Abstract

Space-variant Pancharatnam–Berry phase optical elements based on computer-generated subwavelength gratings are presented. By continuously controlling the local orientation and period of the grating we can achieve any desired phase element. We present a theoretical analysis and experimentally demonstrate a Pancharatnam–Berry phase-based diffraction grating for laser radiation at a wavelength of 10.6 µm.

© 2002 Optical Society of America

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References

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  1. S. Pancharatnam, Proc. Indian Acad. Sci. Sect. A 44, 247 (1956).
  2. M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
    [CrossRef]
  3. R. Simon, H. J. Kimble, and E. C. G. Sudharshan, Phys. Rev. Lett. 61, 19 (1988).
    [CrossRef] [PubMed]
  4. P. G. Kwiat and R. Y. Chiao, Phys. Rev. Lett. 66, 588 (1991).
    [CrossRef] [PubMed]
  5. Z. Bomzon, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 79, 1587 (2001).
    [CrossRef]
  6. Z. Bomzon, V. Kleiner, and E. Hasman, Opt. Lett. 26, 1424 (2001).
    [CrossRef]
  7. R. Bhandari, Phys. Rep. 281, 1 (1997).
    [CrossRef]
  8. F. Gori, Opt. Lett. 24, 584 (1999).
    [CrossRef]
  9. C. R. Fernández-Pousa, I. Moreno, J. A. Davis, and J. Adachi, Opt. Lett. 26, 1651 (2001).
    [CrossRef]
  10. J. Tervo and J. Turunen, Opt. Lett. 25, 785 (2000).
    [CrossRef]
  11. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 27, 188 (2002).
    [CrossRef]
  12. Z. Bomzon, V. Kleiner, and E. Hasman, Opt. Lett. 26, 33 (2001).
    [CrossRef]
  13. Z. Bomzon, V. Kleiner, and E. Hasman, Opt. Commun. 192, 169 (2001).
    [CrossRef]

2002

2001

2000

1999

1997

R. Bhandari, Phys. Rep. 281, 1 (1997).
[CrossRef]

1991

P. G. Kwiat and R. Y. Chiao, Phys. Rev. Lett. 66, 588 (1991).
[CrossRef] [PubMed]

1988

R. Simon, H. J. Kimble, and E. C. G. Sudharshan, Phys. Rev. Lett. 61, 19 (1988).
[CrossRef] [PubMed]

1984

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

1956

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

Adachi, J.

Berry, M. V.

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

Bhandari, R.

R. Bhandari, Phys. Rep. 281, 1 (1997).
[CrossRef]

Biener, G.

Bomzon, Z.

Chiao, R. Y.

P. G. Kwiat and R. Y. Chiao, Phys. Rev. Lett. 66, 588 (1991).
[CrossRef] [PubMed]

Davis, J. A.

Fernández-Pousa, C. R.

Gori, F.

Hasman, E.

Kimble, H. J.

R. Simon, H. J. Kimble, and E. C. G. Sudharshan, Phys. Rev. Lett. 61, 19 (1988).
[CrossRef] [PubMed]

Kleiner, V.

Kwiat, P. G.

P. G. Kwiat and R. Y. Chiao, Phys. Rev. Lett. 66, 588 (1991).
[CrossRef] [PubMed]

Moreno, I.

Pancharatnam, S.

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

Simon, R.

R. Simon, H. J. Kimble, and E. C. G. Sudharshan, Phys. Rev. Lett. 61, 19 (1988).
[CrossRef] [PubMed]

Sudharshan, E. C. G.

R. Simon, H. J. Kimble, and E. C. G. Sudharshan, Phys. Rev. Lett. 61, 19 (1988).
[CrossRef] [PubMed]

Tervo, J.

Turunen, J.

Appl. Phys. Lett.

Z. Bomzon, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 79, 1587 (2001).
[CrossRef]

Opt. Commun.

Z. Bomzon, V. Kleiner, and E. Hasman, Opt. Commun. 192, 169 (2001).
[CrossRef]

Opt. Lett.

Phys. Rep.

R. Bhandari, Phys. Rep. 281, 1 (1997).
[CrossRef]

Phys. Rev. Lett.

R. Simon, H. J. Kimble, and E. C. G. Sudharshan, Phys. Rev. Lett. 61, 19 (1988).
[CrossRef] [PubMed]

P. G. Kwiat and R. Y. Chiao, Phys. Rev. Lett. 66, 588 (1991).
[CrossRef] [PubMed]

Proc. Indian Acad. Sci. Sect. A

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

Proc. R. Soc. London Ser. A

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

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Figures (3)

Fig. 1
Fig. 1

Illustration of the principle of PBOEs by use of the Poincaré sphere.

Fig. 2
Fig. 2

Geometry of the space-variant subwavelength grating as well as the DGPs for incident |R and |L polarizations.

Fig. 3
Fig. 3

Measurements of the transmitted far field for the subwavelength PBOE grating when the retardation is ϕ=π/2 and ϕ=π, respectively, for incident (a) circular left, (b) circular right, (c) linear polarizations.

Equations (6)

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

Tx,y=Rθx,yJϕR-1θx,y,
Tx,y=cosϕ/21001-i sinϕ/2×0expi2θx,yexp-i2θx,y0.
E0=Tx,yEi=cosϕ/2Ei-i sinϕ/2×[Ei|Rexp-i2θ|L+Ei|Lexpi2θ|R].
φpx,y=-θ+arctancos ϕtan θ=-θ+arctansin2χtan θ,
Kg=K0x,ycosφdx,y/2xˆ+sinφdx,y/2yˆ,
Kg=2π/Λ0exp-πy/dcosπx/dxˆ-sinπx/dyˆ,

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