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Two dimensional invisibility cloaking via transformation optics
1. | Department of Mathematics and Statistics, University of Reading, Whiteknights, Reading RG6 6AX, United Kingdom |
2. | Department of Mathematics, University of California, Irvine, Irvine, CA 92697, United States |
References:
[1] |
A. Alu and N. Engheta, Achieving transparency with plasmonic and metamaterial coatings, Phys. Rev. E, 72 (2005), 016623.
doi: 10.1103/PhysRevE.72.016623. |
[2] |
A. Greenleaf, Y. Kurylev, M. Lassas and G. Uhlmann, Full-wave invisibility of active devices at all frequencies, Commu. Math. Phys., 275 (2007), 749-789.
doi: 10.1007/s00220-007-0311-6. |
[3] |
A. Greenleaf, Y. Kurylev, M. Lassas and G. Uhlmann, Cloaking devices, electromagnetic wormholes and transformation optics, SIAM Review, 51 (2009), 3-33.
doi: 10.1137/080716827. |
[4] |
A. Greenleaf, Y. Kurylev, M. Lassas and G. Uhlmann, Improvement of cylindrical cloaking with the SHS lining, Opt. Exp., 15 (2007), 12717.
doi: 10.1364/OE.15.012717. |
[5] |
A. Greenleaf, M. Lassas and G. Uhlmann, On nonuniqueness for Calderón's inverse problem, Math. Res. Lett., 10 (2003), 685-693. |
[6] |
U. Hetmaniuk and H. Y. Liu, On acoustic cloaking devices by transformation media and their simulation, SIAM J. Appl. Math., 70 (2010), 2996-3021.
doi: 10.1137/090771077. |
[7] |
V. Isakov, "Inverse Problems for Partial Differential Equations," 2nd edition, Springer-Verlag, New York, 2006. |
[8] |
R. Kohn, D. Onofrei, M. Vogelius and M. Weinstein, Cloaking via change of variables for the Helmholtz equation, Commu. Pure Appl. Math., 63 (2010), 0973-1016. |
[9] |
R. Kohn, H. Shen, M. Vogelius and M. Weinstein, Cloaking via change of variables in electrical impedance tomography, Inverse Problems, 24 (2008), 015016.
doi: 10.1088/0266-5611/24/1/015016. |
[10] |
U. Leonhardt, Optical conformal mapping, Science, 312 (2006), 1777-1780.
doi: 10.1126/science.1126493. |
[11] |
H. Y. Liu, Virtual reshaping and invisibility in obstacle scattering, Inverse Problems, 25 (2009), 045006.
doi: 10.1088/0266-5611/25/4/045006. |
[12] |
W. McLean, "Strongly Elliptic Systems and Boundary Integral Equations," Cambridge University Press, Cambridge, 2000. |
[13] |
G. W. Milton and N.-A. P. Nicorovici, On the cloaking effects associated with anomalous localized resonance, Proc. Roy. Soc. A, 462 (2006), 3027-3095.
doi: 10.1098/rspa.2006.1715. |
[14] |
H. M. Nguyen, Cloaking via change of variables for the Helmholtz equation in the whole space, Commu. Pure Appl. Math., 63 (2010), 1505-1524.
doi: 10.1002/cpa.20333. |
[15] |
H. M. Nguyen, Approximate cloaking for the Helmholtz equation via transformation optics and consequences for perfect cloaking, preprint, 2011. |
[16] |
A. N. Norris, Acoustic cloaking theory, Proc. R. Soc. A, 464 (2008), 2411-2434.
doi: 10.1098/rspa.2008.0076. |
[17] |
J. B. Pendry, D. Schurig and D. R. Smith, Controlling electromagnetic fields, Science, 312 (2006), 1780-1782.
doi: 10.1126/science.1125907. |
[18] |
G. Uhlmann, Developments in inverse problems since Calderón's foundational paper,, Ch. 19 in, ().
|
[19] |
M. Yan, W. Yan and M. Qiu, Invisibility cloaking by coordinate transformation, Ch. 4 in "Progress in Optics," Elsevier, 2008, 261-304. |
[20] |
B. Zhang, H. Chen, B. I. Wu and J. A. Kong, Extraordinary surface voltage effect in the invisibility cloak with an active device inside, Phys. Rev. Lett., 100 (2008), 063904.
doi: 10.1103/PhysRevLett.100.063904. |
show all references
References:
[1] |
A. Alu and N. Engheta, Achieving transparency with plasmonic and metamaterial coatings, Phys. Rev. E, 72 (2005), 016623.
doi: 10.1103/PhysRevE.72.016623. |
[2] |
A. Greenleaf, Y. Kurylev, M. Lassas and G. Uhlmann, Full-wave invisibility of active devices at all frequencies, Commu. Math. Phys., 275 (2007), 749-789.
doi: 10.1007/s00220-007-0311-6. |
[3] |
A. Greenleaf, Y. Kurylev, M. Lassas and G. Uhlmann, Cloaking devices, electromagnetic wormholes and transformation optics, SIAM Review, 51 (2009), 3-33.
doi: 10.1137/080716827. |
[4] |
A. Greenleaf, Y. Kurylev, M. Lassas and G. Uhlmann, Improvement of cylindrical cloaking with the SHS lining, Opt. Exp., 15 (2007), 12717.
doi: 10.1364/OE.15.012717. |
[5] |
A. Greenleaf, M. Lassas and G. Uhlmann, On nonuniqueness for Calderón's inverse problem, Math. Res. Lett., 10 (2003), 685-693. |
[6] |
U. Hetmaniuk and H. Y. Liu, On acoustic cloaking devices by transformation media and their simulation, SIAM J. Appl. Math., 70 (2010), 2996-3021.
doi: 10.1137/090771077. |
[7] |
V. Isakov, "Inverse Problems for Partial Differential Equations," 2nd edition, Springer-Verlag, New York, 2006. |
[8] |
R. Kohn, D. Onofrei, M. Vogelius and M. Weinstein, Cloaking via change of variables for the Helmholtz equation, Commu. Pure Appl. Math., 63 (2010), 0973-1016. |
[9] |
R. Kohn, H. Shen, M. Vogelius and M. Weinstein, Cloaking via change of variables in electrical impedance tomography, Inverse Problems, 24 (2008), 015016.
doi: 10.1088/0266-5611/24/1/015016. |
[10] |
U. Leonhardt, Optical conformal mapping, Science, 312 (2006), 1777-1780.
doi: 10.1126/science.1126493. |
[11] |
H. Y. Liu, Virtual reshaping and invisibility in obstacle scattering, Inverse Problems, 25 (2009), 045006.
doi: 10.1088/0266-5611/25/4/045006. |
[12] |
W. McLean, "Strongly Elliptic Systems and Boundary Integral Equations," Cambridge University Press, Cambridge, 2000. |
[13] |
G. W. Milton and N.-A. P. Nicorovici, On the cloaking effects associated with anomalous localized resonance, Proc. Roy. Soc. A, 462 (2006), 3027-3095.
doi: 10.1098/rspa.2006.1715. |
[14] |
H. M. Nguyen, Cloaking via change of variables for the Helmholtz equation in the whole space, Commu. Pure Appl. Math., 63 (2010), 1505-1524.
doi: 10.1002/cpa.20333. |
[15] |
H. M. Nguyen, Approximate cloaking for the Helmholtz equation via transformation optics and consequences for perfect cloaking, preprint, 2011. |
[16] |
A. N. Norris, Acoustic cloaking theory, Proc. R. Soc. A, 464 (2008), 2411-2434.
doi: 10.1098/rspa.2008.0076. |
[17] |
J. B. Pendry, D. Schurig and D. R. Smith, Controlling electromagnetic fields, Science, 312 (2006), 1780-1782.
doi: 10.1126/science.1125907. |
[18] |
G. Uhlmann, Developments in inverse problems since Calderón's foundational paper,, Ch. 19 in, ().
|
[19] |
M. Yan, W. Yan and M. Qiu, Invisibility cloaking by coordinate transformation, Ch. 4 in "Progress in Optics," Elsevier, 2008, 261-304. |
[20] |
B. Zhang, H. Chen, B. I. Wu and J. A. Kong, Extraordinary surface voltage effect in the invisibility cloak with an active device inside, Phys. Rev. Lett., 100 (2008), 063904.
doi: 10.1103/PhysRevLett.100.063904. |
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