Abstract

Building on recent work on windows that can be modeled as interfaces between materials with a complex ray-optical refractive-index ratio, we define here objects and images at complex positions. We give an example of an optical component that performs imaging between real and complex object and image positions.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. C. Hamilton and J. Courtial, New J. Phys. 11, 013042 (2009).
    [CrossRef]
  2. A. Sihvola, Metamaterials 1, 2 (2007).
  3. J. Courtial, New J. Phys. 10, 083033 (2008).
    [CrossRef]
  4. J. Courtial and J. Nelson, New J. Phys. 10, 023028 (2008).
    [CrossRef]
  5. A. C. Hamilton and J. Courtial, J. Opt. A 10, 125302 (2008).
    [CrossRef]
  6. A. C. Hamilton and J. Courtial, Opt. Express 16, 20826 (2008).
    [CrossRef]
  7. J. Courtial, Opt. Commun. 282, 2634 (2009).
    [CrossRef]
  8. A. C. Hamilton and J. Courtial, J. Opt. A 11, 065502 (2009).
    [CrossRef]
  9. A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, J. Opt. A 11, 085705 (2009).
    [CrossRef]
  10. A. C. Hamilton, B. Sundar, and J. Courtial, J. Opt. 12, 095101 (2010).
    [CrossRef]
  11. M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299 (2009).
    [CrossRef]
  12. J. Courtial, B. C. Kirkpatrick, E. Logean, and T. Scharf, Opt. Lett. 35, 4060 (2010).
    [CrossRef]
  13. J. Courtial, N. Chen, S. Ogilvie, B. C. Kirkpatrick, A. C. Hamilton, G. Gibson, T. Tyc, E. Logean, and T. Scharf, are preparing a manuscript to be titled “Experimental demonstration of windows representing complex ray-optical refractive-index interfaces.”
  14. B. Sundar, A. C. Hamilton, and J. Courtial, Opt. Lett. 34, 374 (2009).
    [CrossRef]
  15. M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1980).
  16. D. Lambert, A. C. Hamilton, G. Constable, H. Snehanshu, S. Talati, and J. Courtial, Comput. Phys. Commun. 183, 711 (2012).
    [CrossRef]

2012 (1)

D. Lambert, A. C. Hamilton, G. Constable, H. Snehanshu, S. Talati, and J. Courtial, Comput. Phys. Commun. 183, 711 (2012).
[CrossRef]

2010 (2)

A. C. Hamilton, B. Sundar, and J. Courtial, J. Opt. 12, 095101 (2010).
[CrossRef]

J. Courtial, B. C. Kirkpatrick, E. Logean, and T. Scharf, Opt. Lett. 35, 4060 (2010).
[CrossRef]

2009 (6)

B. Sundar, A. C. Hamilton, and J. Courtial, Opt. Lett. 34, 374 (2009).
[CrossRef]

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299 (2009).
[CrossRef]

A. C. Hamilton and J. Courtial, New J. Phys. 11, 013042 (2009).
[CrossRef]

J. Courtial, Opt. Commun. 282, 2634 (2009).
[CrossRef]

A. C. Hamilton and J. Courtial, J. Opt. A 11, 065502 (2009).
[CrossRef]

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, J. Opt. A 11, 085705 (2009).
[CrossRef]

2008 (4)

J. Courtial, New J. Phys. 10, 083033 (2008).
[CrossRef]

J. Courtial and J. Nelson, New J. Phys. 10, 023028 (2008).
[CrossRef]

A. C. Hamilton and J. Courtial, J. Opt. A 10, 125302 (2008).
[CrossRef]

A. C. Hamilton and J. Courtial, Opt. Express 16, 20826 (2008).
[CrossRef]

2007 (1)

A. Sihvola, Metamaterials 1, 2 (2007).

Blair, M.

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299 (2009).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1980).

Chen, N.

J. Courtial, N. Chen, S. Ogilvie, B. C. Kirkpatrick, A. C. Hamilton, G. Gibson, T. Tyc, E. Logean, and T. Scharf, are preparing a manuscript to be titled “Experimental demonstration of windows representing complex ray-optical refractive-index interfaces.”

Clark, L.

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299 (2009).
[CrossRef]

Constable, G.

D. Lambert, A. C. Hamilton, G. Constable, H. Snehanshu, S. Talati, and J. Courtial, Comput. Phys. Commun. 183, 711 (2012).
[CrossRef]

Courtial, J.

D. Lambert, A. C. Hamilton, G. Constable, H. Snehanshu, S. Talati, and J. Courtial, Comput. Phys. Commun. 183, 711 (2012).
[CrossRef]

A. C. Hamilton, B. Sundar, and J. Courtial, J. Opt. 12, 095101 (2010).
[CrossRef]

J. Courtial, B. C. Kirkpatrick, E. Logean, and T. Scharf, Opt. Lett. 35, 4060 (2010).
[CrossRef]

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299 (2009).
[CrossRef]

A. C. Hamilton and J. Courtial, New J. Phys. 11, 013042 (2009).
[CrossRef]

J. Courtial, Opt. Commun. 282, 2634 (2009).
[CrossRef]

A. C. Hamilton and J. Courtial, J. Opt. A 11, 065502 (2009).
[CrossRef]

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, J. Opt. A 11, 085705 (2009).
[CrossRef]

B. Sundar, A. C. Hamilton, and J. Courtial, Opt. Lett. 34, 374 (2009).
[CrossRef]

A. C. Hamilton and J. Courtial, Opt. Express 16, 20826 (2008).
[CrossRef]

J. Courtial, New J. Phys. 10, 083033 (2008).
[CrossRef]

J. Courtial and J. Nelson, New J. Phys. 10, 023028 (2008).
[CrossRef]

A. C. Hamilton and J. Courtial, J. Opt. A 10, 125302 (2008).
[CrossRef]

J. Courtial, N. Chen, S. Ogilvie, B. C. Kirkpatrick, A. C. Hamilton, G. Gibson, T. Tyc, E. Logean, and T. Scharf, are preparing a manuscript to be titled “Experimental demonstration of windows representing complex ray-optical refractive-index interfaces.”

Gibson, G.

J. Courtial, N. Chen, S. Ogilvie, B. C. Kirkpatrick, A. C. Hamilton, G. Gibson, T. Tyc, E. Logean, and T. Scharf, are preparing a manuscript to be titled “Experimental demonstration of windows representing complex ray-optical refractive-index interfaces.”

Hamilton, A. C.

D. Lambert, A. C. Hamilton, G. Constable, H. Snehanshu, S. Talati, and J. Courtial, Comput. Phys. Commun. 183, 711 (2012).
[CrossRef]

A. C. Hamilton, B. Sundar, and J. Courtial, J. Opt. 12, 095101 (2010).
[CrossRef]

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, J. Opt. A 11, 085705 (2009).
[CrossRef]

A. C. Hamilton and J. Courtial, J. Opt. A 11, 065502 (2009).
[CrossRef]

A. C. Hamilton and J. Courtial, New J. Phys. 11, 013042 (2009).
[CrossRef]

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299 (2009).
[CrossRef]

B. Sundar, A. C. Hamilton, and J. Courtial, Opt. Lett. 34, 374 (2009).
[CrossRef]

A. C. Hamilton and J. Courtial, J. Opt. A 10, 125302 (2008).
[CrossRef]

A. C. Hamilton and J. Courtial, Opt. Express 16, 20826 (2008).
[CrossRef]

J. Courtial, N. Chen, S. Ogilvie, B. C. Kirkpatrick, A. C. Hamilton, G. Gibson, T. Tyc, E. Logean, and T. Scharf, are preparing a manuscript to be titled “Experimental demonstration of windows representing complex ray-optical refractive-index interfaces.”

Houston, E. A.

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299 (2009).
[CrossRef]

Kirkpatrick, B. C.

J. Courtial, B. C. Kirkpatrick, E. Logean, and T. Scharf, Opt. Lett. 35, 4060 (2010).
[CrossRef]

J. Courtial, N. Chen, S. Ogilvie, B. C. Kirkpatrick, A. C. Hamilton, G. Gibson, T. Tyc, E. Logean, and T. Scharf, are preparing a manuscript to be titled “Experimental demonstration of windows representing complex ray-optical refractive-index interfaces.”

Lambert, D.

D. Lambert, A. C. Hamilton, G. Constable, H. Snehanshu, S. Talati, and J. Courtial, Comput. Phys. Commun. 183, 711 (2012).
[CrossRef]

Leach, J.

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299 (2009).
[CrossRef]

Logean, E.

J. Courtial, B. C. Kirkpatrick, E. Logean, and T. Scharf, Opt. Lett. 35, 4060 (2010).
[CrossRef]

J. Courtial, N. Chen, S. Ogilvie, B. C. Kirkpatrick, A. C. Hamilton, G. Gibson, T. Tyc, E. Logean, and T. Scharf, are preparing a manuscript to be titled “Experimental demonstration of windows representing complex ray-optical refractive-index interfaces.”

Nelson, J.

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, J. Opt. A 11, 085705 (2009).
[CrossRef]

J. Courtial and J. Nelson, New J. Phys. 10, 023028 (2008).
[CrossRef]

Ogilvie, S.

J. Courtial, N. Chen, S. Ogilvie, B. C. Kirkpatrick, A. C. Hamilton, G. Gibson, T. Tyc, E. Logean, and T. Scharf, are preparing a manuscript to be titled “Experimental demonstration of windows representing complex ray-optical refractive-index interfaces.”

Scharf, T.

J. Courtial, B. C. Kirkpatrick, E. Logean, and T. Scharf, Opt. Lett. 35, 4060 (2010).
[CrossRef]

J. Courtial, N. Chen, S. Ogilvie, B. C. Kirkpatrick, A. C. Hamilton, G. Gibson, T. Tyc, E. Logean, and T. Scharf, are preparing a manuscript to be titled “Experimental demonstration of windows representing complex ray-optical refractive-index interfaces.”

Sihvola, A.

A. Sihvola, Metamaterials 1, 2 (2007).

Smith, G.

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299 (2009).
[CrossRef]

Snehanshu, H.

D. Lambert, A. C. Hamilton, G. Constable, H. Snehanshu, S. Talati, and J. Courtial, Comput. Phys. Commun. 183, 711 (2012).
[CrossRef]

Sundar, B.

A. C. Hamilton, B. Sundar, and J. Courtial, J. Opt. 12, 095101 (2010).
[CrossRef]

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, J. Opt. A 11, 085705 (2009).
[CrossRef]

B. Sundar, A. C. Hamilton, and J. Courtial, Opt. Lett. 34, 374 (2009).
[CrossRef]

Talati, S.

D. Lambert, A. C. Hamilton, G. Constable, H. Snehanshu, S. Talati, and J. Courtial, Comput. Phys. Commun. 183, 711 (2012).
[CrossRef]

Tyc, T.

J. Courtial, N. Chen, S. Ogilvie, B. C. Kirkpatrick, A. C. Hamilton, G. Gibson, T. Tyc, E. Logean, and T. Scharf, are preparing a manuscript to be titled “Experimental demonstration of windows representing complex ray-optical refractive-index interfaces.”

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1980).

Comput. Phys. Commun. (1)

D. Lambert, A. C. Hamilton, G. Constable, H. Snehanshu, S. Talati, and J. Courtial, Comput. Phys. Commun. 183, 711 (2012).
[CrossRef]

J. Opt. (1)

A. C. Hamilton, B. Sundar, and J. Courtial, J. Opt. 12, 095101 (2010).
[CrossRef]

J. Opt. A (3)

A. C. Hamilton and J. Courtial, J. Opt. A 10, 125302 (2008).
[CrossRef]

A. C. Hamilton and J. Courtial, J. Opt. A 11, 065502 (2009).
[CrossRef]

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, J. Opt. A 11, 085705 (2009).
[CrossRef]

Metamaterials (1)

A. Sihvola, Metamaterials 1, 2 (2007).

New J. Phys. (3)

J. Courtial, New J. Phys. 10, 083033 (2008).
[CrossRef]

J. Courtial and J. Nelson, New J. Phys. 10, 023028 (2008).
[CrossRef]

A. C. Hamilton and J. Courtial, New J. Phys. 11, 013042 (2009).
[CrossRef]

Opt. Commun. (2)

J. Courtial, Opt. Commun. 282, 2634 (2009).
[CrossRef]

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Other (2)

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1980).

J. Courtial, N. Chen, S. Ogilvie, B. C. Kirkpatrick, A. C. Hamilton, G. Gibson, T. Tyc, E. Logean, and T. Scharf, are preparing a manuscript to be titled “Experimental demonstration of windows representing complex ray-optical refractive-index interfaces.”

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 (2)

Fig. 1.
Fig. 1.

Transformation of a ray cone originating from a point light source at P into a ray hyperboloid by passage through a ray-rotating window, for different ray-rotation angles, α. Light-ray trajectories are shown as cylinders. After transmission through the window, the rays lie on the surface of hyperboloids. For α=90°, the hyperboloid’s waist plane coincides with the window plane. For α=180°, the hyperboloid is degenerate: a cone. The images were created using the ray-tracing software TIM (The Interactive METATOY) [16].

Fig. 2.
Fig. 2.

Transformation of one ray hyperboloid into another by transmission through a window that rotates ray direction through an angle α around the window normal. (a) 3D view of 30 rays (cylinders). (b) Orthographic projection of a representative ray (thick arrows) into the window plane. A, P, P, and I are, respectively, the projections of the axis common to both hyperboloids, of the centers of the two hyperboloids, and of the point where the ray intersects the window. zr is the distance of P in front of the window, and zr is the distance of P behind the window. θ is the angle between the incident light ray and the window normal, which is also the angle between the outgoing light ray and the window normal (as the ray-rotation axis is a window normal). d and d are the skirt radii of the two hyperboloids.

Equations (10)

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

ZP=zrtanθid,ZP=exp(iα)(zrtanθ+id).
zridtanθ=exp(iα)(zr+idtanθ).
z=zr+idtanθ,z=zr+idtanθ.
z=exp(iα)z*.
z=ssinβsin(α+β)
z1=exp(iα)ssinβsin(α+β).
z2=sz1*=exp(iβ)ssinαsin(α+β)
z=ssinαsin(α+β)
exp(iα)=n1n2.
z=n2n1z*.

Metrics