Optical lens compression via transformation optics

D. A. Roberts; N. Kundtz; D. R. Smith

doi:10.1364/OE.17.016535

Optical lens compression via transformation optics

D. A. Roberts, N. Kundtz, and D. R. Smith

Optics Express
Vol. 17,
Issue 19,
pp. 16535-16542
(2009)
•https://doi.org/10.1364/OE.17.016535

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D. A. Roberts, N. Kundtz, and D. R. Smith, "Optical lens compression via transformation optics," Opt. Express 17, 16535-16542 (2009)

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Related Topics
Table of Contents Category
- Imaging Systems
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Gradient-index lenses (110.2760)
- Optical design of instruments (120.4570)
- Metamaterials (160.3918)
- Lens system design (220.3620)
- Lenses (220.3630)
- Optical devices (230.0230)

About this Article
History
- Original Manuscript: July 7, 2009
- Revised Manuscript: August 15, 2009
- Manuscript Accepted: August 17, 2009
- Published: September 1, 2009

Accessible

Open Access

Abstract

Transformation optics is widely associated with the design of unconventional electromagnetic devices, such as electromagnetic cloaks or concentrators. However, a wide range of conventional optical devices with potentially advantageous properties can be designed by the transformation optical approach. For example, a coordinate transformation can be introduced that compresses a region of space, resulting in an overall decrease in the thickness of an optical instrument such as a lens. The optical properties of a transformed lens, such as Fresnel reflection or aberration profile, are equivalent to those of the original lens, while the transformed lens and the bounding transformation optical material are thinner than the original lens. This approach to flattening the profile of a lens represents an advantage over the use of a higher dielectric material because it does not introduce greater Fresnel reflections or require a redesign of the basic optic. Though transformation optical media are generally anisotropic, with both electric and magnetic response, it is possible to arrive at a dielectric-only transformation optical distribution for a lens interacting with transverse-magnetic (TM) polarized light. The dielectric-only distribution can be implemented using broad-band, low-loss metamaterials. Lens designs for both a full transformation and a dielectric-only implementation are discussed and confirmed via finite-element simulations.

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References

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Publication

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]
U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]
W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]
M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[Crossref] [PubMed]
M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[Crossref] [PubMed]
D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]
D. H. Kwon and D. H. Werner, “Polarization splitter and polarization rotator designs based on transformation optics,” Opt. Express 16(23), 18731–18738 (2008).
[Crossref]
D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15(22), 14772–14782 (2007).
[Crossref] [PubMed]
A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32(23), 3432–3434 (2007).
[Crossref] [PubMed]
M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[Crossref]
L. Lin, W. Wang, C. L. Du, and X. G. Luo, “A cone-shaped concentrator with varying performances of concentrating,” Opt. Express 16(10), 6809–6814 (2008).
[Crossref] [PubMed]
M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
[Crossref]
V. M. Shalaev, “Physics. Transforming light,” Science 322(5900), 384–386 (2008).
[Crossref] [PubMed]
D. H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” N. J. Phys. 10(11), 115023 (2008).
[Crossref]
D. Schurig, “An aberration-free lens with zero F-number,” N. J. Phys. 10(11), 115034 (2008).
[Crossref]
F. M. Kong, B. I. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91(25), 253509 (2007).
[Crossref]
Yu. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the Emission of Electromagnetic Source,” PIERS 4(7), 795–800 (2008).
[Crossref]
N. Kundtz, D. A. Roberts, J. Allen, S. Cummer, and D. R. Smith, “Optical source transformations,” Opt. Express 16(26), 21215–21222 (2008).
[Crossref] [PubMed]
D.-H. Kwon and D. H. Werner, “Restoration of antenna parameters in scattering environments using electromagnetic cloaking,” Appl. Phys. Lett. 92(11), 113507 (2008).
[Crossref]
D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005).
[Crossref] [PubMed]
R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87(9), 091114 (2005).
[Crossref]
T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88(8), 081101 (2006).
[Crossref]
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(5801), 977–980 (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(5912), 366–369 (2009).
[Crossref] [PubMed]
C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232 (2004).
[Crossref]
D. Schurig and D. R. Smith, “Negative index lens aberrations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(6), 065601 (2004).
[Crossref]
A. D. Portnoy, N. P. Pitsianis, X. Sun, and D. J. Brady, “Multichannel sampling schemes for optical imaging systems,” Appl. Opt. 47(10), B76–B85 (2008).
[Crossref] [PubMed]

2009 (1)

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[Crossref] [PubMed]

2008 (14)

A. D. Portnoy, N. P. Pitsianis, X. Sun, and D. J. Brady, “Multichannel sampling schemes for optical imaging systems,” Appl. Opt. 47(10), B76–B85 (2008).
[Crossref] [PubMed]

L. Lin, W. Wang, C. L. Du, and X. G. Luo, “A cone-shaped concentrator with varying performances of concentrating,” Opt. Express 16(10), 6809–6814 (2008).
[Crossref] [PubMed]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[Crossref] [PubMed]

D. H. Kwon and D. H. Werner, “Polarization splitter and polarization rotator designs based on transformation optics,” Opt. Express 16(23), 18731–18738 (2008).
[Crossref]

N. Kundtz, D. A. Roberts, J. Allen, S. Cummer, and D. R. Smith, “Optical source transformations,” Opt. Express 16(26), 21215–21222 (2008).
[Crossref] [PubMed]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[Crossref] [PubMed]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

D.-H. Kwon and D. H. Werner, “Restoration of antenna parameters in scattering environments using electromagnetic cloaking,” Appl. Phys. Lett. 92(11), 113507 (2008).
[Crossref]

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
[Crossref]

V. M. Shalaev, “Physics. Transforming light,” Science 322(5900), 384–386 (2008).
[Crossref] [PubMed]

D. H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” N. J. Phys. 10(11), 115023 (2008).
[Crossref]

D. Schurig, “An aberration-free lens with zero F-number,” N. J. Phys. 10(11), 115034 (2008).
[Crossref]

Yu. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the Emission of Electromagnetic Source,” PIERS 4(7), 795–800 (2008).
[Crossref]

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[Crossref]

2007 (4)

D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15(22), 14772–14782 (2007).
[Crossref] [PubMed]

A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32(23), 3432–3434 (2007).
[Crossref] [PubMed]

F. M. Kong, B. I. I. Wu, J. A. Kong, J. T. Huangfu, S. Xi, and H. S. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91(25), 253509 (2007).
[Crossref]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

2006 (4)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett. 88(8), 081101 (2006).
[Crossref]

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(5801), 977–980 (2006).
[Crossref] [PubMed]

2005 (2)

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005).
[Crossref] [PubMed]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, “Simulation and testing of a graded negative index of refraction lens,” Appl. Phys. Lett. 87(9), 091114 (2005).
[Crossref]

2004 (2)

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232 (2004).
[Crossref]

D. Schurig and D. R. Smith, “Negative index lens aberrations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(6), 065601 (2004).
[Crossref]

Allen, J.

N. Kundtz, D. A. Roberts, J. Allen, S. Cummer, and D. R. Smith, “Optical source transformations,” Opt. Express 16(26), 21215–21222 (2008).
[Crossref] [PubMed]

Basov, D. N.

Brady, D. J.

A. D. Portnoy, N. P. Pitsianis, X. Sun, and D. J. Brady, “Multichannel sampling schemes for optical imaging systems,” Appl. Opt. 47(10), B76–B85 (2008).
[Crossref] [PubMed]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Chen, H.

Yu. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the Emission of Electromagnetic Source,” PIERS 4(7), 795–800 (2008).
[Crossref]

Chen, H. S.

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[Crossref] [PubMed]

Cui, T. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[Crossref] [PubMed]

Cummer, S.

N. Kundtz, D. A. Roberts, J. Allen, S. Cummer, and D. R. Smith, “Optical source transformations,” Opt. Express 16(26), 21215–21222 (2008).
[Crossref] [PubMed]

Cummer, S. A.

Driscoll, T.

Du, C. L.

L. Lin, W. Wang, C. L. Du, and X. G. Luo, “A cone-shaped concentrator with varying performances of concentrating,” Opt. Express 16(10), 6809–6814 (2008).
[Crossref] [PubMed]

Greegor, R. B.

Huangfu, J. T.

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[Crossref] [PubMed]

Justice, B. J.

Kildishev, A. V.

A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32(23), 3432–3434 (2007).
[Crossref] [PubMed]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Kong, F. M.

Kong, J. A.

Yu. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the Emission of Electromagnetic Source,” PIERS 4(7), 795–800 (2008).
[Crossref]

Koschny, T.

Kundtz, N.

N. Kundtz, D. A. Roberts, J. Allen, S. Cummer, and D. R. Smith, “Optical source transformations,” Opt. Express 16(26), 21215–21222 (2008).
[Crossref] [PubMed]

Kwon, D. H.

D. H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” N. J. Phys. 10(11), 115023 (2008).
[Crossref]

D. H. Kwon and D. H. Werner, “Polarization splitter and polarization rotator designs based on transformation optics,” Opt. Express 16(23), 18731–18738 (2008).
[Crossref]

Kwon, D.-H.

D.-H. Kwon and D. H. Werner, “Restoration of antenna parameters in scattering environments using electromagnetic cloaking,” Appl. Phys. Lett. 92(11), 113507 (2008).
[Crossref]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

Li, K.

Lin, L.

L. Lin, W. Wang, C. L. Du, and X. G. Luo, “A cone-shaped concentrator with varying performances of concentrating,” Opt. Express 16(10), 6809–6814 (2008).
[Crossref] [PubMed]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[Crossref] [PubMed]

Luo, X. G.

L. Lin, W. Wang, C. L. Du, and X. G. Luo, “A cone-shaped concentrator with varying performances of concentrating,” Opt. Express 16(10), 6809–6814 (2008).
[Crossref] [PubMed]

Luo, Yu.

Yu. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the Emission of Electromagnetic Source,” PIERS 4(7), 795–800 (2008).
[Crossref]

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[Crossref] [PubMed]

Narimanov, E. E.

A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32(23), 3432–3434 (2007).
[Crossref] [PubMed]

Nemat-Nasser, S.

Nielsen, J. A.

Parazzoli, C. G.

Pendry, J. B.

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[Crossref] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15(22), 14772–14782 (2007).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Pitsianis, N. P.

A. D. Portnoy, N. P. Pitsianis, X. Sun, and D. J. Brady, “Multichannel sampling schemes for optical imaging systems,” Appl. Opt. 47(10), B76–B85 (2008).
[Crossref] [PubMed]

Portnoy, A. D.

A. D. Portnoy, N. P. Pitsianis, X. Sun, and D. J. Brady, “Multichannel sampling schemes for optical imaging systems,” Appl. Opt. 47(10), B76–B85 (2008).
[Crossref] [PubMed]

Psaltis, D.

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[Crossref]

Qiu, M.

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
[Crossref]

Rahm, M.

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[Crossref] [PubMed]

Ran, L.

Yu. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the Emission of Electromagnetic Source,” PIERS 4(7), 795–800 (2008).
[Crossref]

Roberts, D. A.

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[Crossref] [PubMed]

N. Kundtz, D. A. Roberts, J. Allen, S. Cummer, and D. R. Smith, “Optical source transformations,” Opt. Express 16(26), 21215–21222 (2008).
[Crossref] [PubMed]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

Rye, P. M.

Schurig, D.

D. Schurig, “An aberration-free lens with zero F-number,” N. J. Phys. 10(11), 115034 (2008).
[Crossref]

D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15(22), 14772–14782 (2007).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

D. Schurig and D. R. Smith, “Negative index lens aberrations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(6), 065601 (2004).
[Crossref]

Shalaev, V. M.

V. M. Shalaev, “Physics. Transforming light,” Science 322(5900), 384–386 (2008).
[Crossref] [PubMed]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Smith, D. R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[Crossref] [PubMed]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[Crossref] [PubMed]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

N. Kundtz, D. A. Roberts, J. Allen, S. Cummer, and D. R. Smith, “Optical source transformations,” Opt. Express 16(26), 21215–21222 (2008).
[Crossref] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15(22), 14772–14782 (2007).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

D. Schurig and D. R. Smith, “Negative index lens aberrations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(6), 065601 (2004).
[Crossref]

Soukoulis, C. M.

Starr, A. F.

Sun, X.

A. D. Portnoy, N. P. Pitsianis, X. Sun, and D. J. Brady, “Multichannel sampling schemes for optical imaging systems,” Appl. Opt. 47(10), B76–B85 (2008).
[Crossref] [PubMed]

Tanielian, M. H.

Thompson, M. A.

Tsang, M.

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008).
[Crossref]

Vetter, A. M.

Vier, D. C.

Wang, W.

L. Lin, W. Wang, C. L. Du, and X. G. Luo, “A cone-shaped concentrator with varying performances of concentrating,” Opt. Express 16(10), 6809–6814 (2008).
[Crossref] [PubMed]

Werner, D. H.

D. H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” N. J. Phys. 10(11), 115023 (2008).
[Crossref]

D.-H. Kwon and D. H. Werner, “Restoration of antenna parameters in scattering environments using electromagnetic cloaking,” Appl. Phys. Lett. 92(11), 113507 (2008).
[Crossref]

D. H. Kwon and D. H. Werner, “Polarization splitter and polarization rotator designs based on transformation optics,” Opt. Express 16(23), 18731–18738 (2008).
[Crossref]

Wu, B. I. I.

Xi, S.

Yan, M.

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78(12), 125113 (2008).
[Crossref]

Yan, W.

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Fig. 1 (a) Plot of the space compression transformation expressed by Eq. (5). The shaded region in the left plot is compressed by a factor of two in the right plot. In both plots, the lines are of constant x and constant y. The integration constant was chosen so that x = 0 maps to x’ = 0. (b) Plot of x’ versus x, illustrating the compression that occurs in the primed coordinate system.

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Fig. 2 Plot of the z-component of the electric field for a lens with a focal length of 0.2 m: (a) Original planar-convex lens. (b) Transformation optically compressed lens. (c) Plot of intensity across the focal plane for the original planar-convex lens and the transformation optically compressed lens. (d) Material parameters: Non-zero permittivity and permeability components of the original lens and the transformed lens.

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Fig. 3 (a) Plot of the z-component of the magnetic field for the dielectric-only compressed lens with a focal length of 0.2 m. (b) Plot of the z-component of the magnetic field for the dielectric-only gradient transformation compressed lens with a focal length of 0.2 m.

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Fig. 4 (a) Plot of the space compression transformation expressed by Eq. (19). The shaded region shows the compressed region. As opposed to the jump compression, the parabolic compression is graded in. The lines are of constant x and constant y. The integration constant was chosen so that x = 0 maps to x’ = 0. (b) Plot of x’ versus x for the parabolic transformation expressed by Eq. (19) illustrating the compression that occurs in the primed coordinate system. (c) Plot of dx’/dx versus x for the parabolic transformation expressed by Eq. (18).

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Equations (20)

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\begin{array}{l} ε^{i' j'} = \det {(A)}^{- 1} A_{i}^{i'} A_{j}^{j'} ε^{i j} \\ μ^{i' j'} = \det {(A)}^{- 1} A_{i}^{i'} A_{j}^{j'} μ^{i j}, \end{array}

A_{i}^{i'} = \frac{\partial x^{i'}}{\partial x^{i}} .

\begin{array}{l} I . \frac{\partial x^{i'}}{\partial x^{i}} = 1 \\ I I .0 < \frac{\partial x^{i'}}{\partial x^{i}} < 1 \\ I I I . \frac{\partial x^{i'}}{\partial x^{i}} = 1 \end{array}

\frac{d x'}{d x} = {\begin{array}{c} a, & l_{1} < x < l_{2} \\ 1, & x \leq l_{1} \cup x \geq l_{2} \end{array},

x' (x) = {\begin{array}{c} a x + c, & l_{1} < x < l_{2} \\ l_{1}' + (x - l_{1}), & x \leq l_{1} \\ l_{2}' + (x - l_{2}), & x \geq l_{2} \end{array} .

\begin{array}{l} ε^{i j} = [\begin{array}{c} a & 0 & 0 \\ 0 & 1 / a & 0 \\ 0 & 0 & 1 / a \end{array}] n {(x, y)}^{2}, \\ μ^{i j} = [\begin{array}{c} a & 0 & 0 \\ 0 & 1 / a & 0 \\ 0 & 0 & 1 / a \end{array}] . \end{array}

x' (x) = {\begin{array}{c} x + 0.025 \\ \frac{1}{2} x \\ x \end{array} \begin{array}{c} x \leq - 0.05 \\ - 0.05 < x < 0 \\ x \geq 0 \end{array} .

\frac{1}{μ_{z} (x)} \frac{\partial}{\partial x} [\frac{1}{ε_{y} (x)} \frac{\partial H_{z}}{\partial x}] + \frac{1}{μ_{z} (x)} \frac{\partial}{\partial y} [\frac{1}{ε_{x} (x)} \frac{\partial H_{z}}{\partial y}] = \frac{\partial^{2} H_{z}}{\partial t^{2}},

(- \frac{1}{μ_{z}} \frac{1}{ε_{y}^{2}} \frac{\partial ε_{y}}{\partial x} \frac{\partial H_{z}}{\partial x} + \frac{1}{μ_{z} ε_{y}} \frac{\partial^{2} H_{z}}{\partial x^{2}}) .

\frac{1}{n_{x}^{2}} \frac{\partial^{2} H_{z}}{\partial x^{2}} + \frac{1}{n_{y}^{2}} \frac{\partial^{2} H_{z}}{\partial y^{2}} = \frac{\partial^{2} H_{z}}{\partial t^{2}}

n_{x} = \sqrt{μ_{z} ε_{y}},

n_{y} = \sqrt{μ_{z} ε_{x}}

ε_{y}' = μ_{z} ε_{y},

ε_{x}' = μ_{z} ε_{x},

μ_{z}' = 1,

ε^{i j} = [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 / a^{2} & 0 \\ 0 & 0 & 1 \end{array}] n {(x, y)}^{2},

μ = 1.

\frac{d x'}{d x} = {\begin{array}{c} (1 - a) {(\frac{2 x - l_{1} - l_{2}}{l_{1} - l_{2}})}^{2} + a, & l_{1} < x < l_{2} \\ 1, & x \leq l_{1} \cup x \geq l_{2} \end{array},

x' (x) = {\begin{array}{c} \frac{(1 - a)}{6 {(l_{1} - l_{2})}^{2}} {(2 x - l_{1} - l_{2})}^{3} + a x + c, & l_{1} < x < l_{2} \\ l_{1}' + (x - l_{1}), & x \leq l_{1} \\ l_{2}' + (x - l_{2}), & x \geq l_{2} \end{array} .

\frac{l_{2}' - l_{1}'}{l_{2} - l_{1}} = \frac{2}{3} a + \frac{1}{3} .