POINT SOURCE IN THE LAYERED MEDIUM WITH METAMATERIALS: METHOD OF RECURRENT RELATIONS

K. V. Pravdin, I. Y. Popov


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Abstract

Multilayer systems with metamaterials are studied. A system comprising parallel alternated layers filled with metamaterial and vacuum is considered. The problem of obtaining expressions for electric part of the Green’s function is raised for the NIM situation. A NIM situation is a case when electric and magnetic permeabilities are equal –1 for metamaterial and +1 for vacuum. The Maxwell’s equations for a point source of electromagnetic field are considered. A differential equation for electric p-polarized scalar part of the Green’s function for every layer is obtained with standard boundary conditions. Solution is obtained with the fundamental system of solutions with unknown coefficients. For the unknown coefficients the recurrence relations method is chosen as evident in usage and easy in analysis of obtained solutions. The solutions of the recurrence relations are obtained in general form by the method of generating functions. As a result the formulae for required Green’s function are obtained for every layer in the condition of NIM situation. s-polarized part is obtained in a similar way. It is easy to obtain a vector form of the electric Green’s function with its scalar form and the standard alternations. Obtained results can be used by simulations of superlens systems and multilayer covers with metamaterials.


Keywords: metamaterials, negative refractive index, NIM, Maxwell’s equations, recurrence relations, Green’s function

References
1.        Dubinov A.E., Mytareva L.A. Invisible cloaking of material bodies using the wave flow method. Physics-Uspekhi, 2010, vol. 53, no. 5, pp. 475–479. doi: 10.3367/UFNe.0180.201005b.0475
2.        Rozanov N.N. Nevidimost': za i protiv [Invisibility: pro and contra]. Priroda, 2008, no. 6, pp. 3–10.
3.        Ozbay E., Li Z., Aydin K. Super-resolution imaging by one-dimensional microwave left-handed metamaterials with an effective negative index. Journal of Physics Condensed Matter, 2008, vol. 20, no. 30, art. no. 304216. doi: 10.1088/0953-8984/20/30/304216
4.        Iyer A.K., Eleftheriades G.V. Free-space imaging beyond the diffraction limit using a Veselago-Pendry transmission-line metamaterial superlens. IEEE Transactions on Antennas and Propagation, 2009, vol. 57, no. 6, pp. 1720–1727. doi: 10.1109/TAP.2009.2019890
5.        Casse B.D.F., Lu W.T., Huang Y.J., Gultepe E., Menon L., Sridhar S. Super-resolution imaging using a three-dimensional metamaterials nanolens. Applied Physics Letters, 2010, vol. 96, no. 2, art. no 023114. doi: 10.1063/1.3291677
6.        Lequime M., Gralak B., Guenneau S., Zerrad M., Amra C. Optical properties of multilayer optics including negative index materials. Available at: http://arxiv.org/pdf/1312.6288v1.pdf (accessed 16.04.2014).
7.        Burgos S.P., de Waele R., Polman A., Atwater H.A. A single-layer wide-angle negative-index metamaterial at visible frequencies. Nature Materials, 2010, vol. 9, no. 5, p. 407–412. doi: 10.1038/nmat2747
8.        Gralak B., Tip A. Macroscopic Maxwell’s equations and negative index materials. Journal of Mathematical Physics, 2010, vol. 51, no. 5, art. no. 029004JMP. doi: 10.1063/1.3374670
9.        Gralak B., Maystre D. Negative index materials and time-harmonic electromagnetic field. Comptes Rendus Physique, 2012, vol. 13, no. 8, pp. 786–799. doi: 10.1016/j.crhy.2012.04.003
10.     Collin R.E. Frequency dispersion limits resolution in Veselago lens. Progress In Electromagnetics Research B, 2010, vol. 19, pp. 233–261.
11.     Pravdin K.V., Popov I.Yu. Model of the interaction of point source electromagnetic fields with metamaterials. Nanosystems: Physics, Chemistry, Mathematics, 2013, vol. 4, no. 4, pp. 570–576.
12.     Liu Y., Guenneau S., Gralak B. A route to all frequency homogenization of periodic structures. Available at: http://arxiv.org/pdf/1210.6171v2.pdf (accessed 16.04.2014).
13.     Lequime M., Gralak B., Guenneau S., Zerrad M., Amra C. Negative Index Materials: The Key to «White» Multilayer Fabry-Perot. Available at: http://arxiv.org/pdf/1312.6281v1.pdf (accessed 16.04.2014).
14.     Lai K.L., Tsang L., Huang C.C. Spatial domain green’s functions for planar multilayered structures microwave and optical technology letters. Microwave and optical technology letters, 2005, vol. 44, no. 1, pp. 86–91. doi: 10.1002/mop.20555
15.     Maksimovic M., Hammer M., Jaksic Z. Thermal radiation antennas made of multilayer structures containing negative index metamaterials. Proceedings of SPIE - The International Society for Optical Engineering, 2008, vol. 6896, art. no. 689605. doi: 10.1117/12.762616
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