Abstract

We have built microstructured sheets that rotate, on transmission, the direction of light rays by an arbitrary, but fixed, angle around the sheet normal. These ray-rotation sheets comprise two pairs of confocal lenticular arrays. In addition to rotating the direction of transmitted light rays, our sheets also offset ray position sideways on the scale of the diameter of the lenticules. If this ray offset is sufficiently small so that it cannot be resolved, our ray-rotation sheets appear to perform generalized refraction.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Full Article  |  PDF Article
OSA Recommended Articles
Imaging with parallel ray-rotation sheets

Alasdair C. Hamilton and Johannes Courtial
Opt. Express 16(25) 20826-20833 (2008)

Omnidirectional transformation-optics cloak made from lenses and glenses

Tomáš Tyc, Stephen Oxburgh, Euan N. Cowie, Gregory J. Chaplain, Gavin Macauley, Chris D. White, and Johannes Courtial
J. Opt. Soc. Am. A 33(6) 1032-1040 (2016)

Perfect imaging with planar interfaces

Stephen Oxburgh and Johannes Courtial
J. Opt. Soc. Am. A 30(11) 2334-2338 (2013)

References

  • View by:
  • |
  • |
  • |

  1. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
    [Crossref]
  2. J. Courtial and T. Tyc, “Generalised laws of refraction that can lead to wave-optically forbidden light-ray fields,” J. Opt. Soc. Am. A 29, 1407–1411 (2012).
    [Crossref]
  3. A. C. Hamilton and J. Courtial, “Metamaterials for light rays: ray optics without wave-optical analog in the ray-optics limit,” New J. Phys. 11, 013042 (2009).
    [Crossref]
  4. F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
    [Crossref]
  5. J. Courtial, “Ray-optical refraction with confocal lenslet arrays,” New J. Phys. 10, 083033 (2008).
    [Crossref]
  6. J. Courtial, B. C. Kirkpatrick, E. Logean, and T. Scharf, “Experimental demonstration of ray-optical refraction with confocal lenslet arrays,” Opt. Lett. 35, 4060–4062 (2010).
    [Crossref]
  7. A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, “Local light-ray rotation,” J. Opt. A 11, 085705 (2009).
    [Crossref]
  8. E. G. Paek, J. Y. Choe, T. K. Oh, J. H. Hong, and T. Y. Chang, “Nonmechanical image rotation with an acousto-optic dove prism,” Opt. Lett. 22, 1195–1197 (1997).
    [Crossref]
  9. Y. Yan, “Optical image rotating device used with afocal image relaying optics and laser diode array,” U.S. patent6,243,210 (June5, 2001).
  10. D. Gabor, “Improvements in or relating to optical systems composed of lenticules,” UK patent541,753 (December10, 1941).
  11. C. Hembd-Sölner, R. F. Stevens, and M. C. Hutley, “Imaging properties of the Gabor superlens,” J. Opt. A 1, 94–102 (1999).
    [Crossref]
  12. R. F. Stevens and T. G. Harvey, “Lens arrays for a three-dimensional imaging system,” J. Opt. A 4, S17–S21 (2002).
    [Crossref]
  13. X. Xiao, B. Javidi, M. Martinez-Corral, and A. Stern, “Advances in three-dimensional integral imaging: sensing, display, and applications invited,” Appl. Opt. 52, 546–560 (2013).
    [Crossref]
  14. G. Lippmann, “La photographie intégrale,” Comptes Rendus Acad. Sci. 146, 446–451 (1908).
  15. R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” (Stanford University, 2005).
  16. A. C. Hamilton and J. Courtial, “Generalized refraction using lenslet arrays,” J. Opt. A 11, 065502 (2009).
    [Crossref]
  17. J. Courtial and J. Nelson, “Ray-optical negative refraction and pseudoscopic imaging with Dove-prism arrays,” New J. Phys. 10, 023028 (2008).
    [Crossref]
  18. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [Crossref]
  19. A. C. Hamilton and J. Courtial, “Optical properties of a Dove-prism sheet,” J. Opt. A 10, 125302 (2008).
    [Crossref]
  20. B. Sundar, A. C. Hamilton, and J. Courtial, “Fermat’s principle and the formal equivalence of local light-ray rotation and refraction at the interface between homogeneous media with a complex refractive index ratio,” Opt. Lett. 34, 374–376 (2009).
    [Crossref]
  21. A. C. Hamilton, B. Sundar, and J. Courtial, “Local light-ray rotation around arbitrary axes,” J. Opt. 12, 095101 (2010).
    [Crossref]
  22. M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, “Experimental demonstration of a light-ray-direction-flipping METATOY based on confocal lenticular arrays,” Opt. Commun. 282, 4299–4302 (2009).
    [Crossref]
  23. M. C. Hutley, R. Hunt, R. F. Stevens, and P. Savander, “The moiré magnifier,” Pure Appl. Opt. 3, 133–142 (1994).
    [Crossref]
  24. J. Courtial, “Standard and non-standard metarefraction with confocal lenslet arrays,” Opt. Commun. 282, 2634–2641 (2009).
    [Crossref]
  25. T. Maceina, G. Juzeliūnas, and J. Courtial, “Quantifying metarefraction with confocal lenslet arrays,” Opt. Commun. 284, 5008–5019 (2011).
    [Crossref]
  26. M.-S. Kim, T. Scharf, S. Mühlig, M. Fruhnert, C. Rockstuhl, R. Bitterli, W. Noell, R. Voelkel, and H. P. Herzig, “Refraction limit of miniaturized optical systems: a ball-lens example,” Opt. Express 24, 6996–7005 (2016).
    [Crossref]

2016 (1)

2013 (1)

2012 (2)

J. Courtial and T. Tyc, “Generalised laws of refraction that can lead to wave-optically forbidden light-ray fields,” J. Opt. Soc. Am. A 29, 1407–1411 (2012).
[Crossref]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref]

2011 (2)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

T. Maceina, G. Juzeliūnas, and J. Courtial, “Quantifying metarefraction with confocal lenslet arrays,” Opt. Commun. 284, 5008–5019 (2011).
[Crossref]

2010 (2)

2009 (6)

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, “Experimental demonstration of a light-ray-direction-flipping METATOY based on confocal lenticular arrays,” Opt. Commun. 282, 4299–4302 (2009).
[Crossref]

A. C. Hamilton and J. Courtial, “Generalized refraction using lenslet arrays,” J. Opt. A 11, 065502 (2009).
[Crossref]

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, “Local light-ray rotation,” J. Opt. A 11, 085705 (2009).
[Crossref]

A. C. Hamilton and J. Courtial, “Metamaterials for light rays: ray optics without wave-optical analog in the ray-optics limit,” New J. Phys. 11, 013042 (2009).
[Crossref]

B. Sundar, A. C. Hamilton, and J. Courtial, “Fermat’s principle and the formal equivalence of local light-ray rotation and refraction at the interface between homogeneous media with a complex refractive index ratio,” Opt. Lett. 34, 374–376 (2009).
[Crossref]

J. Courtial, “Standard and non-standard metarefraction with confocal lenslet arrays,” Opt. Commun. 282, 2634–2641 (2009).
[Crossref]

2008 (3)

J. Courtial, “Ray-optical refraction with confocal lenslet arrays,” New J. Phys. 10, 083033 (2008).
[Crossref]

J. Courtial and J. Nelson, “Ray-optical negative refraction and pseudoscopic imaging with Dove-prism arrays,” New J. Phys. 10, 023028 (2008).
[Crossref]

A. C. Hamilton and J. Courtial, “Optical properties of a Dove-prism sheet,” J. Opt. A 10, 125302 (2008).
[Crossref]

2002 (1)

R. F. Stevens and T. G. Harvey, “Lens arrays for a three-dimensional imaging system,” J. Opt. A 4, S17–S21 (2002).
[Crossref]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref]

1999 (1)

C. Hembd-Sölner, R. F. Stevens, and M. C. Hutley, “Imaging properties of the Gabor superlens,” J. Opt. A 1, 94–102 (1999).
[Crossref]

1997 (1)

1994 (1)

M. C. Hutley, R. Hunt, R. F. Stevens, and P. Savander, “The moiré magnifier,” Pure Appl. Opt. 3, 133–142 (1994).
[Crossref]

1908 (1)

G. Lippmann, “La photographie intégrale,” Comptes Rendus Acad. Sci. 146, 446–451 (1908).

Aieta, F.

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Bitterli, R.

Blair, M.

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, “Experimental demonstration of a light-ray-direction-flipping METATOY based on confocal lenticular arrays,” Opt. Commun. 282, 4299–4302 (2009).
[Crossref]

Brédif, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” (Stanford University, 2005).

Capasso, F.

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Chang, T. Y.

Choe, J. Y.

Clark, L.

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, “Experimental demonstration of a light-ray-direction-flipping METATOY based on confocal lenticular arrays,” Opt. Commun. 282, 4299–4302 (2009).
[Crossref]

Courtial, J.

J. Courtial and T. Tyc, “Generalised laws of refraction that can lead to wave-optically forbidden light-ray fields,” J. Opt. Soc. Am. A 29, 1407–1411 (2012).
[Crossref]

T. Maceina, G. Juzeliūnas, and J. Courtial, “Quantifying metarefraction with confocal lenslet arrays,” Opt. Commun. 284, 5008–5019 (2011).
[Crossref]

J. Courtial, B. C. Kirkpatrick, E. Logean, and T. Scharf, “Experimental demonstration of ray-optical refraction with confocal lenslet arrays,” Opt. Lett. 35, 4060–4062 (2010).
[Crossref]

A. C. Hamilton, B. Sundar, and J. Courtial, “Local light-ray rotation around arbitrary axes,” J. Opt. 12, 095101 (2010).
[Crossref]

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, “Experimental demonstration of a light-ray-direction-flipping METATOY based on confocal lenticular arrays,” Opt. Commun. 282, 4299–4302 (2009).
[Crossref]

J. Courtial, “Standard and non-standard metarefraction with confocal lenslet arrays,” Opt. Commun. 282, 2634–2641 (2009).
[Crossref]

A. C. Hamilton and J. Courtial, “Metamaterials for light rays: ray optics without wave-optical analog in the ray-optics limit,” New J. Phys. 11, 013042 (2009).
[Crossref]

A. C. Hamilton and J. Courtial, “Generalized refraction using lenslet arrays,” J. Opt. A 11, 065502 (2009).
[Crossref]

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, “Local light-ray rotation,” J. Opt. A 11, 085705 (2009).
[Crossref]

B. Sundar, A. C. Hamilton, and J. Courtial, “Fermat’s principle and the formal equivalence of local light-ray rotation and refraction at the interface between homogeneous media with a complex refractive index ratio,” Opt. Lett. 34, 374–376 (2009).
[Crossref]

J. Courtial and J. Nelson, “Ray-optical negative refraction and pseudoscopic imaging with Dove-prism arrays,” New J. Phys. 10, 023028 (2008).
[Crossref]

J. Courtial, “Ray-optical refraction with confocal lenslet arrays,” New J. Phys. 10, 083033 (2008).
[Crossref]

A. C. Hamilton and J. Courtial, “Optical properties of a Dove-prism sheet,” J. Opt. A 10, 125302 (2008).
[Crossref]

Duval, G.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” (Stanford University, 2005).

Fruhnert, M.

Gabor, D.

D. Gabor, “Improvements in or relating to optical systems composed of lenticules,” UK patent541,753 (December10, 1941).

Gaburro, Z.

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Genevet, P.

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Hamilton, A. C.

A. C. Hamilton, B. Sundar, and J. Courtial, “Local light-ray rotation around arbitrary axes,” J. Opt. 12, 095101 (2010).
[Crossref]

A. C. Hamilton and J. Courtial, “Generalized refraction using lenslet arrays,” J. Opt. A 11, 065502 (2009).
[Crossref]

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, “Experimental demonstration of a light-ray-direction-flipping METATOY based on confocal lenticular arrays,” Opt. Commun. 282, 4299–4302 (2009).
[Crossref]

B. Sundar, A. C. Hamilton, and J. Courtial, “Fermat’s principle and the formal equivalence of local light-ray rotation and refraction at the interface between homogeneous media with a complex refractive index ratio,” Opt. Lett. 34, 374–376 (2009).
[Crossref]

A. C. Hamilton and J. Courtial, “Metamaterials for light rays: ray optics without wave-optical analog in the ray-optics limit,” New J. Phys. 11, 013042 (2009).
[Crossref]

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, “Local light-ray rotation,” J. Opt. A 11, 085705 (2009).
[Crossref]

A. C. Hamilton and J. Courtial, “Optical properties of a Dove-prism sheet,” J. Opt. A 10, 125302 (2008).
[Crossref]

Hanrahan, P.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” (Stanford University, 2005).

Harvey, T. G.

R. F. Stevens and T. G. Harvey, “Lens arrays for a three-dimensional imaging system,” J. Opt. A 4, S17–S21 (2002).
[Crossref]

Hembd-Sölner, C.

C. Hembd-Sölner, R. F. Stevens, and M. C. Hutley, “Imaging properties of the Gabor superlens,” J. Opt. A 1, 94–102 (1999).
[Crossref]

Herzig, H. P.

Hong, J. H.

Horowitz, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” (Stanford University, 2005).

Houston, E. A.

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, “Experimental demonstration of a light-ray-direction-flipping METATOY based on confocal lenticular arrays,” Opt. Commun. 282, 4299–4302 (2009).
[Crossref]

Hunt, R.

M. C. Hutley, R. Hunt, R. F. Stevens, and P. Savander, “The moiré magnifier,” Pure Appl. Opt. 3, 133–142 (1994).
[Crossref]

Hutley, M. C.

C. Hembd-Sölner, R. F. Stevens, and M. C. Hutley, “Imaging properties of the Gabor superlens,” J. Opt. A 1, 94–102 (1999).
[Crossref]

M. C. Hutley, R. Hunt, R. F. Stevens, and P. Savander, “The moiré magnifier,” Pure Appl. Opt. 3, 133–142 (1994).
[Crossref]

Javidi, B.

Juzeliunas, G.

T. Maceina, G. Juzeliūnas, and J. Courtial, “Quantifying metarefraction with confocal lenslet arrays,” Opt. Commun. 284, 5008–5019 (2011).
[Crossref]

Kats, M. A.

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Kim, M.-S.

Kirkpatrick, B. C.

Leach, J.

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, “Experimental demonstration of a light-ray-direction-flipping METATOY based on confocal lenticular arrays,” Opt. Commun. 282, 4299–4302 (2009).
[Crossref]

Levoy, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” (Stanford University, 2005).

Lippmann, G.

G. Lippmann, “La photographie intégrale,” Comptes Rendus Acad. Sci. 146, 446–451 (1908).

Logean, E.

Maceina, T.

T. Maceina, G. Juzeliūnas, and J. Courtial, “Quantifying metarefraction with confocal lenslet arrays,” Opt. Commun. 284, 5008–5019 (2011).
[Crossref]

Martinez-Corral, M.

Mühlig, S.

Nelson, J.

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, “Local light-ray rotation,” J. Opt. A 11, 085705 (2009).
[Crossref]

J. Courtial and J. Nelson, “Ray-optical negative refraction and pseudoscopic imaging with Dove-prism arrays,” New J. Phys. 10, 023028 (2008).
[Crossref]

Ng, R.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” (Stanford University, 2005).

Noell, W.

Oh, T. K.

Paek, E. G.

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref]

Rockstuhl, C.

Savander, P.

M. C. Hutley, R. Hunt, R. F. Stevens, and P. Savander, “The moiré magnifier,” Pure Appl. Opt. 3, 133–142 (1994).
[Crossref]

Scharf, T.

Smith, G.

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, “Experimental demonstration of a light-ray-direction-flipping METATOY based on confocal lenticular arrays,” Opt. Commun. 282, 4299–4302 (2009).
[Crossref]

Stern, A.

Stevens, R. F.

R. F. Stevens and T. G. Harvey, “Lens arrays for a three-dimensional imaging system,” J. Opt. A 4, S17–S21 (2002).
[Crossref]

C. Hembd-Sölner, R. F. Stevens, and M. C. Hutley, “Imaging properties of the Gabor superlens,” J. Opt. A 1, 94–102 (1999).
[Crossref]

M. C. Hutley, R. Hunt, R. F. Stevens, and P. Savander, “The moiré magnifier,” Pure Appl. Opt. 3, 133–142 (1994).
[Crossref]

Sundar, B.

A. C. Hamilton, B. Sundar, and J. Courtial, “Local light-ray rotation around arbitrary axes,” J. Opt. 12, 095101 (2010).
[Crossref]

B. Sundar, A. C. Hamilton, and J. Courtial, “Fermat’s principle and the formal equivalence of local light-ray rotation and refraction at the interface between homogeneous media with a complex refractive index ratio,” Opt. Lett. 34, 374–376 (2009).
[Crossref]

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, “Local light-ray rotation,” J. Opt. A 11, 085705 (2009).
[Crossref]

Tetienne, J.-P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Tyc, T.

Voelkel, R.

Xiao, X.

Yan, Y.

Y. Yan, “Optical image rotating device used with afocal image relaying optics and laser diode array,” U.S. patent6,243,210 (June5, 2001).

Yu, N.

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Appl. Opt. (1)

Comptes Rendus Acad. Sci. (1)

G. Lippmann, “La photographie intégrale,” Comptes Rendus Acad. Sci. 146, 446–451 (1908).

J. Opt. (1)

A. C. Hamilton, B. Sundar, and J. Courtial, “Local light-ray rotation around arbitrary axes,” J. Opt. 12, 095101 (2010).
[Crossref]

J. Opt. A (5)

C. Hembd-Sölner, R. F. Stevens, and M. C. Hutley, “Imaging properties of the Gabor superlens,” J. Opt. A 1, 94–102 (1999).
[Crossref]

R. F. Stevens and T. G. Harvey, “Lens arrays for a three-dimensional imaging system,” J. Opt. A 4, S17–S21 (2002).
[Crossref]

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, “Local light-ray rotation,” J. Opt. A 11, 085705 (2009).
[Crossref]

A. C. Hamilton and J. Courtial, “Generalized refraction using lenslet arrays,” J. Opt. A 11, 065502 (2009).
[Crossref]

A. C. Hamilton and J. Courtial, “Optical properties of a Dove-prism sheet,” J. Opt. A 10, 125302 (2008).
[Crossref]

J. Opt. Soc. Am. A (1)

Nano Lett. (1)

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
[Crossref]

New J. Phys. (3)

J. Courtial, “Ray-optical refraction with confocal lenslet arrays,” New J. Phys. 10, 083033 (2008).
[Crossref]

A. C. Hamilton and J. Courtial, “Metamaterials for light rays: ray optics without wave-optical analog in the ray-optics limit,” New J. Phys. 11, 013042 (2009).
[Crossref]

J. Courtial and J. Nelson, “Ray-optical negative refraction and pseudoscopic imaging with Dove-prism arrays,” New J. Phys. 10, 023028 (2008).
[Crossref]

Opt. Commun. (3)

J. Courtial, “Standard and non-standard metarefraction with confocal lenslet arrays,” Opt. Commun. 282, 2634–2641 (2009).
[Crossref]

T. Maceina, G. Juzeliūnas, and J. Courtial, “Quantifying metarefraction with confocal lenslet arrays,” Opt. Commun. 284, 5008–5019 (2011).
[Crossref]

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, “Experimental demonstration of a light-ray-direction-flipping METATOY based on confocal lenticular arrays,” Opt. Commun. 282, 4299–4302 (2009).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref]

Pure Appl. Opt. (1)

M. C. Hutley, R. Hunt, R. F. Stevens, and P. Savander, “The moiré magnifier,” Pure Appl. Opt. 3, 133–142 (1994).
[Crossref]

Science (1)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Other (3)

Y. Yan, “Optical image rotating device used with afocal image relaying optics and laser diode array,” U.S. patent6,243,210 (June5, 2001).

D. Gabor, “Improvements in or relating to optical systems composed of lenticules,” UK patent541,753 (December10, 1941).

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” (Stanford University, 2005).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1. Possible realizations of ray-flipping sheets. (a) Ray-flipping sheets were initially proposed in the form of an array of Dove prisms [19]. (b) The first experimental demonstration [22] used confocal lenticular arrays ( F is the common focal plane).
Fig. 2.
Fig. 2. Views through different ray-rotating sheets. The ray-rotation angles are (a)  0 ° (parallel ray-flipping sheets); (b)  90 ° (actually 82°; the ray-flipping sheets are rotated through 41°); (c)  180 ° (ray-flipping sheets rotated through 90°). Clearly visible imperfections include blurring and additional images [visible in (a); an additional image can be seen to the right of the main image] and light scattering [resulting in a milky appearance of the sheets, clearly visible in (b) and (c)]. The object seen through the sheets, a Rubik’s cube, is shown without a sheet in (d). Rubik’s Cube® used with permission from Rubik’s Brand Ltd.
Fig. 3.
Fig. 3. (a) Array of inclined Dove prisms and (b) displaced confocal lenticular arrays.
Fig. 4.
Fig. 4. View through a ray-rotating sheet ( α 180 ° ) from different directions. (a) was taken from a position approximately head-on. It shows the main image. (b) and (c) were taken from positions further and further to one side. In (b) a ghost image becomes visible; in (c) the main image has disappeared almost completely. Rubik’s Cube® used with permission from Rubik’s Brand Ltd.
Fig. 5.
Fig. 5. Calculation of the angle, ν , by which a point light source, L, appears rotated when it is seen through a ray-rotating sheet from eye position E. (a) Three-dimensional positions of the light source and observer relative to the ray-rotating sheet. The sheet is in the shaded plane; P is the point where the light ray from L the observer sees passes through the sheet. (b) Orthographic projection into the plane of the ray-rotation sheet, into which an Argand plane has been placed whose origin coincides with the projection of E. L , P , and E = 0 are the complex numbers that correspond to the orthographic projections of L, P, and E. [Adapted from [7], Figs. 5(a) and 5(b). © IOP Publishing. Reproduced with permission. All rights reserved.]
Fig. 6.
Fig. 6. Apparent rotation angle of a planar object when seen through a sheet that rotates light-ray rotation through α = 92 ° around the local sheet normal for different values of r . Points mark measurements, and the solid line was calculated according to Eq. (4). Insets show photos of the test pattern seen on its own (“no sheet”) and through the ray-rotating sheet for different values of z 1 . In all cases, z 2 = 50    cm . Visible imperfections include blurring and view distortion, leading to a different apparent rotation angle at different points in the photo (the error bars, which correspond to ± 0.5 ° , indicate the estimated average effect these imperfections have on the measured values).

Equations (5)

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

p 2 = p 1 z 2 z 1 exp ( i α ) .
P = L 1 + ( z 1 / z 2 ) exp ( i α ) .
P 0 = P ( α = 0 ) = L z 2 z 1 + z 2 .
ν = arg P P 0 = tan 1 ( sin α z 2 / z 1 + cos α )
| P P 0 | = | 1 + z 2 / z 1 1 + exp ( i α ) z 2 / z 1 | .

Metrics