Abstract

We demonstrate an efficient method to design the diffractive phase element for modulating the electric field at the out-of-focus plane of a lens system by using an equivalent Fresnel diffraction in free space. In the monochromatic illumination, we show an example to certify the validity of our method experimentally. In the nonmonochromatic illumination, we theoretically display that the spectral beam splitting and highly confined intensity can be obtained simultaneously at the out-of-focus plane, which has the potential in the solar concentrating system and optical encryption.

© 2012 Optical Society of America

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References

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  1. M. A. Kutay and H. W. Ozoktas, “Optimal filtering in fractional Fourier domains,” IEEE Trans. Signal Process. 45, 1129–1143 (1997).
    [CrossRef]
  2. W. Wang and T. Li, “Design of large-caliber phase element used in ICF,” Chin. J. Lasers A 26, 395–399 (1999).
  3. T. C. Poon, ed., Digital Holography and Three-Dimensional Display (Springer, 2006).
  4. E. Buckley, “Holographic projector with one lens,” Opt. Lett. 35, 3399–3401 (2010).
    [CrossRef]
  5. A. G. Imenes and D. R. Mills, “Spectral beam splitting technology for increased conversion efficiency in solar concentrating systems: a review,” Solar Energy Mater. Solar Cells 84, 19–69 (2004).
    [CrossRef]
  6. J. Bengtsson, “Kinoforms designed to produce different fan-out patterns for two wavelengths,” Appl. Opt. 37, 2011–2020 (1998).
    [CrossRef]
  7. A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Diffractive optical tweezers in the Fresnel regime,” Opt. Express 12, 2243–2250 (2004).
    [CrossRef]
  8. Y. Ogura, N. Shirai, J. Tanida, and Y. Ichioka, “Wavelength-multiplexing diffractive phase elements: design, fabrication, and performance evaluation,” J. Opt. Soc. Am. A 18, 1082–1092 (2001).
    [CrossRef]
  9. J. W. Goodman, Introduction to Fourier Optics (Robert & Company Publishers, 2004).
  10. X. G. Deng, B. Bihari, J. H. Gan, F. Zhao, and R. T. Chen, “Fast algorithm for chirp transforms with zooming-in ability and its applications,” J. Opt. Soc. Am. A 17, 762–771 (2000).
    [CrossRef]
  11. J. Bengtsson, “Design of fan-out kinoforms in the entire scalar diffraction regime with an optimal-rotation-angle method,” Appl. Opt. 36, 8435–8444 (1997).
    [CrossRef]
  12. X. G. Deng and R. T. Chen, “Design of cascaded diffractive phase elements for three-dimensional multiwavelength optical interconnects,” Opt. Lett. 25, 1046–1048 (2000).
    [CrossRef]
  13. R. Tudela, E. Martn-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A 5, S189–S194 (2003).
    [CrossRef]
  14. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  15. M. P. Chang and O. K. Erosy, “The modified inputaoutput algorithm for the synthesis of computer generated holograms,” Optik 95, 155–160 (1994).
  16. X. G. Deng and Y. P. Li, “Phase-mixture algorithm applied to the design of pure phase elements,” Chin. J. Lasers 4, 447–454 (1995).
  17. J. Amako, H. Miura, and T. Sonehara, “Wave-front control using liquid-crystal devices,” Appl. Opt. 32, 4323–4329(1993).
    [CrossRef]
  18. H. Zhang, J. H. Xie, J. Liu, and Y. T. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48, 5834–5841 (2009).
    [CrossRef]

2010 (1)

2009 (1)

2004 (2)

A. G. Imenes and D. R. Mills, “Spectral beam splitting technology for increased conversion efficiency in solar concentrating systems: a review,” Solar Energy Mater. Solar Cells 84, 19–69 (2004).
[CrossRef]

A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Diffractive optical tweezers in the Fresnel regime,” Opt. Express 12, 2243–2250 (2004).
[CrossRef]

2003 (1)

R. Tudela, E. Martn-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A 5, S189–S194 (2003).
[CrossRef]

2001 (1)

2000 (2)

1999 (1)

W. Wang and T. Li, “Design of large-caliber phase element used in ICF,” Chin. J. Lasers A 26, 395–399 (1999).

1998 (1)

1997 (2)

M. A. Kutay and H. W. Ozoktas, “Optimal filtering in fractional Fourier domains,” IEEE Trans. Signal Process. 45, 1129–1143 (1997).
[CrossRef]

J. Bengtsson, “Design of fan-out kinoforms in the entire scalar diffraction regime with an optimal-rotation-angle method,” Appl. Opt. 36, 8435–8444 (1997).
[CrossRef]

1995 (1)

X. G. Deng and Y. P. Li, “Phase-mixture algorithm applied to the design of pure phase elements,” Chin. J. Lasers 4, 447–454 (1995).

1994 (1)

M. P. Chang and O. K. Erosy, “The modified inputaoutput algorithm for the synthesis of computer generated holograms,” Optik 95, 155–160 (1994).

1993 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Amako, J.

Bengtsson, J.

Bernet, S.

Bihari, B.

Buckley, E.

Carnicer, A.

R. Tudela, E. Martn-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A 5, S189–S194 (2003).
[CrossRef]

Chang, M. P.

M. P. Chang and O. K. Erosy, “The modified inputaoutput algorithm for the synthesis of computer generated holograms,” Optik 95, 155–160 (1994).

Chen, R. T.

Deng, X. G.

Erosy, O. K.

M. P. Chang and O. K. Erosy, “The modified inputaoutput algorithm for the synthesis of computer generated holograms,” Optik 95, 155–160 (1994).

Furhapter, S.

Gan, J. H.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Robert & Company Publishers, 2004).

Ichioka, Y.

Imenes, A. G.

A. G. Imenes and D. R. Mills, “Spectral beam splitting technology for increased conversion efficiency in solar concentrating systems: a review,” Solar Energy Mater. Solar Cells 84, 19–69 (2004).
[CrossRef]

Jesacher, A.

Juvells, I.

R. Tudela, E. Martn-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A 5, S189–S194 (2003).
[CrossRef]

Kutay, M. A.

M. A. Kutay and H. W. Ozoktas, “Optimal filtering in fractional Fourier domains,” IEEE Trans. Signal Process. 45, 1129–1143 (1997).
[CrossRef]

Labastida, I.

R. Tudela, E. Martn-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A 5, S189–S194 (2003).
[CrossRef]

Li, T.

W. Wang and T. Li, “Design of large-caliber phase element used in ICF,” Chin. J. Lasers A 26, 395–399 (1999).

Li, Y. P.

X. G. Deng and Y. P. Li, “Phase-mixture algorithm applied to the design of pure phase elements,” Chin. J. Lasers 4, 447–454 (1995).

Liu, J.

Martn-Badosa, E.

R. Tudela, E. Martn-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A 5, S189–S194 (2003).
[CrossRef]

Mills, D. R.

A. G. Imenes and D. R. Mills, “Spectral beam splitting technology for increased conversion efficiency in solar concentrating systems: a review,” Solar Energy Mater. Solar Cells 84, 19–69 (2004).
[CrossRef]

Miura, H.

Ogura, Y.

Ozoktas, H. W.

M. A. Kutay and H. W. Ozoktas, “Optimal filtering in fractional Fourier domains,” IEEE Trans. Signal Process. 45, 1129–1143 (1997).
[CrossRef]

Ritsch-Marte, M.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Shirai, N.

Sonehara, T.

Tanida, J.

Tudela, R.

R. Tudela, E. Martn-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A 5, S189–S194 (2003).
[CrossRef]

Vallmitjana, S.

R. Tudela, E. Martn-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A 5, S189–S194 (2003).
[CrossRef]

Wang, W.

W. Wang and T. Li, “Design of large-caliber phase element used in ICF,” Chin. J. Lasers A 26, 395–399 (1999).

Wang, Y. T.

Xie, J. H.

Zhang, H.

Zhao, F.

Appl. Opt. (4)

Chin. J. Lasers (1)

X. G. Deng and Y. P. Li, “Phase-mixture algorithm applied to the design of pure phase elements,” Chin. J. Lasers 4, 447–454 (1995).

Chin. J. Lasers A (1)

W. Wang and T. Li, “Design of large-caliber phase element used in ICF,” Chin. J. Lasers A 26, 395–399 (1999).

IEEE Trans. Signal Process. (1)

M. A. Kutay and H. W. Ozoktas, “Optimal filtering in fractional Fourier domains,” IEEE Trans. Signal Process. 45, 1129–1143 (1997).
[CrossRef]

J. Opt. A (1)

R. Tudela, E. Martn-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, “Full complex Fresnel holograms displayed on liquid crystal devices,” J. Opt. A 5, S189–S194 (2003).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Express (1)

Opt. Lett. (2)

Optik (2)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

M. P. Chang and O. K. Erosy, “The modified inputaoutput algorithm for the synthesis of computer generated holograms,” Optik 95, 155–160 (1994).

Solar Energy Mater. Solar Cells (1)

A. G. Imenes and D. R. Mills, “Spectral beam splitting technology for increased conversion efficiency in solar concentrating systems: a review,” Solar Energy Mater. Solar Cells 84, 19–69 (2004).
[CrossRef]

Other (2)

T. C. Poon, ed., Digital Holography and Three-Dimensional Display (Springer, 2006).

J. W. Goodman, Introduction to Fourier Optics (Robert & Company Publishers, 2004).

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Figures (3)

Fig. 1.
Fig. 1.

Schematic of modulating the electric fields by a DPE at an out-of-focus plane of a lens (a) and at a plane where z=z0 in the free space (b). The electric field of the incident light is u0(ξ,η). f is the focus of the lens. Δz is the distance between the target plane (TP) and the focal plane.

Fig. 2.
Fig. 2.

Experimental verification of the DPE design for single wavelength. (a) Experimental setup; (b) the phase profile of designed DPE. The phase in (b) is in units of radian. The simulated (c) and experimental (d) intensity (normalized) at the target plane are also given. The experimental data (d) is obtained with a charge-coupled-device (CCD) camera.

Fig. 3.
Fig. 3.

Design of DPE in the nonmonochromatic illumination. (a) Schematic of modulating the electric field by a DPE at the out-of-focus plane of a lens in the nonmonochromatic illumination. (b) The relief profile of the designed DPE. The colorbar is in units of μm. (c) The ideal intensity and position for three wavelengths at the target plane. (d) (f) The normalized intensity profiles for three wavelengths [λ1=0.5μm (d), λ2=0.8μm (e), and λ3=1.2μm (f)] at the target plane using the designed DPE in (b).

Equations (2)

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U(x,y)=eik(fΔz)iλ(fΔz)eik(x2+y2)2(fΔz)[u(ξ,η)·eik(ξ2+η2)2feik(ξ2+η2)2(fΔz)]ei2π(xξ+yη)λ(fΔz)dξdη,
U(x,y)=AfΔz{eikz0iλz0eik(x2+y2)2z0[u(ξ,η)·eik(ξ2+η2)2z0]ei2π(xξ+yη)λz0dξdη}=AfΔzFresnelT[u(ξ,η)]|z=z0,

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