A class of rigorous formulas for the efficient extraction of the full polarizability matrix of electrically small particles is introduced in this paper. After the dipole approximation of the scatterer, under study, the latter is placed on a two-dimensional square array, illuminated by four normally incident plane waves, and eventually its polarizabilities are expressed in terms of induced dipole moments. Then, by applying an equivalent surface model for the array, the induced dipoles are calculated as a function of the reflection/transmission coefficients from the array. Lastly, the combination of the previous formulations leads to the final expressions for the polarizability matrix of the particle. In order to verify the featured methodology, the extracted polarizabilities are involved in radar cross section and total radiated power calculations for various incidences and are compared with their simulated counterparts.
2. Alu, A., "First-principles homogenization theory for periodic metamaterials," Phys. Rev. B, Vol. 84, No. 7, 075153, 2011.
3. Liu, X. X. and A. Alu, "Generalized retrieval method for metamaterial constitutive parameters based on a physically driven homogenization approach," Phys. Rev. B, Vol. 87, No. 23, 235136, 2013.
4. Karamanos, T. D., S. D. Assimonis, A. I. Dimitriadis, and N. V. Kantartzis, "Effective parameter extraction of 3D metamaterial arrays via first-principles homogenization theory," Photonics Nanostructures: Fundam. Appl., Vol. 12, No. 4, 291-297, 2014.
5. Simovski, C. R., B. Sauviac, and S. L. Prosvirnin, "Homogenization of an array of S-shaped particles located on a dielectric interface," Progress In Electromagnetics Research, Vol. 39, 249-264, 2003.
6. Mohamed, M. A., E. F. Kuester, M. Piket-May, and C. L. Holloway, "The field of an electric dipole and the polarizability of a conducting object embedded in the interface between dielectric materials," Progress In Electromagnetics Research B, Vol. 16, 1-20, 2009.
7. Dimitriadis, A. I., N. V. Kantartzis, T. D. Tsiboukis, and C. Hafner, "Generalized non-local surface susceptibility model and Fresnel coefficients for the characterization of periodic metafilms with bianisotropic scatterers," J. Comput. Phys., Vol. 281, 251-268, 2015.
8. Andryieuski, A., A. V. Lavrinenko, M. Petrov, and S. A. Tretyakov, "Homogenization of metasurfaces formed by random resonant particles in periodical lattices," Phys. Rev. B, Vol. 93, No. 20, 205127, 2016.
9. Dimitriadis, A. I., T. D. Karamanos, N. V. Kantartzis, and T. D. Tsiboukis, "Effective-surface modeling of infinite periodic metascreens exhibiting the extraordinary transmission phenomenon," J. Opt. Soc. Am. B, Vol. 33, No. 3, 434-444, 2016.
10. Alaee, R., M. Albooyeh, and C. Rockstuhl, "Theory of metasurface based perfect absorbers," J. Phys. D: Appl. Phys., Vol. 50, No. 50, 503002, 2017.
11. Sihvola, A. H., Electromagnetic Mixing Formulas and Applications, IET Publishers, Stevenage, 1999.
12. Marques, R., F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge-and broadside-coupled split ring resonators for metamaterial design-theory and experiments," IEEE Trans. Antennas Propag., Vol. 51, No. 10, 2572-2581, 2003.
13. Mirmoosa, M., Y. Ra'di, V. Asadchy, C. Simovski, and S. Tretyakov, "Polarizabilities of nonreciprocal bianisotropic particles," Phys. Rev. Appl., Vol. 1, No. 3, 034005, 2014.
14. Terekhov, Y. E., A. V. Zhuravlev, and G. V. Belokopytov, "The polarizability matrix of split-ring resonators," Moscow Univ. Phys. Bull., Vol. 66, 254-259, 2011.
15. Yazdi, M. and N. Komjani, "Polarizability tensor calculation using induced charge and current distributions," Progress In Electromagnetics Research M, Vol. 45, 123-130, 2016.
16. Asadchy, V. S., I. A. Faniayeu, Y. Ra'di, and S. A. Tretyakov, "Determining polarizability tensors for an arbitrary small electromagnetic scatterer," Photonics Nanostructures: Fundam. Appl., Vol. 12, No. 4, 298-304, 2014.
17. Alaee, R., M. Albooyeh, M. Yazdi, N. Komjani, C. Simovski, F. Lederer, and C. Rockstuhl, "Magnetoelectric coupling in nonidentical plasmonic nanoparticles: Theory and applications," Phys. Rev. B, Vol. 91, 115119, 2015.
18. Scher, A. D. and E. F. Kuester, "Extracting the bulk effective parameters of a metamaterial via the scattering from a single planar array of particles," Metamaterials, Vol. 3, No. 1, 44-55, 2009.
19. Karamanos, T. D., A. I. Dimitriadis, and N. V. Kantartzis, "Robust technique for the polarisability matrix retrieval of bianisotropic scatterers via their reflection and transmission coefficients," IET Microw. Antennas Propag., Vol. 8, No. 15, 1398-1407, 2014.
20. Karamanos, T. and N. Kantartzis, "Polarizability matrix retrieval of a non-planar chiral particle through scattering parameter," Appl. Phys. A, Vol. 122, No. 4, 378, 2016.
21. Jelinek, L. and J. Machac, "A polarizability measurement method for electrically small particles," IEEE Antennas Wireless Propag. Lett., Vol. 13, 1051-1053, 2014.
22. Pulido-Mancera, L., P. T. Bowen, M. F. Imani, N. Kundtz, and D. Smith, "Polarizability extraction of complementary metamaterial elements in waveguides for aperture modeling," Phys. Rev. B, Vol. 96, No. 23, 235402, 2017.
23. Liu, X.-X., Y. Zhao, and A. Alu, "Polarizability tensor retrieval for subwavelength particles of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 64, No. 6, 2301-2310, 2016.
24. Tai, C.-T., Dyadic Green Functions in Electromagnetic Theory, IEEE Press, Piscataway, 1994.
25. Belov, P. A. and C. R. Simovski, "Homogenization of electromagnetic crystals formed by uniaxial resonant scatterers," Phys. Rev. E, Vol. 72, No. 2, 026615, 2005.
26. Scher, A. and E. Kuester, "Boundary effects in the electromagnetic response of a metamaterial in the case of normal incidence," Progress In Electromagnetics Research B, No. 14, 341-381, 2009.
27. Lee, S., B. Kang, H. Keum, N. Ahmed, J. Rogers, P. Ferreira, S. Kim, and B. Min, "Heterogeneously assembled metamaterials and metadevices via 3D modular transfer printing," Sci. Rep., Vol. 6, 27621, 2016.
28. Serdyukov, A., I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials: Theory and Applications, Gordon and Breach, Amsterdam, 2001.
29. Withayachumnankul, W., C. Fumeaux, and D. Abbott, "Compact electric-LC resonators for metamaterials," Opt. Express, Vol. 18, No. 25, 25912-25921, 2010.
30. CST Microwave StudioTM, Computer Simulation Technology, 2017.
31. Bilotti, F., A. Toscano, and L. Vegni, "Design of spiral and multiple split-ring resonators for the realization of miniaturized metamaterial samples," IEEE Trans. Antennas Propag., Vol. 55, No. 8, 2258-2267, 2007.
32. Baena, J. D., R. Marques, F. Medina, and J. Martel, "Artificial magnetic metamaterial design by using spiral resonators," Phys. Rev. B, Vol. 69, No. 1, 014402, 2004.
33. Marques, R., F. Martin, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design and Microwave Applications, John Wiley & Sons, New York, 2011.
34. Sersic, I., C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, "Magnetoelectric point scattering theory for metamaterial scatterers," Phys. Rev. B, Vol. 83, No. 24, 245102, 2011.
35. Gansel, J. K., M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, "Gold helix photonic metamaterial as broadband circular polarizer," Science, Vol. 325, No. 5947, 1513-1515, 2009.
36. Marques, R., L. Jelinek, and F. Mesa, "Negative refraction from balanced quasi-planar chiral inclusions," Microw. Opt. Technol. Lett., Vol. 49, No. 10, 2606-2609, 2007.
37. Wang, B., J. Zhou, T. Koschny, and C. M. Soukoulis, "Nonplanar chiral metamaterials with negative index," Appl. Phys. Lett., Vol. 94, No. 15, 151112, 2009.
38. Silveirinha, M. G., "Boundary conditions for quadrupolar metamaterials," New J. Phys., Vol. 16, No. 8, 083042, 2014.
39. Yaghjian, A., "Boundary conditions for electric quadrupolar continua," Radio Sci., Vol. 49, No. 12, 1289-1299, 2014.
40. Jackson, J. D., Classical Electrodynamics, Wiley, New York, 1999.
41. Yaghjian, A. D., M. Silveirinha, A. Askarpour, and A. Alu, "Electric quadrupolarizability of a source-driven dielectric sphere," Progress In Electromagnetics Research B, Vol. 63, 95-106, 2015.
42. Alaee, A., C. Rockstuhl, and I. Fernandez-Corbaton, "An electromagnetic multipole expansion beyond the long-wavelength approximation," Opt. Commun., Vol. 407, 17-21, 2018.
43. Volakis, J., Integral Equation Methods for Electromagnetics, IET Publishers, Stevenage, 2012.
44. Weber, W. and G. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B, Vol. 70, No. 12, 125429, 2004.
45. Scher, A. D., "Boundary effects in the electromagnetic response of a metamaterial using the point-dipole interaction model,", Ph.D. Thesis, University of Colorado at Boulder, Boulder, 2008.