Mathematical analysis of the two dimensional active exterior cloaking in the quasistatic regime

Alú A., Engheta N.: Plasmonic and metamaterial cloaking: physical mechanisms and potentials. J. Opt. A Pure Appl. Opt. 10, 093002 (2008)

Berger G., Tasche M.: Hermite–Lagrange interpolation and Schur’s expansion of sinπ x. J. Approx. Theory. 53(1), 17–25 (1988). ISSN 0021-9045. doi: 10.1016/0021-9045(88)90072-X

Chen H., Chan C.T.: Acoustic cloaking in three dimensions using acoustic metamaterials. Appl. Phys. Lett. 91, 183518 (2007)

Dolin L.S.: To the possibility of comparison of three-dimensional electromagnetic systems with nonuniform anisotropic filling. Izv. Vyssh. Uchebn. Zaved. Radiofizika 4(5), 964–967 (1961)

Gardiner S.J.: Harmonic approximation, volume 221 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (1995). ISBN 0-521-49799-X. doi: 10.1017/CBO9780511526220

Greenleaf A., Lassas M., Uhlmann G.: Anisotropic conductivities that cannot be detected by EIT. Physiol. Meas. 24, 413–419 (2003)

Greenleaf A., Kurylev Y., Lassas M., Uhlmann G.: Invisibility and inverse problems. Bull. Am. Math. Soc. (N.S.) 46(1), 55–97 (2009). ISSN 0273-0979. doi: 10.1090/S0273-0979-08-01232-9

Guevara Vasquez F., Milton G.W., Onofrei D.: Active exterior cloaking for the 2D Laplace and Helmholtz equations. Phys. Rev. Lett. 103, 073901 (2009). doi: 10.1103/PhysRevLett.103.073901

Guevara Vasquez F., Milton G.W., Onofrei D.: Broadband exterior cloaking. Opt. Express 17, 14800–14805 (2009). doi: 10.1364/OE.17.014800

Guevara Vasquez, F., Milton, G.W., Onofrei, D.: Exterior cloaking with active sources in two dimensional acoustics. Wave Motion 48(6), 515–524 (2011). ISSN 0165-2125. doi: 10.1016/j.wavemoti.2011.03.005 (special issue on cloaking of wave motion)

Guevara Vasquez, F., Milton, G.W., Onofrei, D., Seppecher, P.: Transformation elastodynamics and active exterior acoustic cloaking. In: Guenneau, S., Craster, R. (eds.) Acoustic metamaterials: negative refraction, imaging, lensing and cloaking. Springer (2011). arXiv:1105.1221 (submitted)

Kohn R.V., Onofrei D., Vogelius M.S., Weinstein M.I.: Cloaking via change of variables for the Helmholtz equation. Commun. Pure Appl. Math. 63(8), 973–1016 (2010) ISSN 0010-3640

Lai Y., Chen H., Zhang Z.-Q., Chan C.T.: Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell. Phys. Rev. Lett. 102, 093901 (2009)

Leonhardt U.: Notes on conformal invisibility devices. New J. Phys. 8, 118 (2006)

Leonhardt U.: Optical conformal mapping. Science 312, 1777–1780 (2006)

Miller D.A.B.: On perfect cloaking. Opt. Express 14, 12457–12466 (2006)

Milton G.W., Nicorovici N.-A.P.: On the cloaking effects associated with anomalous localized resonance. Proc. R. Soc. Lond. Ser. A. Math. Phys. Sci. 462, 3027–3059 (2006) ISSN 0080-4630

Milton G.W., Nicorovici N.-A.P., McPhedran R.C., Cherednichenko K., Jacob Z.: Solutions in folded geometries, and associated cloaking due to anomalous resonance. New J. Phys. 10, 115021 (2008)

Nicorovici N.-A.P., Milton G.W., McPhedran R.C., Botten L.C.: Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance. Opt. Express 15, 6314–6323 (2007)

Pendry J.B., Schurig D., Smith D.R.: Controlling electromagnetic fields. Science 312(5781), 1780–1782 (2006)

Ramharter G.: A remark on Hermite–Lagrange interpolation. J. Approx. Theory 66(1), 109–113 (1991). ISSN 0021-9045. doi: 10.1016/0021-9045(91)90061-E

Silveirinha M.G., Alù A., Engheta N.: Cloaking mechanism with antiphase plasmonic satellites. Phys. Rev. B 78(20), 205109 (2008) 10.1103/PhysRevB.78.205109

Smolyaninov I.I., Smolyaninova V.N., Kildishev A.V., Shalaev V.M.: Anisotropic metamaterials mulated by tapered waveguides: application to optical cloaking. Phys. Rev. Lett. 102, 213901 (2009)

Stoer J., Bulirsch R.: Introduction to numerical analysis, vol. 12 Texts in Applied athematics, 3rd edn. Springer, New York (2002) ISBN 0-387-95452-X (translated from the German by R. Bartels, W. Gautschi and C. Witzgall)