Abstract
In this chapter, we present a general theory of effective media to establish the relationship between the local field responses on metamaterial structure and the macroscopical behaviors for artificial metamaterials composed of periodic resonant structures. By treating the unit cell of the periodic structure as a particle, we average the local field to define the local average permittivity and permeability for different unit structures and derive a general form of discrete Maxwell’s equations in macroscale. We obtain different wave modes in metamaterials including propagation mode, pure plasma mode, and resonant crystal bandgap mode. The distortion in the electromagnetic parameters has been well explained by the derived spatial dispersion model. Thus, the unfamiliar behaviors of metamaterials from the numerical S-parameter retrieval approach is further verified and described. The excellent agreements between the theoretical predictions and the numerical retrieval results indicate that the new defined model and method of analysis fit better to the physical structures and is thereafter a more advanced form of fitting formula for the effective electromagnetic parameters of metamaterials.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chen, X., Grzegorczyk, T.M., Wu, B.-I., Pacheco, J., Jr., Kong, J.A.: Robust method to retrieve the constitutive effective parameters of metamaterials. Phys. Rev. E 70, 016608 (2004)
Koschny, T., Markos, P., Smith, D.R., Soukoulis, C.M.: Resonant and antiresonant frequency dependence of the effective parameters of metamaterials. Phys. Rev. E 68, 065602 (2003)
Liu, R., Cui, T.J., Huang, D., Zhao, B., Smith, D.R.: Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory. Phys. Rev. E 76, 026606 (2007)
Liu, R., Cui, T.J., Zhao, B., Lin, X.Q., Ma, H.F., Huang, D., Smith, D.R.: Resonant crystal band gap metamaterials in the microwave regime and their exotic amplification of evanescent waves. Appl. Phys. Lett. 90, 091912 (2007)
Pendry, J.B.: Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966 (2000)
Pendry, J.B., Holden, A.J., Robbins, D.J., Stewart, W.J.: Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Micro. Theory Tech. 47, 2075 (1999)
Pendry, J.B., Holden, A.J., Stewart, W.J., Youngs, I.: Extremely low frequency plasmons in metallic mesostructures. Phys. Rev. Lett. 76, 4773–4776 (1996)
Pendry, J.B., Schurig, D., Smith, D.R.: Controlling electromagnetic fields. Science 312, 1780 (2006)
Schruig, D., Mock, J.J., Justice, B.J., Cummer, S.A., Pendry, J.B., Starr, A.F., Smith, D.R.: Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977–980 (2006)
Schurig, D., Mock, J.J., Smith, D.R.: Electric-field-coupled resonators for negative permittivity metamaterials. Appl. Phys. Lett. 88, 041109 (2006)
Shelby, R.A., Smith, D.R., Schultz, S.: Experimental verification of a negative index of refraction. Science 292, 77 (2001)
Simovski, C.R., Belov, P.A., He, S.: Backward wave region and negative material parameters of a structure formed by lattices of wires and split-ring resonators. IEEE Trans. Ant. Prop. 51, 2582 (2003)
Smith, D.R., Padilla, W.J., Vier, D.C., Nemat-Nasser, S.C., Schultz, S.: Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 84, 4184 (2000)
Smith, D.R., Pendry, J.B.: Homogenization of metamaterials by field averaging. J Opt. Soc. Am. B 23, 321 (2006)
Smith, D.R., Vier, D.C., Koschny, T., Soukoulis, C.M.: Electromagnetic parameter retrieval from inhomogeneous metamaterials. Phys. Rev. E 71, 036617 (2005)
Starr, A.F., Rye, P.M., Smith, D.R., Nemat-Nasser, S.: Fabrication and characterization of a negative-refractive-index composite metamaterial. Phys. Rev. B 70, 115113 (2004)
Varadan, V., Sheng, Z., Penumarthy, S., Puligalla, S.: Comparison of measurement and simulation of both amplitude and phase of reflected and transmitted fields in resonant Omega media. Micro. Opt. Tech. Lett. 48, 1549 (2006)
Yen, T.J., Padilla, W.J., Fang, N., Vier, D.C., Smith, D.R., Pendry, J.B., Basov, D.N., Zhang, X.: Terahertz magnetic response from artificial materials. Science 303, 1494–1496 (2004)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Liu, R., Cui, T.J., Smith, D.R. (2010). General Theory on Artificial Metamaterials. In: Cui, T., Smith, D., Liu, R. (eds) Metamaterials. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-0573-4_3
Download citation
DOI: https://doi.org/10.1007/978-1-4419-0573-4_3
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-0572-7
Online ISBN: 978-1-4419-0573-4
eBook Packages: EngineeringEngineering (R0)