Virtual Singular Scattering of Electromagnetic Waves in Transformation Media Concept
Main Article Content
Abstract
If a scatterer and an observation point (receive) both approach the so-called near field zone of a source of electromagnetic waves, the scattering process becomes singular one which is mathematically attributed to the spatial singularity of the free space Green function at the origin. Starting from less well known property of left-handed material slab to transfer the singularity of the free space Green function by implementing coordinate transformation, we present a phenomenon of virtual singular scattering of electromagnetic wave on an inhomogeneity located in the volume of left – handed material slab. Virtual singular scattering means that a scatterer is situated only virtually in the near field zone of a source, being, in fact, positioned in the far field zone. Such a situation is realized if a scatterer is embedded into a flat Veselago’s lens and approaches the lens’s inner focus because a slab of Veselago medium produces virtual sources inside and behind the slab and virtual scatterer (as a source of secondary waves) from both slab sides. Considering a line-like dielectric scatterer we demonstrate that the scattering efficiency is proportional to product of singular quasistatic parts of two empty space Green functions that means a multiplicative quasistatic singularity of the Green function for a slab of inhomogeneous Veselago medium. We calculate a resonance value of the scattering amplitude in the regime similar to the known Mie resonance scattering.
Downloads
Article Details
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
References
J. B. Pendry, D. Schurig, D. R. Smith, Controlling electromagnetic fields, Science, 312, 1780, 2006.
U. Leonardt, T. G. Philbin, General relativity in electrical engineering, New J. Phys. 8, 247, 2006.
U. Leonhardt, Optical conformal mapping, Science 312: 1777- 1780, 2006.
F. de Felice, On the gravitational field acting as an optical medium, General Relativity and Gravitation 2: 347-357, 1971.
W. Gordon, Zur lichtfortpflanzung nach der relativitätstheorie, Ann. Phys. (Leipzig) 72: 421-456, 1923.
S. Antoci, L. Mihich, A forgotten argument by Gordon uniquely selects Abraham’s tensor as the energy-momentum tensor for the electromagnetic field in homogeneous, isotropic matter, arxiv.org/abs/gr-qc/9704055v1
L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields, Fourth Revised English Edition, Pergamon, Oxford, UK, p. 275, 1975.
Yu. N. Barabanenkov, Maxwell equations in rotating system of reference, Scientific Reports of Higher School, Phys-Math Sciences 1: 141 – 145, 1959.
A. Einstein, Die Grundlage der allgemeinen Relativitätstheorie, Ann. Phys. 49: 769-822, 1916; translated without p.769 as The Foundation of the General Theory of Relativity, The Principle of Relativity, Dover, New York, pp. 111–164,1952.
J. Plebanski, Electromagnetic waves in gravitational fields, Phys. Rev. 118: 1396 – 1408, 1960.
H. Chen, Bae-Ian Wu, B. Zhang, J.A. Kong, Electromagnetic wave interactions with a metamaterial Cloak, Phys. Rev. Lett. 99: 063903, 2007.
V. G. Veselago, The electrodynamics of substances with simultaneously negative values of and, Sov. Phys. Usp. 10: 509-514, 1968.
N. Fang, H. Lee, Ch. Sun, X. Zhang, Sub–diffraction-limited optical imaging with a silver superlens, Science 308: 534-537, 2005.
S. C. Kehr, Y.M. Liu, L. W. Martin, P. Yu, M. Gajek, S.-Y. Yang, C.-H. Yang, M. T. Wenzel, R. Jacob, H.-G. von Ribbeck, M. Helm, X. Zhang, L. M. Eng, R. Ramesh, Near-field examination of perovskite-based superlenses and superlens-enhanced probe-object coupling, Nature Communications 249: 1-9, 2011.
P. Schau, K. Frennera, L. Fub, H. Schweizer, H. Giessenb, W. Osten, Rigorous modeling of meander-type metamaterials for sub-lambda imaging, Proc. SPIE 8083: 808303, 2011.
Yu. N. Barabanenkov, M.Yu. Barabanenkov, S.A. Nikitov, Line source wave scattering by line inhomogeneities inside left-handed material slab: Green function approach, Proc. PIERS Cambridge, USA, pp.789-799, 2008.
L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media, Pergamon, Oxford, UK, p. 251, 1981. R. Merlin, Metamaterials and Landau-Lifshitz permeability arguments: large permittivity begets high-frequency magnetism, PNAS:106, 1693-1698, 2009.
L. Tsang, J.A. Kong, R. Shin, Theory of Microwave Remote Sensing, John Wiley, New York, 1985. B. Pendry, Negative refraction makes a perfect lens, Phys. Rev. Lett. 85: 3966 – 3969, 2000.
Yu. N. Barabanenkov, M.Yu. Barabanenkov, Radiative transfer theory with time delay for effect of a pulse imprisonment in a resonant random media: general transfer equation and point-like scatterer model, Waves in Random Media 7: 607-633, 1997.
J. R. Taylor, Scattering Theory: the Quantum Theory of Nonrelativistic Collisions, John Wiley, New York, 1972.
Pi-G. Luan, H.-Da Chien, Ch.-Ch. Chen, Chi-Sh. Tang, Analysis on the imaging properties of a left-handed material slab, arXiv:physics/0311122v2
C. A. Valagiannopoulos, N. K. Uzunoglu, Simplified model for EM inverse scattering by longitudinal subterranean inhomogeneities exploiting the dawn/dusk ionospheric ridge, IET-Micro. Antennas Propag. 5: 1319 – 1327, 2011.
M. Born, E. Wolf, Principles of Optics, Pergamon Press, New York, 1964.
M. Yu. Barabanenkov, Yu. N. Barabanenkov, S. A. Nikitov, Near field introscopy of two dimensional nonhomogeneous left-handed material slab, Proc. SPIE 8083: 808305, 2011.
D. Schuring, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, Metamaterial electromagnetic cloak at microwave frequencies, Science 314: 977-980, 2006.
B. Zhang, Bae-Ian Wu, Electromagnetic detection of a perfect invisibility cloak, Phys. Rev. Lett. 103: 243901, 2009.