Model of point source for layered metamaterials

By: K.V. Pravdin, I. Yi. Popov

Main Information

Volume:
Vol.48-N1 / 2015 - Ordinario
Section:
Electromagnetic theory
Pages:
31-53
DOI:
http://dx.doi.org/10.7149/OPA.48.1.31
Type:
Research paper/ Artículo de Investigación
Language:
English /Inglés
Attachments:
Keywords:
Metamaterials, negative index material, Maxwell's equations, Green's function.

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Abstract

The multilayer system including negative index material (NIM) layers is examined. We deal with the NIM system composed of arbitrary finite number of parallel alternated layers filled with isotropic homogeneous NIM and vacuum. The Maxwell's equations for the point source are considered. The NIM layer has the electric permittivity and magnetic permeability, which are equal to -1 for the certain frequency (NIM frequency). We set the goal of obtaining expressions for the electric Green's function. The Laplace and Fourier transforms are used. The differential equations for the scalar s- and p- polarization parts of the electric Green's function are obtained. The solutions of the differential equations are obtained in the travelling wave form with unknown coefficients. With the standard boundary conditions for every layer, the recurrence relations for the coefficients are obtained. The solution is obtained by the generating function method. The expressions for the scalar s- and p- polarization and vector part of the electric Green's function are derived. Under some assumptions, we observe the reflection absence (for the main term of the solution asymptotics near the NIM frequency). The obtained results can be used in simulation or engineering of real objects, such as superlens systems and multilayer NIM coverings.


References

[1] A. E. Dubinov, L. A. Mytareva, "Invisible cloaking of material bodies using the wave flow method," Phys Usp 53, 455-479 (2010). DOI

[2] N.N. Rozanov, Priroda 6 (3), (2008) (in Russian).

[3] E. Ozbay, Z. Li, K. Aydin, "Super-resolution imaging by one-dimensional, microwave left-handed metamaterials with an effective negative index," J Phys Condens Matt 20, 304216 (2008). DOI

[4] A. Iyer, G. Eleftheriades, "Free-space imaging beyond the diffraction limit using a Veselago-Pendry transmission-line metamaterial superlens," IEEE Trans Antennas Propag 57, 1720-1727 (2009). DOI

[5] B. Casse, W. Lu, Y. Huang, E. Gultepe, L. Menon, S. Sridhar, "Super-resolution imaging using a three- dimensional metamaterials nanolens," Appl Phys Lett 96, 023114 (2010). DOI

[6] M. Lequime, B. Gralak, S. Guenneau, M. Zerrad, C. Amra, "Optical properties of multilayer optics including negative index materials," arXiv:1312.6288 (2013)

[7] S. Burgos, R. de Waelwe, A. Polman, H. Atwater, "A single-layer wide-angle negative-index metamaterial at visible frequencies," Nat Mater 9, 407-412 (2010). DOI ?

[8] B. Gralak, A. Tip, "Macroscopic Maxwell's equations and negative index materials," J Math Phys 51, 052902 (2010). DOI

[9] B. Gralak, D. Maystre, "Negative index materials and time-harmonic electromagnetic field," C R Physique 13, 786-799 (2012). DOI

[10] R. Collin, "Frequency dispersion limits resolution in Veselago lens," PIER B 19, 233-261 (2010). DOI

[11] K. V. Pravdin, I. Y. Popov, "Photonic Crystal with negative index materials layers," Nanosystems: Phys., Chem., Math. 5, 626-643 (2014).

[12] Y. Liu, S. Guenneau, B. Gralak, "A route to all frequency homogenization of periodic structures," arXiv:1210.6171 (2012).

[13] M. Lequime, B. Gralak, S. Guenneau, M. Zerrad, C. Amra, "Negative Index Materials: The Key to «White» Multilayer Fabry-Perot," arXiv:1312.6281 (2013).

[14] K. Lai, L. Tsang, C. Huang, "Spatial domain Green's functions for planar multilayered structures," Micro Opt Tech Lett 44, 86-91 (2005) DOI

[15] M. Maksimovic, M. Hammer, Z. Jaksic, "Thermal radiation antennas made of multilayer structures containing negative index metamaterials", Proc. SPIE 6896, 689605 (2008) DOI

[16] A. Tip, "Linear dispersive dielectrics as limits of Drude-Lorentz systems", Phys Rev E 69, 016610 (2004) DOI