “Diffraction gratings and applications,” CRC Press, 1997.
R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag., vol. 4, pp. 396-402, 1902.
L. Rayleigh, “Note on the remarkable case of diffraction spectra described by prof. wood,” Philos. Mag., vol. 14, pp. 60-65, 1907.
L. Rayleigh, “On the dynamical theory of gratings,” Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 79 (532), pp. 399-416, 1907.
U. Fano, “The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (sommerfeld’s waves),” J. Opt. Soc. Am., vol. 31, pp. 213-222, March 1941.
A. Hessel and A. A. Oliner, “A new theory of wood’s anomalies on optical gratings,” Applied Optics, 4.10, 1275-1297, 1965.
G. Marconi and C. S. Franklin, “Reflector for use in wireless telegraphy and telephony,” US Patent 1,301,473, April 1919.
G. von Trentini, “Partially reflecting sheet arrays,” IRE Trans. Antennas Propagation, vol. AP-4, pp. 666-671, 1956.
N. Marcuvitz (ed.), “Waveguide handbook,” IEE Electromagnetic Waves Series 21, McGraw-Hill, New York, 1951.
W. Rotman and A. A. Oliner, “Periodic structures in trough waveguide,” IRE Trans. on Microwave Theory and Tech., vol. 7, no. 1, pp. 134,142, January 1959.
L. Goldstone and A. A. Oliner, “Leaky-wave antennas I: rectangular waveguides,” IRE Trans. on Antennas and Propag., vol. 7, no. 4, pp. 307,319, October 1959.
D. R. Jackson and N. G. Alexópoulos, “Gain enhancement methods for printed circuit antennas,” IEEE Trans. Antennas Propag., vol. 33, pp. 976- 987, September 1985.
D. R. Jackson and A. A. Oliner, “A leaky-wave analysis of the high gain printed antenna configuration,” IEEE Trans. Antennas Propag., vol. 36, no. 7, pp. 905-910, 1988.
T. Zhao, D. R. Jackson, J. T. Williams, H. D. Yang, and A. A. Oliner, “2-D periodic leaky-wave antennas-part I: metal patch design,” IEEE Trans. Antennas Propag., vol. 53, no. 11, pp. 3505-3514, 2005.
G. Lovat, P. Burghignoli, and D. R. Jackson, “Fundamental properties and optimization of broadside radiation from uniform leaky-wave antennas,” IEEE Trans. Antennas Propag., vol. 54, pp. 1442-1452, 2006.
V. Agrawal and W. Imbriale, “Design of a dichroic cassegrain subreflector,” IEEE Trans. on Antennas and Propag., vol. 27, no. 4, pp. 466-473, July 1979.
T. K. Wu, “Four-band frequency selective surface with double-square-loop patch elements,” IEEE Trans. on Antennas and Propag., vol. 42, no. 12, 1994.
B. A. Munk, “Frequency selective surfaces-theory and design,” John Wiley & Sons, New York, 2000.
T. K. Wu, “Frequency selective surface and grid array,” New York, John Wiley & Sons, Inc., 1995.
F. Costa and A. Monorchio, “A frequency selective radome with wideband absorbing properties,” IEEE Trans. on Antennas and Propag., vol. 60, no. 6, pp. 2740-2747, 2012.
D. R. Jackson, P. Burghignoli, G. Lovat, F. Capolino, J. Chen, D. R. Wilton, and A. A. Oliner, “The fundamental physics of directive beaming at microwave and optical frequencies and the role of leaky waves,” Proc. of the IEEE, vol. 99, no. 10, pp. 1780-1805, 2011.
F. Costa, O. Luukkonen, C. R. Simovski, A. Monorchio, S. A. Tretyakov, and P. De Maagt, “TE surface wave resonances on high-impedance surface based antennas: analysis and modeling,” IEEE Trans. on Antennas and Propag., vol. 59, no. 10, pp. 3588-3596, October 2011.
S. Genovesi, F. Costa, A. Monorchio, “Wideband Radar Cross Section Reduction of Slot Antennas Arrays” IEEE Trans. on Antennas and Propag., vol. 62, no. 1, pp. 163-173, January 2014.
N. Gagnon, A. Petosa, and D. A. McNamara, “Research and development on phase-shifting surfaces (PSSs),” IEEE Antennas and Propagation Magazine, vol. 55, no. 2, pp. 29-48, April 2013.
J. Huang, “Reflectarray antenna,” John Wiley & Sons, Inc., 2007.
R. Lech, M. Mazur, and J. Mazur, “Analysis and design of a polarizer rotator system,” IEEE Trans. on Antennas and Propag., vol. 56, no. 3, pp. 844- 847, March 2008.
F. Costa, C. Amabile, A. Monorchio, and E. Prati, “Waveguide dielectric permittivity measurement technique based on resonant FSS filters,” IEEE Microwave and Wireless Comp. Letters, vol. 21, no. 5, pp. 273-275, May 2011.
M. Philippakis, et al., “Application of FSS structures to selectively control the propagation of signals into and out of buildings,” Ofcom Ref. AY4464A, 2004.
F. Costa, A. Monorchio, and G. Manara, “Analysis and design of ultra thin electromagnetic absorbers comprising resistively loaded high impedance surfaces,” IEEE Trans. on Antennas and Propag., vol. 58, no. 5, pp. 1551-1558, 2010.
J. B. Pendry and D. R. Smith, “The quest for the superlens,” Sci. Amer., vol. 295, no. 1, pp. 60-67, July 2006.
T. Maier and H. Bruckl, “Wavelength-tunable microbolometers with metamaterial absorbers,” Optics Letters, vol. 34 (19), p. 3012, 2009.
S. A. Kuznetsov, A. G. Paulish, A. V. Gelfand, P. A. Lazorskiy, and V. N. Fedorinin, “Bolometric THz-to-IR converter for terahertz imaging,” Appl. Phys. Lett., vol. 99, 023501, 2011.
H. T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid state terahertz phase modulator,” Nature Photonics, vol. 3, 148-151, 2009.
E. Rephaeli and S. Fan, “Absorber and emitter for solar thermophotovoltaic systems to achieve efficiency exceeding the shockley-queisser limit,” Opt. Express, 17, 15, 145-159, 2009.
Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett., 107(4), p. 045901, 2011.
C. C. Chen, “Transmission through a conductive screen perforated periodically with apertures,” IEEE Trans. Microwave Theory & Tech., vol. 18, no. 9, pp. 627-632, 1970.
R. Mittra, C. H. Chan, and T. Cwik, “Techniques for analyzing frequency selective surfaces, a review,” Proc. of the IEEE, vol. 76, no. 12, pp. 1593-1615, 1988.
R. Orta, R. Tascone, and R. Zich, “A unified formulation for the analysis of general frequency selective surfaces,” Electromagnetics, vol. 5, no. 4, pp. 307-329, 1985.
M. Bozzi and L. Perregrini, “Efficient analysis of thin conductive screens perforated periodically with arbitrarily shaped apertures,” Electronics Letters, vol. 35, no. 13, pp. 1085-1087, June 1999.
G. G. MacFarlane, “Surface impedance of an infinite wire grid, at oblique angles of incidence,” J. IEE, vol. 93 (III E), pp. 1523-1527, December 1946.
W. Wessel, “On the passage of electromagnetic waves through a wire grid,” Hochfrequenztechnik, vol. 54, pp. 62-69, January 1939.
R. Hornejäger, “Electromagnetic properties of wire grids,” Ann. der Physik, vol. 4, pp. 25-35, January 1948.
G. von Trentini, “Gratings as circuit elements of electric waves in space,” Zeit. angew. Phys., vol. 5, pp. 221-231, June 1953.
J. R. Wait, “The impedance of wire grid parallel to a dielectric interface,” IRE Trans. Microwave Theory Tech., vol. MTT-5, no. 2, pp. 99-102, April 1957.
J. Young and J. R. Wait, “Note on the impedance of a wire grid parallel to a homogeneous interface,” IEEE Trans. Microwave Theory Tech., vol. 37, no. 7, pp. 1136-1138, July 1989.
R. Ulrich, K. F. Renk, and L. Genzel, “Tunable submillimeter interferometers of the fabry-perot type,” IEEE Trans. Microwave Theory Tech., vol. 11, no. 5, pp. 363-371, 1963.
S. W. Lee, G. Zarrillo, and C. L. Law, “Simple formulas for transmission through periodic metal grids or plates,” IEEE Trans. Antennas Propag., vol. AP-30, no. 5, pp. 904-909, 1982.
M. I. Kontorovich, V. Y. Petrunkin, N. A. Yesepkina, and M. I. Astrakhan, “The coefficient of reflection of a plane electromagnetic wave from a plane wire mesh,” Radio Eng. Electron Phys., no. 7, pp. 222-231, 1962.
M. I. Astrakhan, “Averaged boundary conditions on the surface of a lattice with rectangular cells,” Radio Eng. Electron Phys., no. 9, pp. 1239-1241, 1964.
O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. V. Räisänen, and S. A. Tretyakov, “Simple and accurate analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. on Antennas and Propag., vol. 56, no. 6, pp. 1624- 1632, 2008.
V. V. Yatsenko, S. A. Tretyakov, S. I. Maslovski, and A. A. Sochava, “Higher order impedance boundary conditions for sparse wire grids,” IEEE Trans. Antennas Propag., vol. 48, no. 5, pp. 720- 727, 2000.
R. J. Langley and A. J. Drinkwater, “An improved empirical model for the Jerusalem cross,” IEE Proc. H, Microw. Optics and Antennas, vol. 129, no. 1, pp. 1-6, 1982.
R. J. Langley and E. A. Parker, “Equivalent circuit model for arrays of square loops,” Electronics Letters, vol. 18, no. 7, pp. 294-296, April 1982.
R. J. Langley and E. A. Parker, “Double square frequency selective surfaces and their equivalent circuit,” Electronics Letters, vol. 19, no. 17, pp. 675-677, August 1983.
C. K. Lee and R. J. Langley, “Equivalent-circuit models for frequency selective surfaces at oblique angles of incidence,” IEE Proc. H, Microwaves, Antennas and Propagation, vol. 132, no. 6, pp. 395-399, October 1985.
S. B. Savia and E. A. Parker, “Equivalent circuit model for superdense linear dipole FSS,” IEE Proc. H, Microwaves, Antennas and Propagation, vol. 150, no. 1, pp. 37-42, February 2003.
F. Costa, A. Monorchio, and G. Manara, “Efficient analysis of frequency selective surfaces by a simple equivalent circuit model,” IEEE Antennas and Propagation Magazine, vol. 54, no. 4, pp. 35-48, 2012.
P. Callaghan, E. A. Parker, and R. J. Langley, “Influence of supporting dielectric layers on the transmission properties of frequency selective surfaces,” IEE Proc. H, Microwaves, Antennas and Propagation, vol. 138, no. 5, pp. 448-454, 1991.
R. Dubrovka, J. Vazquez, C. Parini, and D. Moore, “Equivalent circuit method for analysis and synthesis of frequency selective surfaces,” IEE Proc. Microwaves, Antennas and Propag., vol. 153, no. 3, pp. 213-220, June 2006.
S. Monni, G. Gerini, A. Neto, and A. G. Tijhuis, “Multi-mode equivalent networks for the design and analysis of frequency selective surfaces,” IEEE Trans. Antennas Propag., vol. 55, pp. 2824-2835, 2007.
R. Rodriguez-Berral, F. Medina, F. Mesa, and M. Garcia-Vigueras, “Quasi-analytical modeling of transmission/reflection in strip/slit gratings loaded with dielectric slabs,” IEEE Trans. on Microwave Theory and Tech., vol. 60, no. 3, pp. 405-418, March 2012.
M. Garcia-Vigueras, F. Mesa, F. Medina, R. Rodriguez-Berral, and J. L. Gomez-Tornero, “Simplified circuit model for arrays of metallic dipoles sandwiched between dielectric slabs under arbitrary incidence,” IEEE Trans. Antennas Propag., vol. 60, no. 10, pp. 4637,4649, October 2012.
C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: the two-dimensional equivalents of metamaterials,” IEEE Antennas and Propagation Magazine, vol. 54, no. 2, pp. 10,35, April 2012.
S. Tretyakov, “Analytical modelling in applied electromagnetics,” Artech House, Boston, 2003.
A. B. Yakovlev, O. Luukkonen, C. R. Simovski, S. A. Tretyakov, S. Paulotto, P. Baccarelli, and G. W. Hanson, “Analytical modeling of surface waves on high impedance surfaces,” Metamaterials and Plasmonics: Fundamentals, Modelling, Applications NATO Science for Peace and Security Series B, pp. 239-254, 2009.
I. Andersson, “On the theory of self-resonant grids,” The Bell System Technical Journal, vol. 55, pp. 1725-1731, 1975.
J. E. Raynolds, B. A. Munk, J. B. Pryor, and R. J. Marhefka, “Ohmic loss in frequency-selective surfaces,” Journal of Applied Physics, vol. 93, no. 9, pp. 5346-5358, May 2003.
F. Costa, S. Genovesi, A. Monorchio, and G. Manara, “A circuit-based model for the interpretation of perfect metamaterial absorbers,” IEEE Trans. Antennas Propag., vol. 61, no. 3, pp. 1201-1209, March 2013.
F. Costa and A. Monorchio, “Closed-form analysis of reflection losses of microstrip reflectarray antennas,” IEEE Trans. Antennas Propag., vol. 60, no. 10, pp. 4650-4660, October 2012.
Y. E. Erdemli, K. Sertel, R. A. Gilbert, D. E. Wright, and J. L. Volakis, “Frequency selective surface to enhance performance of broad-band reconfigurable arrays,” IEEE Trans. Antennas Propag., vol. 40, no. 12, pp. 1716-1724, 2002.
C. Mias, C. Tsokonas, and C. Oswald, “An investigation into the feasibility of designing frequency selective windows employing periodic structures,” Technical Report AY3922, The Nottingham Trent University, Burton Street, Nottingham, NG1 4BU, U.K., 2002.
M. Ohira, H. Deguchi, M. Tsuji, and H. Shigesawa, “Analysis of frequency-selective surfaces with arbitrarily shaped element by equivalent circuit model,” Electronics and Communications in Japan (Part II: Electronics), vol. 88, no. 6, pp. 9-17, June 2005.
C. C. Chen, “Scattering by a two-dimensional periodic array of conducting plates,” IEEE Trans. Antennas Propag., AP-18, 660-665, 1970.
S. Maci, M. Caiazzo, A. Cucini, and M. Casaletti, “A pole-zero mathcing method for EBG surfaces composed of a dipole FSS printed on a grounded dielectirc slab,” IEEE Trans. Antennas Propag., vol. 53, no. 1, pp. 70-81, January 2005.
D. M. Pozar, “Microwave engineering,” 2nd ed., Toronto: John Wiley &Sons, 1998.
D. J. Kern, D. H. Werner, A. Monorchio, L. Lanuzza, and M. J. Wilhelm, “The design synthesis of multi-band artificial magnetic conductors using high impedance frequency selective surfaces,” IEEE Trans. Antennas Propag., vol. 53, no. 1, pp. 8-17, 2005.
F. Costa, S. Genovesi, and A. Monorchio, “A chipless RFID based on multi-resonant highimpedance surfaces,” IEEE Trans. on Microwave Theory and Tech., vol. 61, no. 1, pp. 146-153, 2013.
S. Genovesi, F. Costa, B. Cioni, V. Miceli, G. Annino, G. Gallone, G. Levita, A. Lazzeri, A. Monorchio, and G. Manara, “Miniaturized high impedance surfaces with angular stability by using zirconium tin titanate (ZST) substrates and convoluted FSS elements,” Microwave and Optical Technology Letters, vol. 51, no. 11, pp. 2753-2758, August 2009.
A. Vallecchi and A. G. Schuchinsky, “Entwined planar spirals for artificial surfaces,” IEEE Antennas and Wireless Propagation Letters, vol. 9, pp. 994-997, 2010.
