Abstract

We report on an experimental realization of polarization-holographic optical elements (PHOEs) for laser beam shaping. The PHOEs were written into an azobenzene polymer layer by illumination with linearly polarized, focused light with spatially varying orientation. We propose a noniterative design method for the calculation of PHOEs that transform laser beams into arbitrary rotationally symmetric or separable intensity distributions such as flattop or ring profiles. The experimentally observed intensity distributions are compared with those predicted by numerical simulations based on the Fresnel diffraction approximation. Diffraction efficiencies up to 79% were determined experimentally.

© 2009 Optical Society of America

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References

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  1. A. J. Caley, M. J. Thomson, J. Liu, A. J. Waddie, and M. R. Taghizadeh, “Diffractive optical elements for high gain lasers with arbitrary output beam profiles,” Opt. Express 15, 10699-10704 (2007).
    [CrossRef] [PubMed]
  2. H. Aagedal, M. Schmid, S. Egner, J. Müller-Quade, T. Beth, and F. Wyrowski, “Analytical beam shaping with application to laser-diode array,” J. Opt. Soc. Am. A 14, 1549-1553 (1997).
    [CrossRef]
  3. M. Fratz, D. Eberhard, W. J. Riedel, and D. Giel, “Direct laser-writing of diffractive optical elements in photopolymer layers,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (Optical Society of America, 2008), paper DWB7.
  4. M. Fratz, D. M. Giel, and P. Fischer, “Digital polarization holograms with defined magnitude and orientation of each pixel's birefringence,” Opt. Lett. 34, 1270-1272 (2009).
    [CrossRef] [PubMed]
  5. J. Tervo and J. Turunen, “Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings,” Opt. Lett. 25, 785-786 (2000).
    [CrossRef]
  6. L. Nikolova, and T. Todorov, “Diffraction efficiency and selectivity of polarization holographic recording,” Opt. Acta 31, 579-588 (1984).
    [CrossRef]
  7. E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328-330(2003).
    [CrossRef]
  8. S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. Indian Acad. Sci. A 44, 247-262(1956).
  9. T. Kreis, Handbook of Holographic Interferometry (Wiley, 2004).
    [CrossRef]
  10. R. G. Dorsch, A. W. Lohmann, and S. Sinzinger, “Fresnel ping-pong algorithm for two-plane computer-generated hologram display,” Appl. Opt. 33, 869-875 (1994).
    [CrossRef] [PubMed]
  11. R. Wu, F. Shu, W. Zhang, X. Zhang, and Y. Li, “Extended algorithm for the design of diffractive optical elements around the focal plane,” Appl. Opt. 46, 5779-5783 (2007).
    [CrossRef] [PubMed]
  12. R. El-Agmy, H. Bulte, A. H. Greenaway, and D. Reid, “Adaptive beam profile control using a simulated annealing algorithm,” Opt. Express 13, 6085-6091 (2005).
    [CrossRef] [PubMed]
  13. O. Bryngdahl, “Optical map transformations,” Opt. Commun. 10, 164-168 (1974).
    [CrossRef]
  14. W. Singer, M. Trotzeck, and H. Gross, Handbook of Optical Systems. Volume 2: Physical Image Formation (Wiley, 2005).
  15. I. Mancheva, E. Nacheva, T. Petrova, N. Tomova, V. Dragostinova, T. Todorov, and L. Nikolova, “Light-controlled polarization switches in azobenzene-containing polymers,” Proc. SPIE 5226, 199-203 (2003).
    [CrossRef]
  16. D. Rais, Y. Zakrevsky, J. Stumpe, S. Nešpůrek, and Z. Sedláková, “Photoorientation of azobenzene side groups in a liquid-crystalline polybutadiene-based polymer,” Opt. Mater. 30, 1335-1342 (2008).
    [CrossRef]
  17. Y. Sabi, M. Yamamoto, H. Watanabe, T. Bieringer, D. Haarer, R. Hagen, S. Kostromine, and H. Berneth, “Photoaddressable polymers for rewritable optical disc systems,” Jpn. J. Appl. Phys. 40, 1613-1618 (2001).
    [CrossRef]
  18. P. Várhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lőrincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397-402 (2003).
    [CrossRef]
  19. H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, Y. Wang, H. Ming, and Z. Zheng, “Transparent electro-optic ceramics and devices,” Proc. SPIE 5644, 380-394 (2005).
    [CrossRef]

2009 (1)

2008 (1)

D. Rais, Y. Zakrevsky, J. Stumpe, S. Nešpůrek, and Z. Sedláková, “Photoorientation of azobenzene side groups in a liquid-crystalline polybutadiene-based polymer,” Opt. Mater. 30, 1335-1342 (2008).
[CrossRef]

2007 (2)

2005 (2)

R. El-Agmy, H. Bulte, A. H. Greenaway, and D. Reid, “Adaptive beam profile control using a simulated annealing algorithm,” Opt. Express 13, 6085-6091 (2005).
[CrossRef] [PubMed]

H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, Y. Wang, H. Ming, and Z. Zheng, “Transparent electro-optic ceramics and devices,” Proc. SPIE 5644, 380-394 (2005).
[CrossRef]

2003 (3)

P. Várhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lőrincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

I. Mancheva, E. Nacheva, T. Petrova, N. Tomova, V. Dragostinova, T. Todorov, and L. Nikolova, “Light-controlled polarization switches in azobenzene-containing polymers,” Proc. SPIE 5226, 199-203 (2003).
[CrossRef]

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328-330(2003).
[CrossRef]

2001 (1)

Y. Sabi, M. Yamamoto, H. Watanabe, T. Bieringer, D. Haarer, R. Hagen, S. Kostromine, and H. Berneth, “Photoaddressable polymers for rewritable optical disc systems,” Jpn. J. Appl. Phys. 40, 1613-1618 (2001).
[CrossRef]

2000 (1)

1997 (1)

1994 (1)

1984 (1)

L. Nikolova, and T. Todorov, “Diffraction efficiency and selectivity of polarization holographic recording,” Opt. Acta 31, 579-588 (1984).
[CrossRef]

1974 (1)

O. Bryngdahl, “Optical map transformations,” Opt. Commun. 10, 164-168 (1974).
[CrossRef]

1956 (1)

S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. Indian Acad. Sci. A 44, 247-262(1956).

Aagedal, H.

Berneth, H.

Y. Sabi, M. Yamamoto, H. Watanabe, T. Bieringer, D. Haarer, R. Hagen, S. Kostromine, and H. Berneth, “Photoaddressable polymers for rewritable optical disc systems,” Jpn. J. Appl. Phys. 40, 1613-1618 (2001).
[CrossRef]

Beth, T.

Biener, G.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328-330(2003).
[CrossRef]

Bieringer, T.

Y. Sabi, M. Yamamoto, H. Watanabe, T. Bieringer, D. Haarer, R. Hagen, S. Kostromine, and H. Berneth, “Photoaddressable polymers for rewritable optical disc systems,” Jpn. J. Appl. Phys. 40, 1613-1618 (2001).
[CrossRef]

Bryngdahl, O.

O. Bryngdahl, “Optical map transformations,” Opt. Commun. 10, 164-168 (1974).
[CrossRef]

Bulte, H.

Caley, A. J.

Chen, Q.

H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, Y. Wang, H. Ming, and Z. Zheng, “Transparent electro-optic ceramics and devices,” Proc. SPIE 5644, 380-394 (2005).
[CrossRef]

Dorsch, R. G.

Dragostinova, V.

I. Mancheva, E. Nacheva, T. Petrova, N. Tomova, V. Dragostinova, T. Todorov, and L. Nikolova, “Light-controlled polarization switches in azobenzene-containing polymers,” Proc. SPIE 5226, 199-203 (2003).
[CrossRef]

Eberhard, D.

M. Fratz, D. Eberhard, W. J. Riedel, and D. Giel, “Direct laser-writing of diffractive optical elements in photopolymer layers,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (Optical Society of America, 2008), paper DWB7.

Egner, S.

El-Agmy, R.

Fischer, P.

Fratz, M.

M. Fratz, D. M. Giel, and P. Fischer, “Digital polarization holograms with defined magnitude and orientation of each pixel's birefringence,” Opt. Lett. 34, 1270-1272 (2009).
[CrossRef] [PubMed]

M. Fratz, D. Eberhard, W. J. Riedel, and D. Giel, “Direct laser-writing of diffractive optical elements in photopolymer layers,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (Optical Society of America, 2008), paper DWB7.

Giel, D.

M. Fratz, D. Eberhard, W. J. Riedel, and D. Giel, “Direct laser-writing of diffractive optical elements in photopolymer layers,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (Optical Society of America, 2008), paper DWB7.

Giel, D. M.

Greenaway, A. H.

Gross, H.

W. Singer, M. Trotzeck, and H. Gross, Handbook of Optical Systems. Volume 2: Physical Image Formation (Wiley, 2005).

Haarer, D.

Y. Sabi, M. Yamamoto, H. Watanabe, T. Bieringer, D. Haarer, R. Hagen, S. Kostromine, and H. Berneth, “Photoaddressable polymers for rewritable optical disc systems,” Jpn. J. Appl. Phys. 40, 1613-1618 (2001).
[CrossRef]

Hagen, R.

Y. Sabi, M. Yamamoto, H. Watanabe, T. Bieringer, D. Haarer, R. Hagen, S. Kostromine, and H. Berneth, “Photoaddressable polymers for rewritable optical disc systems,” Jpn. J. Appl. Phys. 40, 1613-1618 (2001).
[CrossRef]

Hasman, E.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328-330(2003).
[CrossRef]

Jiang, H.

H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, Y. Wang, H. Ming, and Z. Zheng, “Transparent electro-optic ceramics and devices,” Proc. SPIE 5644, 380-394 (2005).
[CrossRef]

Kerekes, A.

P. Várhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lőrincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

Kleiner, V.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328-330(2003).
[CrossRef]

Koppa, P.

P. Várhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lőrincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

Kostromine, S.

Y. Sabi, M. Yamamoto, H. Watanabe, T. Bieringer, D. Haarer, R. Hagen, S. Kostromine, and H. Berneth, “Photoaddressable polymers for rewritable optical disc systems,” Jpn. J. Appl. Phys. 40, 1613-1618 (2001).
[CrossRef]

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry (Wiley, 2004).
[CrossRef]

Li, K. K.

H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, Y. Wang, H. Ming, and Z. Zheng, “Transparent electro-optic ceramics and devices,” Proc. SPIE 5644, 380-394 (2005).
[CrossRef]

Li, Y.

Liu, J.

Lohmann, A. W.

Lorincz, E.

P. Várhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lőrincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

Mancheva, I.

I. Mancheva, E. Nacheva, T. Petrova, N. Tomova, V. Dragostinova, T. Todorov, and L. Nikolova, “Light-controlled polarization switches in azobenzene-containing polymers,” Proc. SPIE 5226, 199-203 (2003).
[CrossRef]

Ming, H.

H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, Y. Wang, H. Ming, and Z. Zheng, “Transparent electro-optic ceramics and devices,” Proc. SPIE 5644, 380-394 (2005).
[CrossRef]

Müller-Quade, J.

Nacheva, E.

I. Mancheva, E. Nacheva, T. Petrova, N. Tomova, V. Dragostinova, T. Todorov, and L. Nikolova, “Light-controlled polarization switches in azobenzene-containing polymers,” Proc. SPIE 5226, 199-203 (2003).
[CrossRef]

Nešpurek, S.

D. Rais, Y. Zakrevsky, J. Stumpe, S. Nešpůrek, and Z. Sedláková, “Photoorientation of azobenzene side groups in a liquid-crystalline polybutadiene-based polymer,” Opt. Mater. 30, 1335-1342 (2008).
[CrossRef]

Nikolova, L.

I. Mancheva, E. Nacheva, T. Petrova, N. Tomova, V. Dragostinova, T. Todorov, and L. Nikolova, “Light-controlled polarization switches in azobenzene-containing polymers,” Proc. SPIE 5226, 199-203 (2003).
[CrossRef]

L. Nikolova, and T. Todorov, “Diffraction efficiency and selectivity of polarization holographic recording,” Opt. Acta 31, 579-588 (1984).
[CrossRef]

Niv, A.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328-330(2003).
[CrossRef]

Pancharatnam, S.

S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. Indian Acad. Sci. A 44, 247-262(1956).

Petrova, T.

I. Mancheva, E. Nacheva, T. Petrova, N. Tomova, V. Dragostinova, T. Todorov, and L. Nikolova, “Light-controlled polarization switches in azobenzene-containing polymers,” Proc. SPIE 5226, 199-203 (2003).
[CrossRef]

Rais, D.

D. Rais, Y. Zakrevsky, J. Stumpe, S. Nešpůrek, and Z. Sedláková, “Photoorientation of azobenzene side groups in a liquid-crystalline polybutadiene-based polymer,” Opt. Mater. 30, 1335-1342 (2008).
[CrossRef]

Reid, D.

Riedel, W. J.

M. Fratz, D. Eberhard, W. J. Riedel, and D. Giel, “Direct laser-writing of diffractive optical elements in photopolymer layers,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (Optical Society of America, 2008), paper DWB7.

Sabi, Y.

Y. Sabi, M. Yamamoto, H. Watanabe, T. Bieringer, D. Haarer, R. Hagen, S. Kostromine, and H. Berneth, “Photoaddressable polymers for rewritable optical disc systems,” Jpn. J. Appl. Phys. 40, 1613-1618 (2001).
[CrossRef]

Sajti, S.

P. Várhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lőrincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

Schmid, M.

Sedláková, Z.

D. Rais, Y. Zakrevsky, J. Stumpe, S. Nešpůrek, and Z. Sedláková, “Photoorientation of azobenzene side groups in a liquid-crystalline polybutadiene-based polymer,” Opt. Mater. 30, 1335-1342 (2008).
[CrossRef]

Shu, F.

Singer, W.

W. Singer, M. Trotzeck, and H. Gross, Handbook of Optical Systems. Volume 2: Physical Image Formation (Wiley, 2005).

Sinzinger, S.

Stumpe, J.

D. Rais, Y. Zakrevsky, J. Stumpe, S. Nešpůrek, and Z. Sedláková, “Photoorientation of azobenzene side groups in a liquid-crystalline polybutadiene-based polymer,” Opt. Mater. 30, 1335-1342 (2008).
[CrossRef]

Szarvas, G.

P. Várhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lőrincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

Taghizadeh, M. R.

Tervo, J.

Thomson, M. J.

Todorov, T.

I. Mancheva, E. Nacheva, T. Petrova, N. Tomova, V. Dragostinova, T. Todorov, and L. Nikolova, “Light-controlled polarization switches in azobenzene-containing polymers,” Proc. SPIE 5226, 199-203 (2003).
[CrossRef]

L. Nikolova, and T. Todorov, “Diffraction efficiency and selectivity of polarization holographic recording,” Opt. Acta 31, 579-588 (1984).
[CrossRef]

Tomova, N.

I. Mancheva, E. Nacheva, T. Petrova, N. Tomova, V. Dragostinova, T. Todorov, and L. Nikolova, “Light-controlled polarization switches in azobenzene-containing polymers,” Proc. SPIE 5226, 199-203 (2003).
[CrossRef]

Trotzeck, M.

W. Singer, M. Trotzeck, and H. Gross, Handbook of Optical Systems. Volume 2: Physical Image Formation (Wiley, 2005).

Turunen, J.

Ujhelyi, F.

P. Várhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lőrincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

Várhegyi, P.

P. Várhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lőrincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

Waddie, A. J.

Wang, Y.

H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, Y. Wang, H. Ming, and Z. Zheng, “Transparent electro-optic ceramics and devices,” Proc. SPIE 5644, 380-394 (2005).
[CrossRef]

Watanabe, H.

Y. Sabi, M. Yamamoto, H. Watanabe, T. Bieringer, D. Haarer, R. Hagen, S. Kostromine, and H. Berneth, “Photoaddressable polymers for rewritable optical disc systems,” Jpn. J. Appl. Phys. 40, 1613-1618 (2001).
[CrossRef]

Wu, R.

Wyrowski, F.

Yamamoto, M.

Y. Sabi, M. Yamamoto, H. Watanabe, T. Bieringer, D. Haarer, R. Hagen, S. Kostromine, and H. Berneth, “Photoaddressable polymers for rewritable optical disc systems,” Jpn. J. Appl. Phys. 40, 1613-1618 (2001).
[CrossRef]

Zakrevsky, Y.

D. Rais, Y. Zakrevsky, J. Stumpe, S. Nešpůrek, and Z. Sedláková, “Photoorientation of azobenzene side groups in a liquid-crystalline polybutadiene-based polymer,” Opt. Mater. 30, 1335-1342 (2008).
[CrossRef]

Zhang, R.

H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, Y. Wang, H. Ming, and Z. Zheng, “Transparent electro-optic ceramics and devices,” Proc. SPIE 5644, 380-394 (2005).
[CrossRef]

Zhang, W.

Zhang, X.

Zheng, Z.

H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, Y. Wang, H. Ming, and Z. Zheng, “Transparent electro-optic ceramics and devices,” Proc. SPIE 5644, 380-394 (2005).
[CrossRef]

Zou, Y. K.

H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, Y. Wang, H. Ming, and Z. Zheng, “Transparent electro-optic ceramics and devices,” Proc. SPIE 5644, 380-394 (2005).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

P. Várhegyi, A. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, G. Szarvas, and E. Lőrincz, “Saturation effect in azobenzene polymers used for polarization holography,” Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328-330(2003).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

Y. Sabi, M. Yamamoto, H. Watanabe, T. Bieringer, D. Haarer, R. Hagen, S. Kostromine, and H. Berneth, “Photoaddressable polymers for rewritable optical disc systems,” Jpn. J. Appl. Phys. 40, 1613-1618 (2001).
[CrossRef]

Opt. Acta (1)

L. Nikolova, and T. Todorov, “Diffraction efficiency and selectivity of polarization holographic recording,” Opt. Acta 31, 579-588 (1984).
[CrossRef]

Opt. Commun. (1)

O. Bryngdahl, “Optical map transformations,” Opt. Commun. 10, 164-168 (1974).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Opt. Mater. (1)

D. Rais, Y. Zakrevsky, J. Stumpe, S. Nešpůrek, and Z. Sedláková, “Photoorientation of azobenzene side groups in a liquid-crystalline polybutadiene-based polymer,” Opt. Mater. 30, 1335-1342 (2008).
[CrossRef]

Proc. Indian Acad. Sci. A (1)

S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. Indian Acad. Sci. A 44, 247-262(1956).

Proc. SPIE (2)

I. Mancheva, E. Nacheva, T. Petrova, N. Tomova, V. Dragostinova, T. Todorov, and L. Nikolova, “Light-controlled polarization switches in azobenzene-containing polymers,” Proc. SPIE 5226, 199-203 (2003).
[CrossRef]

H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, Y. Wang, H. Ming, and Z. Zheng, “Transparent electro-optic ceramics and devices,” Proc. SPIE 5644, 380-394 (2005).
[CrossRef]

Other (3)

W. Singer, M. Trotzeck, and H. Gross, Handbook of Optical Systems. Volume 2: Physical Image Formation (Wiley, 2005).

T. Kreis, Handbook of Holographic Interferometry (Wiley, 2004).
[CrossRef]

M. Fratz, D. Eberhard, W. J. Riedel, and D. Giel, “Direct laser-writing of diffractive optical elements in photopolymer layers,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (Optical Society of America, 2008), paper DWB7.

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Figures (8)

Fig. 1
Fig. 1

Vector diagrams for two pixels of a PHOE under lcp illumination (green dashed vector, E in ; red solid vector, E out ). The upper row represents the situation in a PHOE point where the local HWP has an orientation of α = 45 ° ; the lower row depicts a PHOE point where α = 0 ° . These orientations are illustrated as blue index ellipses. From left to right, time is increasing from t = 0 to 3 T / 16 , with T = 1 / f denoting the oscillation period of the incident light. E in is assumed to be lcp and thus rotates counterclockwise. The effect of the local HWP is that E out rotates clockwise, i.e., is rcp. Furthermore, the rotation of α delays E out by 2 α in the upper row with respect to E out in the lower row.

Fig. 2
Fig. 2

Illustration of the PA. An input distribution [inset of (a)], e.g., Gaussian, is to be transformed into an arbitrary distribution, e.g., ring profile [inset of (b)]. (a), (b) Quantization of the cross sections of insets of (a) and (b), respectively, and the mapping of light elements ( 1 1 , 2 2 , ) .

Fig. 3
Fig. 3

Geometric considerations for the design of PHOEs by a mapping transform approach. (a) Rays (arrows) emerging from the PHOE plane with spatial coordinate r and traveling to the plane of the desired distribution with coordinate r . The incoming and desired intensity distributions are shown as dashed lines. (b) Detail of (a). The relation between rays and wavefronts (red liness) for one pixel of the PHOE at spatial coordinate k Δ r is illustrated. From optical path difference Δ L , the local gradient of the orientation of birefringence in the PHOE can be calculated as Δ α / Δ r = Δ L / λ π .

Fig. 4
Fig. 4

Comparison between (a)–(c) desired distributions and (d)–(e) simulated distributions for a Gaussian-to-flattop shaper. Scale bars correspond to 10 mm . (g)–(i) Cross sections of the desired (red) and the respective simulated distributions (blue).

Fig. 5
Fig. 5

Comparison of PHOEs for the generation of flattop arrays from a Gaussian beam. (a)–(c) Desired distributions, (d)–(f) simulated diffraction patterns, and (g)–(i) cross sections of simulated distributions along the dotted lines, respectively.

Fig. 6
Fig. 6

Experimental setups. (a) In the writing setup, the polymer sample is mounted on an ( x , y ) scanning stage and moved in the focus plane of an optical system. For evaluation of the function of a PHOE, the linear polarized light from a diode laser was converted into circularly polarized light. (b) The optical field diffracted by reflection PHOE can be observed with a CCD camera.

Fig. 7
Fig. 7

Measured intensity distribution of (a) a collimated diode laser and (b) Gaussian fit. (c) Desired distribution and (d) calculated PHOE. Simulation of the PHOE by means of (e) convolutional propagation and (f) experimentally measured distribution on a CCD camera. (g), (h) Radial profiles I ( r ) in arbitrary units of (e) and (f), respectively. Scale bars correspond to 500 μm .

Fig. 8
Fig. 8

Simulated intensity distribution for (a) a rectangle beam shaper and (b) observed diffracted field. Scale bars in the upper left corners correspond to 500 μm . (c), (d) Cross sections of (a) and (b) in arbitrary intensity units along the dotted lines, respectively.

Equations (17)

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T = [ A cos 2 α ( x , y ) + B sin 2 α ( x , y ) ( A B ) sin α ( x , y ) cos α ( x , y ) ( A B ) sin α ( x , y ) cos α ( x , y ) B cos 2 α ( x , y ) + A sin 2 α ( x , y ) ] ,
E out = 1 2 ( cos ( δ 2 ) [ 1 i ] + sin ( δ 2 ) × exp ( i ( 2 α ( x , y ) + π 2 ) ) [ 1 i ] ) .
E out = 1 2 exp ( i ( 2 α + π 2 ) ) [ 1 i ] = 1 2 exp ( i ( 2 α ( x , y ) ) ) [ i 1 ] .
E ( x , y ) = E out ( x , y ) exp ( i π λ d ) exp ( i ( ( x x ) 2 + ( y y ) 2 ) d x d y .
E ( x , y ) = F { E out ( x , y ) exp [ i π λ d ( x 2 + y 2 ) ] } ,
E ( x , y ) = F 1 { F { E out ( x , y ) } H ( ξ , η ) } ,
H ( ξ , η ) = exp ( ( 2 i π / λ ) ξ 2 + η 2 + d 2 ) .
Δ α ( k Δ r ) Δ r = π ( k Δ r m a Δ r ) λ d ,
α ( l Δ r ) = k = 0 l Δ α ( k Δ r ) Δ r Δ r .
A d ( x , y ) A cont ( x , y ) = F { A ( x , y ) exp [ i 2 α ( x , y ) ] × exp [ i π λ d ( x 2 + y 2 ) ] } = F { A ( x , y ) exp [ i 2 α ( x , y ) ] } F { exp [ i π λ d ( x 2 + y 2 ) ] } .
P ( x , y ) = [ [ exp ( 2 α ( x , y ) i ) comb ( x / Δ x ) comb ( y / Δ y ) ] [ rect ( x / Δ x ) rect ( y / Δ y ) ] ] × rect ( x / X ) rect ( y / Y ) .
A ( x , y ) = F { A ( x , y ) [ [ exp ( 2 α ( x , y ) i ) C ( x , y ) ] [ R ( x , y ) ] ] · W ( x , y ) } F { exp [ i π λ d ( x 2 + y 2 ) ] } .
δ = a Δ n λ = π .
E out = 1 2 ( cos ( π + ε 2 ) [ 1 i ] + sin ( π + ε 2 ) × exp ( i ( 2 α ( x , y ) ) ) [ i 1 ] ) .
E out rcp = 1 2 sin ( π + ε 2 ) exp ( i ( 2 α ( x , y ) ) ) [ i 1 ] = 1 2 cos ( ε 2 ) exp ( i ( 2 α ( x , y ) ) ) [ i 1 ] .
E out rcp = F { cos ( ε 2 ) 1 2 exp ( i ( 2 α ( x , y ) ) C ( x , y ) ) [ i 1 ] } = F { cos ( ε 2 ) } F { 1 2 exp ( i ( 2 α ( x , y ) ) C ( x , y ) ) [ i 1 ] } ,
E out lcp = 1 2 cos ( π + ε 2 ) [ 1 i ] = 1 2 sin ( ε 2 ) [ 1 i ] .

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