Spherical cloaking using nonlinear
transformations for improved
segmentation into concentric isotropic
coatings

doi:10.1364/OE.17.013467

Spherical cloaking using nonlinear transformations for improved segmentation into concentric isotropic coatings

Chengwei Qiu, Li Hu, Baile Zhang, Bae-Ian Wu, Steven G. Johnson, and John D. Joannopoulos »View Author Affiliations

Optics Express, Vol. 17, Issue 16, pp. 13467-13478 (2009)
http://dx.doi.org/10.1364/OE.17.013467

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Abstract
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Abstract

Two novel classes of spherical invisibility cloaks based on nonlinear transformation have been studied. The cloaking characteristics are presented by segmenting the nonlinear transformation based spherical cloak into concentric isotropic homogeneous coatings. Detailed investigations of the optimal discretization (e.g., thickness control of each layer, nonlinear factor, etc.) are presented for both linear and nonlinear spherical cloaks and their effects on invisibility performance are also discussed. The cloaking properties and our choice of optimal segmentation are verified by the numerical simulation of not only near-field electric-field distribution but also the far-field radar cross section (RCS).

OCIS Codes
(160.1190) Materials : Anisotropic optical materials
(230.3205) Optical devices : Invisibility cloaks
(290.5839) Scattering : Scattering, invisibility

ToC Category:
Physical Optics

History
Original Manuscript: May 12, 2009
Revised Manuscript: July 7, 2009
Manuscript Accepted: July 10, 2009
Published: July 21, 2009

Citation
Chengwei Qiu, Li Hu, Baile Zhang, Bae-Ian Wu, Steven G. Johnson, and John D. Joannopoulos, "Spherical cloaking using nonlinear transformations for improved segmentation into concentric isotropic coatings," Opt. Express 17, 13467-13478 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-13467

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References

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006). [CrossRef] [PubMed]
D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006). [CrossRef] [PubMed]
U. Leonhardt,"Optical conformal mapping," Science 312, 1777-1780 (2006). [CrossRef] [PubMed]
D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007). [CrossRef] [PubMed]
A. Greenleaf, M. Lassas, and G. Uhlmann, "Anisotropic conductivities that cannot be detected by EIT," Physiol. Meas. 24, 413-419 (2003). [CrossRef] [PubMed]
H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (2007). [CrossRef]
M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, "Broadband cylindrical acoustic cloak for linear surface waves in a fluid," Phys. Rev. Lett. 101, 1345011 (2008). [CrossRef]
H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic Wave Interactions with a Metamaterial Cloak," Phys. Rev. Lett. 99, 063903 (2007). [CrossRef] [PubMed]
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, 063904 (2008). [CrossRef] [PubMed]
G.W. Milton, M. Briane, and J. R. Willis, "On cloaking for elasticity and physical equations with a transformation invariant form," New J. Phys. 8, 248 (2006). [CrossRef]
M. Farhat, S. Guenneau, S. Enoch, and A. Movchan, "Cloaking bending waves propagating in thin elastic plates," Phys. Rev. B 79, 033102 (2009). [CrossRef]
M. Brun, S. Guenneau, and A. B. Movchan, "Achieving control of in-plane elastic waves," Appl. Phys. Lett. 94, 061903 (2009). [CrossRef]
M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, and D. R. Smith, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photonics Nanostruc. Fundam. Appl. 6, 87 (2008). [CrossRef]
D. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008). [CrossRef]
W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng and J. Y. Chin, "Arbitrarily ellipticalCcylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504 (2008). [CrossRef]
M. Yan, Z. Chao, and M. Qiu, "Cylindrical invisibility cloak with simplified material parameters is inherently visible," Phys. Rev. Lett. 99, 233901 (2007). [CrossRef]
M. Yan, Z. Chao, and M. Qiu, "Scattering characteristics of simplified cylindrical invisibility cloaks," Opt. Express 15, 17772C17782 (2007). [CrossRef]
H. Ma, S. B. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008). [CrossRef]
W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 063904 (2007). [CrossRef]
B. Zhang, H. Chen, and B. I. Wu, "Limitations of high-order transformation and incident angle on simplified invisibility cloaks," Opt. Express 16, 5445-5452 (2008).
D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977 (2006). [CrossRef] [PubMed]
R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, "Broadband Ground-Plane Cloak," Science 323, 366-369 (2009). [CrossRef] [PubMed]
W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped objects," Phys. Rev. E 77, 066607 (2008). [CrossRef]
H. Ma, S. Qu, Z. Xu, and J. Wang, "Numerical method for designing approximate cloaks with arbitrary shapes," Phys. Rev. E 78, 036608 (2008). [CrossRef]
A. Nicolet, F. Zolla, and S. Guenneau, "Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section," Opt. Lett. 33, 1584 (2008). [CrossRef] [PubMed]
C. W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, "Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies," Phys. Rev. E 75, 026609 (2007). [CrossRef]
W. Cai, U. K. Chettiar, A. K. Kildishev, G. W. Milton, and V. M. Shalaev, "Non-magnetic cloak without reflection," arXiv:0707.3641v1.
R. Weder, "A rigorous analysis of high-order electromagnetic invisibility cloaks," J. Phys. A: Math. Theor. 41, 065207 (2008). [CrossRef]
C. W. Qiu, L. W. Li, Q. Wu, and T. S. Yeo, "Field representations in general gyrotropic media in spherical coordinates," IEEE Antennas Wirel. Propagat. Lett. 4, 467-470 (2007). [CrossRef]
C. W. Qiu, S. Zouhdi, and A. Razek, "Modified spherical wave functions with anisotropy ratio: Application to the analysis of scattering by multilayered anisotropic shells," IEEE Trans. Antennas Propagat. 55, 3515-3523 (2007). [CrossRef]
J. C. E. Sten, "DC fields and analytical image solutions for a radially anisotropic spherical conductor," IEEE Trans. Diel. Elec. Insul. 2, 360-367 (1995). [CrossRef]
B. I. Popa and S. A. Cummer, "Cloaking with optimized homogeneous anisotropic layers," Phys. Rev. A 79, 023806 (2009). [CrossRef]
C. W. Qiu, L. Hu, and L. Gao, "Trade-off between forward and backward scatterings of Linear and Nonlinear Spherical Invisibility Cloaks," Progress In Electromagnetics Research, to be submitted (2009).

Briane, M.
Brun, M.
Cai, W.
Chan, C. T.
Chao, Z.
Chen, B. W.
Chen, H.
Cheng, Q.
Chettiar, U. K.
Chin, J. Y.
Cui, T. J.
Cummer, S. A.
Enoch, S.
Farhat, M.
Greenleaf, A.
Guenneau, S.
Ji, C.
Jiang, W. X.
Justice, B. J.
Kildishev, A. V.
Kong, J. A.
Kwon, D.
Lassas, M.
Leonhardt, U.
Li, L. W.
Li, Z.
Lin, X. Q.
Liu, R.
Ma, H.
Milton, G.W.
Mock, J. J.
Movchan, A.
Movchan, A. B.
Movchan, A.B.
Nicolet, A.
Pendry, J. B.
Popa, B. I.
Qiu, C. W.
Qiu, M.
Qu, S.
Qu, S. B.
Rahm, M.
Razek, A.
Roberts, D. A.
Schurig, D.
Shalaev, V. M.
Smith, D. R.
Starr, A. F.
Sten, J. C. E.
Uhlmann, G.
Wang, J.
Wang, J. F.
Weder, R.
Werner, D. H.
Willis, J. R.
Wu, B. I.
Wu, Q.
Xu, Z.
Yan, M.
Yeo, T. S.
Yu, G. X.
Zhang, B.
Zhang, J. Q.
Zolla, F.
Zouhdi, S.

Appl. Phys. Lett.

H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (2007). [CrossRef]
M. Brun, S. Guenneau, and A. B. Movchan, "Achieving control of in-plane elastic waves," Appl. Phys. Lett. 94, 061903 (2009). [CrossRef]
D. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008). [CrossRef]

IEEE Antennas Wirel. Propagat. Lett.

C. W. Qiu, L. W. Li, Q. Wu, and T. S. Yeo, "Field representations in general gyrotropic media in spherical coordinates," IEEE Antennas Wirel. Propagat. Lett. 4, 467-470 (2007). [CrossRef]

IEEE Trans. Antennas Propagat.

C. W. Qiu, S. Zouhdi, and A. Razek, "Modified spherical wave functions with anisotropy ratio: Application to the analysis of scattering by multilayered anisotropic shells," IEEE Trans. Antennas Propagat. 55, 3515-3523 (2007). [CrossRef]

IEEE Trans. Diel. Elec. Insul.

J. C. E. Sten, "DC fields and analytical image solutions for a radially anisotropic spherical conductor," IEEE Trans. Diel. Elec. Insul. 2, 360-367 (1995). [CrossRef]

J. Phys. A: Math. Theor.

R. Weder, "A rigorous analysis of high-order electromagnetic invisibility cloaks," J. Phys. A: Math. Theor. 41, 065207 (2008). [CrossRef]

J. Phys. D: Appl. Phys.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng and J. Y. Chin, "Arbitrarily ellipticalCcylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504 (2008). [CrossRef]

Nat. Photonics

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 063904 (2007). [CrossRef]

New J. Phys.

G.W. Milton, M. Briane, and J. R. Willis, "On cloaking for elasticity and physical equations with a transformation invariant form," New J. Phys. 8, 248 (2006). [CrossRef]

Opt. Express

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006). [CrossRef] [PubMed]
D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007). [CrossRef] [PubMed]
B. Zhang, H. Chen, and B. I. Wu, "Limitations of high-order transformation and incident angle on simplified invisibility cloaks," Opt. Express 16, 5445-5452 (2008).

Opt. Lett.

A. Nicolet, F. Zolla, and S. Guenneau, "Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section," Opt. Lett. 33, 1584 (2008). [CrossRef] [PubMed]

Photonics Nanostruc. Fundam. Appl.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, and D. R. Smith, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photonics Nanostruc. Fundam. Appl. 6, 87 (2008). [CrossRef]

Phys. Rev. A

B. I. Popa and S. A. Cummer, "Cloaking with optimized homogeneous anisotropic layers," Phys. Rev. A 79, 023806 (2009). [CrossRef]
H. Ma, S. B. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008). [CrossRef]

Phys. Rev. B

M. Farhat, S. Guenneau, S. Enoch, and A. Movchan, "Cloaking bending waves propagating in thin elastic plates," Phys. Rev. B 79, 033102 (2009). [CrossRef]

Phys. Rev. E

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped objects," Phys. Rev. E 77, 066607 (2008). [CrossRef]
H. Ma, S. Qu, Z. Xu, and J. Wang, "Numerical method for designing approximate cloaks with arbitrary shapes," Phys. Rev. E 78, 036608 (2008). [CrossRef]
C. W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, "Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies," Phys. Rev. E 75, 026609 (2007). [CrossRef]

Phys. Rev. Lett.

M. Yan, Z. Chao, and M. Qiu, "Cylindrical invisibility cloak with simplified material parameters is inherently visible," Phys. Rev. Lett. 99, 233901 (2007). [CrossRef]
M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, "Broadband cylindrical acoustic cloak for linear surface waves in a fluid," Phys. Rev. Lett. 101, 1345011 (2008). [CrossRef]
H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic Wave Interactions with a Metamaterial Cloak," Phys. Rev. Lett. 99, 063903 (2007). [CrossRef] [PubMed]
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, 063904 (2008). [CrossRef] [PubMed]

Physiol. Meas.

A. Greenleaf, M. Lassas, and G. Uhlmann, "Anisotropic conductivities that cannot be detected by EIT," Physiol. Meas. 24, 413-419 (2003). [CrossRef] [PubMed]

Science

U. Leonhardt,"Optical conformal mapping," Science 312, 1777-1780 (2006). [CrossRef] [PubMed]
J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006). [CrossRef] [PubMed]
D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977 (2006). [CrossRef] [PubMed]
R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, "Broadband Ground-Plane Cloak," Science 323, 366-369 (2009). [CrossRef] [PubMed]

Other

W. Cai, U. K. Chettiar, A. K. Kildishev, G. W. Milton, and V. M. Shalaev, "Non-magnetic cloak without reflection," arXiv:0707.3641v1.
C. W. Qiu, L. Hu, and L. Gao, "Trade-off between forward and backward scatterings of Linear and Nonlinear Spherical Invisibility Cloaks," Progress In Electromagnetics Research, to be submitted (2009).
M. Yan, Z. Chao, and M. Qiu, "Scattering characteristics of simplified cylindrical invisibility cloaks," Opt. Express 15, 17772C17782 (2007). [CrossRef]

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[1] J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006). [CrossRef] [PubMed]

[2] D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006). [CrossRef] [PubMed]

[3] U. Leonhardt,"Optical conformal mapping," Science 312, 1777-1780 (2006). [CrossRef] [PubMed]

[4] D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007). [CrossRef] [PubMed]

[5] A. Greenleaf, M. Lassas, and G. Uhlmann, "Anisotropic conductivities that cannot be detected by EIT," Physiol. Meas. 24, 413-419 (2003). [CrossRef] [PubMed]

[6] H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (2007). [CrossRef]

[7] M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, "Broadband cylindrical acoustic cloak for linear surface waves in a fluid," Phys. Rev. Lett. 101, 1345011 (2008). [CrossRef]

[8] H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic Wave Interactions with a Metamaterial Cloak," Phys. Rev. Lett. 99, 063903 (2007). [CrossRef] [PubMed]

[9] 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, 063904 (2008). [CrossRef] [PubMed]

[10] G.W. Milton, M. Briane, and J. R. Willis, "On cloaking for elasticity and physical equations with a transformation invariant form," New J. Phys. 8, 248 (2006). [CrossRef]

[11] M. Farhat, S. Guenneau, S. Enoch, and A. Movchan, "Cloaking bending waves propagating in thin elastic plates," Phys. Rev. B 79, 033102 (2009). [CrossRef]

[12] M. Brun, S. Guenneau, and A. B. Movchan, "Achieving control of in-plane elastic waves," Appl. Phys. Lett. 94, 061903 (2009). [CrossRef]

[13] M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, and D. R. Smith, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photonics Nanostruc. Fundam. Appl. 6, 87 (2008). [CrossRef]

[14] D. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008). [CrossRef]

[15] W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng and J. Y. Chin, "Arbitrarily ellipticalCcylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504 (2008). [CrossRef]

[16] M. Yan, Z. Chao, and M. Qiu, "Cylindrical invisibility cloak with simplified material parameters is inherently visible," Phys. Rev. Lett. 99, 233901 (2007). [CrossRef]

[17] M. Yan, Z. Chao, and M. Qiu, "Scattering characteristics of simplified cylindrical invisibility cloaks," Opt. Express 15, 17772C17782 (2007). [CrossRef]

[18] H. Ma, S. B. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008). [CrossRef]

[19] W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 063904 (2007). [CrossRef]

[20] B. Zhang, H. Chen, and B. I. Wu, "Limitations of high-order transformation and incident angle on simplified invisibility cloaks," Opt. Express 16, 5445-5452 (2008).

[21] D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977 (2006). [CrossRef] [PubMed]

[22] R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, "Broadband Ground-Plane Cloak," Science 323, 366-369 (2009). [CrossRef] [PubMed]

[23] W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped objects," Phys. Rev. E 77, 066607 (2008). [CrossRef]

[24] H. Ma, S. Qu, Z. Xu, and J. Wang, "Numerical method for designing approximate cloaks with arbitrary shapes," Phys. Rev. E 78, 036608 (2008). [CrossRef]

[25] A. Nicolet, F. Zolla, and S. Guenneau, "Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section," Opt. Lett. 33, 1584 (2008). [CrossRef] [PubMed]

[26] C. W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, "Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies," Phys. Rev. E 75, 026609 (2007). [CrossRef]

[27] W. Cai, U. K. Chettiar, A. K. Kildishev, G. W. Milton, and V. M. Shalaev, "Non-magnetic cloak without reflection," arXiv:0707.3641v1.

[28] R. Weder, "A rigorous analysis of high-order electromagnetic invisibility cloaks," J. Phys. A: Math. Theor. 41, 065207 (2008). [CrossRef]

[29] C. W. Qiu, L. W. Li, Q. Wu, and T. S. Yeo, "Field representations in general gyrotropic media in spherical coordinates," IEEE Antennas Wirel. Propagat. Lett. 4, 467-470 (2007). [CrossRef]

[30] C. W. Qiu, S. Zouhdi, and A. Razek, "Modified spherical wave functions with anisotropy ratio: Application to the analysis of scattering by multilayered anisotropic shells," IEEE Trans. Antennas Propagat. 55, 3515-3523 (2007). [CrossRef]

[31] J. C. E. Sten, "DC fields and analytical image solutions for a radially anisotropic spherical conductor," IEEE Trans. Diel. Elec. Insul. 2, 360-367 (1995). [CrossRef]

[32] B. I. Popa and S. A. Cummer, "Cloaking with optimized homogeneous anisotropic layers," Phys. Rev. A 79, 023806 (2009). [CrossRef]

[33] C. W. Qiu, L. Hu, and L. Gao, "Trade-off between forward and backward scatterings of Linear and Nonlinear Spherical Invisibility Cloaks," Progress In Electromagnetics Research, to be submitted (2009).

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