Abstract

An optical encryption method based on a geometrical phase produced by space-variant polarization manipulation is presented. The decrypted picture is retrieved either by a polarization measurement of the beam emerging from the encrypted element or by a single intensity measurement of the beam transmitted through the encrypted element followed by an optical key element. Both elements are realized by use of computer-generated space-variant subwavelength dielectric gratings. Theoretical analyses of the optical concept are presented along with experimental results.

© 2005 Optical Society of America

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References

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  1. P. Refregier and B. Javidi, Opt. Lett. 20, 767 (1995).
    [Crossref] [PubMed]
  2. N. Towghi, B. Javidi, and Z. Luo, J. Opt. Soc. Am. A 16, 1915 (1999).
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  3. P. C. Mogensen and J. Glückstad, Opt. Commun. 173, 177 (2000).
    [Crossref]
  4. G. Unnikrishnan, M. Pohit, and K. Singh, Opt. Commun. 185, 25 (2000).
    [Crossref]
  5. S. Pancharatnam, Proc. Indian Acad. Sci. Sect. A 44, 247 (1956).
  6. M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
    [Crossref]
  7. A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
    [Crossref] [PubMed]
  8. E. Hasman, V. Kleiner, G. Biener, and A. Niv, Appl. Phys. Lett. 82, 328 (2003).
    [Crossref]
  9. E. Hasman, G. Biener, A. Niv, and V. Kleiner, Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, to be published), Vol. 47.
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    [Crossref]

2004 (1)

2003 (1)

E. Hasman, V. Kleiner, G. Biener, and A. Niv, Appl. Phys. Lett. 82, 328 (2003).
[Crossref]

2000 (2)

P. C. Mogensen and J. Glückstad, Opt. Commun. 173, 177 (2000).
[Crossref]

G. Unnikrishnan, M. Pohit, and K. Singh, Opt. Commun. 185, 25 (2000).
[Crossref]

1999 (1)

1995 (1)

1994 (1)

B. Javidi and J. L. Horner, Opt. Eng. 33, 1752 (1994).
[Crossref]

1984 (1)

M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[Crossref]

1956 (1)

S. Pancharatnam, Proc. Indian Acad. Sci. Sect. A 44, 247 (1956).

Berry, M. V.

M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[Crossref]

Biener, G.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
[Crossref] [PubMed]

E. Hasman, V. Kleiner, G. Biener, and A. Niv, Appl. Phys. Lett. 82, 328 (2003).
[Crossref]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, to be published), Vol. 47.

Glückstad, J.

P. C. Mogensen and J. Glückstad, Opt. Commun. 173, 177 (2000).
[Crossref]

Hasman, E.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
[Crossref] [PubMed]

E. Hasman, V. Kleiner, G. Biener, and A. Niv, Appl. Phys. Lett. 82, 328 (2003).
[Crossref]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, to be published), Vol. 47.

Horner, J. L.

B. Javidi and J. L. Horner, Opt. Eng. 33, 1752 (1994).
[Crossref]

Javidi, B.

Kleiner, V.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
[Crossref] [PubMed]

E. Hasman, V. Kleiner, G. Biener, and A. Niv, Appl. Phys. Lett. 82, 328 (2003).
[Crossref]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, to be published), Vol. 47.

Luo, Z.

Mogensen, P. C.

P. C. Mogensen and J. Glückstad, Opt. Commun. 173, 177 (2000).
[Crossref]

Niv, A.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
[Crossref] [PubMed]

E. Hasman, V. Kleiner, G. Biener, and A. Niv, Appl. Phys. Lett. 82, 328 (2003).
[Crossref]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, to be published), Vol. 47.

Pancharatnam, S.

S. Pancharatnam, Proc. Indian Acad. Sci. Sect. A 44, 247 (1956).

Pohit, M.

G. Unnikrishnan, M. Pohit, and K. Singh, Opt. Commun. 185, 25 (2000).
[Crossref]

Refregier, P.

Singh, K.

G. Unnikrishnan, M. Pohit, and K. Singh, Opt. Commun. 185, 25 (2000).
[Crossref]

Towghi, N.

Unnikrishnan, G.

G. Unnikrishnan, M. Pohit, and K. Singh, Opt. Commun. 185, 25 (2000).
[Crossref]

Appl. Phys. Lett. (1)

E. Hasman, V. Kleiner, G. Biener, and A. Niv, Appl. Phys. Lett. 82, 328 (2003).
[Crossref]

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

Opt. Commun. (2)

P. C. Mogensen and J. Glückstad, Opt. Commun. 173, 177 (2000).
[Crossref]

G. Unnikrishnan, M. Pohit, and K. Singh, Opt. Commun. 185, 25 (2000).
[Crossref]

Opt. Eng. (1)

B. Javidi and J. L. Horner, Opt. Eng. 33, 1752 (1994).
[Crossref]

Opt. Lett. (2)

Proc. Indian Acad. Sci. Sect. A (1)

S. Pancharatnam, Proc. Indian Acad. Sci. Sect. A 44, 247 (1956).

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

M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[Crossref]

Other (1)

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, to be published), Vol. 47.

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic representation of the concept of geometrical phase encryption. (b) Primary image intensity to be encrypted. (c) SWG mask of the central region of the SWG. (d) The wave plate’s orientation function, θ k , of the key element is shown in grayscale. (e) Measured polarization state of the beam emerging from the encrypted element taken from the central region. (f) Scanning electron microscope image of the encrypted element taken from a small region in the element.

Fig. 2
Fig. 2

(a)–(c) Three pictures of the measured intensity obtained by the decryption process with the polarizer in varying orientations: (a) 0°, (b) 45°, and (c) 90°. The white arrows indicate the orientation angle of the polarizer. (d) Decrypted image achieved by the decryption process using the intensities shown in (a)–(c).

Fig. 3
Fig. 3

(a) Wrong geometrical phase key. (b) White noise decrypted image that resulted from using the key depicted in (a).

Fig. 4
Fig. 4

Optical decryption setup comprising the encrypted and key elements. The telescope between the two elements is used to image the complex amplitude of the beam emerging from the encrypted element onto the key element. The beam emerging from the key is transmitted through a circular polarizer and then imaged onto a camera. The inset represents the experimental result of the optical decryption.

Equations (7)

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T C = R 1 [ θ ( x , y ) ] W R [ θ ( x , y ) ] .
T ( x , y ) = t x + t y exp ( i ϕ ) 2 [ 1 0 0 1 ] + t x t y exp ( i ϕ ) 2 { 0 exp [ i 2 θ ( x , y ) ] exp [ i 2 θ ( x , y ) ] 0 } ,
E out = η R R + η L exp [ i 2 θ ( x , y ) ] L ,
S 0 = E out R 2 + E out L 2 ,
S 1 = 2 Re { E out R L E out } ,
S 2 = 2 Im { E out R L E out } ,
φ i = arctan ( S 2 S 1 ) arg { η R η L * } φ k ,

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