Abstract

Conceptual studies and numerical simulations are performed for imaging devices that transform a near-field pattern into magnified far-zone images and are based on high-order spatial transformation in cylindrical domains. A lens translating a near-field pattern from an almost circular input boundary onto a magnified far-field image at a flat output boundary is considered. The lens is made of a metamaterial with anisotropic permittivity and permeability both depending on a single “scaling” parameter of the transformation. Open designs of the lens with a truncated body (34-body and 14-body lenses) are suggested and analyzed. It is shown that the ideal full lens and the 34-body lens produce identical images. Numerical simulations of 14-body designs indicate that further truncation of the lens could limit its performance. A light concentrator “focusing” far-zone fields into a nanometer-scale area is also considered.

© 2008 Optical Society of America

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References

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    [CrossRef] [PubMed]

2007 (5)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef] [PubMed]

A. V. Kildishev and E. E. Narimanov, Opt. Lett. 32, 3432 (2007).
[CrossRef] [PubMed]

2006 (7)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, Opt. Express 14, 8247 (2006).
[CrossRef] [PubMed]

D. A. B. Miller, Opt. Express 14, 12457 (2006).
[CrossRef] [PubMed]

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

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

U. Leonhardt and T. G. Philbin, New J. Phys. 8, 247 (2006).
[CrossRef]

G. W. Milton and N. A. P. Nicorovici, Proc. R. Soc. London, Ser. A 462, 3027 (2006).
[CrossRef]

2005 (2)

A. Alu and N. Engheta, Phys. Rev. E 72, 016623 (2005).
[CrossRef]

F. J. Garcia de Abajo, G. Gómez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, Phys. Rev. Lett. 95, 067403 (2005).
[CrossRef]

2003 (1)

A. Greenleaf, M. Lassas, and G. Uhlmann, Bone Marrow Transplant 24, 413 (2003).

1996 (1)

A. J. Ward and J. B. Pendry, J. Mod. Opt. 43, 773 (1996).
[CrossRef]

Appl. Phys. Lett. (1)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Bone Marrow Transplant (1)

A. Greenleaf, M. Lassas, and G. Uhlmann, Bone Marrow Transplant 24, 413 (2003).

J. Mod. Opt. (1)

A. J. Ward and J. B. Pendry, J. Mod. Opt. 43, 773 (1996).
[CrossRef]

Nat. Photonics (1)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

New J. Phys. (1)

U. Leonhardt and T. G. Philbin, New J. Phys. 8, 247 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. E (1)

A. Alu and N. Engheta, Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

F. J. Garcia de Abajo, G. Gómez-Santos, L. A. Blanco, A. G. Borisov, and S. V. Shabanov, Phys. Rev. Lett. 95, 067403 (2005).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

G. W. Milton and N. A. P. Nicorovici, Proc. R. Soc. London, Ser. A 462, 3027 (2006).
[CrossRef]

Science (5)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

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

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef] [PubMed]

Other (1)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, http://aps. arxiv.org/abs/0706.2452 (2007).

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Figures (4)

Fig. 1
Fig. 1

Transformation of concentric cylindrical domains. (a) One-quarter x y -map generated by Eqs. (4) with x 0 = 1 μ m , 0 ϕ π 2 , and 0 η 3 . (b) Mapping of virtual domain (hatched quarter-ring) onto the physical domain (solid region), where the shared boundary is at ρ = η = 2 . For example, points A and B from the curvilinear boundary at η = 1.5 are mapped onto the points A and B of the external boundary of the lens at ρ = 0 .

Fig. 2
Fig. 2

Test of near-to-far-field projection. (a) Magnetic field intensity generated by two coherent test sources in air. (b) Magnetic field intensity generated by the pair of test sources inside and just outside the lens. Shaded areas indicate the lens cross section in (a) and (b). (c) H-field magnitude generated by the sources along the curvilinear (input) surface of the lens, ρ = η = 2 . (d) H-field magnitude created by the sources at the flat (output) edge, ρ = 0 .

Fig. 3
Fig. 3

Open designs of the lens. (a) Magnetic field map inside a 3 4 -body lens. (b) Field map inside a 1 4 -body lens. Shaded areas indicate the lens cross-section in (a) and (b). (c) H-field generated by the sources along the flat surface of either the closed or open lens designs.

Fig. 4
Fig. 4

Comparison of the full design of the light-concentrator (a) with an open 3 4 -body design (b). (cс) and (d), 1 2 -body and 1 4 -body designs of the concentrator. All the panels show the time-averaged energy density on a logarithmic scale for a TM-polarized 750 nm plane wave propagating from right to left.

Equations (8)

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( s 1 ϵ ϕ 1 h ( ρ ) ) ( ρ ) + ( s 1 ϵ ρ 1 h ( ϕ ) ) ( ϕ ) + μ s k 0 2 h = 0 .
( s ̃ 1 h ( η ) ) ( η ) + ( s ̃ 1 h ( ϕ ) ) ( ϕ ) + s ̃ k 0 2 h = 0 .
[ ( η ( ρ ) s ̃ ϵ ϕ s ) s ̃ 1 h ( η ) ] ( η ) + [ ( s ̃ η ( ρ ) s ϵ ρ ) s ̃ 1 h ( ϕ ) ] ( ϕ ) + k 0 2 ( μ s η ( ρ ) s ̃ ) s ̃ h = 0 .
ϵ ϕ = η ( ρ ) s ̃ s , ϵ ρ = s ̃ ( s η ( ρ ) ) , μ = ϵ ϕ .
x = α [ π 2 tan 1 ( sinh ρ cos ϕ ) ] , y = α 2 ln ( cosh ρ + sin ϕ cosh ρ sin ϕ ) ,
ϵ ϕ = κ τ , ϵ ρ = κ τ , μ = ϵ ϕ ,
ρ = 1 2 ln ( cosh y ̑ + cos x ̑ cosh y ̑ cos x ̑ ) , ϕ = tan 1 ( sin x ̑ sinh y ̑ ) ,
ϵ = κ 2 [ ( τ + τ 1 ) i + τ τ 1 cosh 2 y ̑ cos 2 x ̑ u ] ,

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