Abstract

Photorealistic ray tracing methods have been developed that allow us to see how devices such as imperfect invisible spheres and invisibility cloaks would appear if actually constructed and placed in outdoor environments. The methods developed allow photorealistic depiction of devices with gradient indices of refraction and birefringence or trirefringence in non-Cartesian coordinate systems (and hence accurately handle ray splitting/beam walkoff). The resulting images, which can be rendered in real time to produce animations as will be shown, allow subjective assessment of the performance of optical instruments such as invisibility devices in environments in which they are intended to ultimately be used.

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2009

J. C. Halimeh, T. Ergin, J. Mueller, N. Stenger, and M. Wegener, “Photorealistic images of carpet cloaks,” Opt. Express 17(22), 19328–19336 (2009).
[CrossRef] [PubMed]

T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” N. J. Phys. 10, 1–8 (2009).

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
[CrossRef]

2007

M. Brown and D. Lowe, “Automatic panoramic image stitching using invariant features,” Int. J. Comput. Vis. 74(1), 59–73 (2007).
[CrossRef]

2006

Brown, M.

M. Brown and D. Lowe, “Automatic panoramic image stitching using invariant features,” Int. J. Comput. Vis. 74(1), 59–73 (2007).
[CrossRef]

Dolling, G.

Ergin, T.

Halimeh, J. C.

Hendi, A.

A. Hendi, J. Henn, and U. Leonhardt, “Ambiguities in the scattering tomography for central potentials,” Phys. Rev. Lett. 97(7), 073902 (2006).
[CrossRef] [PubMed]

Henn, J.

A. Hendi, J. Henn, and U. Leonhardt, “Ambiguities in the scattering tomography for central potentials,” Phys. Rev. Lett. 97(7), 073902 (2006).
[CrossRef] [PubMed]

Hormann, C.

Leonhardt, U.

T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” N. J. Phys. 10, 1–8 (2009).

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
[CrossRef]

A. Hendi, J. Henn, and U. Leonhardt, “Ambiguities in the scattering tomography for central potentials,” Phys. Rev. Lett. 97(7), 073902 (2006).
[CrossRef] [PubMed]

Linden, S.

Lowe, D.

M. Brown and D. Lowe, “Automatic panoramic image stitching using invariant features,” Int. J. Comput. Vis. 74(1), 59–73 (2007).
[CrossRef]

Ma, Y. G.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

Miñano, J. C.

Mueller, J.

Ong, C. K.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

Pendry, J. B.

Schurig, D.

Smith, D. R.

Stenger, N.

Tyc, T.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” N. J. Phys. 10, 1–8 (2009).

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
[CrossRef]

Wegener, M.

Int. J. Comput. Vis.

M. Brown and D. Lowe, “Automatic panoramic image stitching using invariant features,” Int. J. Comput. Vis. 74(1), 59–73 (2007).
[CrossRef]

N. J. Phys.

T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” N. J. Phys. 10, 1–8 (2009).

Nat. Mater.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev. Lett.

A. Hendi, J. Henn, and U. Leonhardt, “Ambiguities in the scattering tomography for central potentials,” Phys. Rev. Lett. 97(7), 073902 (2006).
[CrossRef] [PubMed]

Science

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
[CrossRef]

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

Other

A. J. Danner, “Photorealistic rendering of metamaterials, gradient index devices, and polarization-dependent invisibility cloaks,” presented at Frontiers in Optics (Optical Society of America Annual Meeting), San Jose, California, 11–15 October, 2009.

A. J. Danner, and U. Leonhardt, “Lossless design of an Eaton lens and invisible sphere by transformation optics with no bandwidth limitation,” presented at the Conference on Lasers and Electro-optics (CLEO), Baltimore, Maryland, 1–5 June 2009.

Supplementary Material (1)

» Media 1: MOV (2885 KB)     

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Figures (3)

Fig. 1
Fig. 1

(a) Swimming pool with no water, (b) Swimming pool with normal water (n = 1.33), (c) Swimming pool demonstrating total external reflection (n = 0.9), and (d) Swimming pool with negative index water (n = −1.33) with dark lines added showing bottom inner edges of the pool.

Fig. 2
Fig. 2

(a) Ray trajectories of standard invisible sphere with no birefringence; definition of impact parameter b is shown, (b) Ray trajectories for the correct polarization of the modified dielectric invisible sphere, (c) Ray trajectories for the other polarization of the modified dielectric invisible sphere.

Fig. 3
Fig. 3

(a) Background image of Chinese Garden, Singapore, (b) Single frame of an animation of the polarization-dependent invisible sphere designed through transformation optics (Media 1).

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

n ( r ) = ( 1 3 u u ) 2 where u = ( 1 r + 1 r 2 + 1 27 ) 1 / 3
n M o d i f i e d ( R ) = n ( r ( R ) ) [ r R 0 0 0 r R 0 0 0 r R ] R φ θ
R ( r ) = 1 2 r 1 / 3 + 1 3 r 4 / 3 + 1 6 r 7 / 3

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