Abstract

We report what we believe to be the first realization of a computer-generated complex-valued hologram recorded in a single film of photoactive polymer. Complex-valued holograms give rise to a diffracted optical field with control over its amplitude and phase. The holograms are generated by a one-step direct laser writing process in which a spatial light modulator (SLM) is imaged onto a polymer film. Temporal modulation of the SLM during exposure controls both the strength of the induced birefringence and the orientation of the fast axis. We demonstrate that complex holograms can be used to impart arbitrary amplitude and phase profiles onto a beam and thereby open new possibilities in the control of optical beams.

© 2009 Optical Society of America

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J. Eickmans, T. Bieringer, S. Kostromine, H. Berneth, and R. Thoma, Jpn. J. Appl. Ph. 38, 1835 (1999).
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[CrossRef]

Fienup, J.

Fischer, P.

Flores, D.

S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, Nature 451, 694 (2008).
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D. G. Grier, Nature 424, 810 (2003).
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S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, Nature 451, 694 (2008).
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M. Honkanen, V. Kettunen, J. Tervo, and J. Turunen, J. Mod. Opt. 47, 2351 (2000).

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Kettunen, V.

M. Honkanen, V. Kettunen, J. Tervo, and J. Turunen, J. Mod. Opt. 47, 2351 (2000).

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P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

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J. Eickmans, T. Bieringer, S. Kostromine, H. Berneth, and R. Thoma, Jpn. J. Appl. Ph. 38, 1835 (1999).
[CrossRef]

Li, G.

S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, Nature 451, 694 (2008).
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P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
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L. Nikolova and P. S. Ramanujam, Polarization Holography (Cambridge U. Press, 2009).
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S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, Nature 451, 694 (2008).
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Ohtake, Y.

Peyghambarian, N.

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[CrossRef] [PubMed]

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P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Ramanujam, P. S.

L. Nikolova and P. S. Ramanujam, Polarization Holography (Cambridge U. Press, 2009).
[CrossRef]

Rokutanda, S.

S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, Nature 451, 694 (2008).
[CrossRef] [PubMed]

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Schmid, M.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, F. Wyrowski, and R. Chaussee, J. Mod. Opt. 43, 1409 (1996).
[CrossRef]

Sinzinger, S.

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
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S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, Nature 451, 694 (2008).
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Tay, S.

S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, Nature 451, 694 (2008).
[CrossRef] [PubMed]

Teiwes, S.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, F. Wyrowski, and R. Chaussee, J. Mod. Opt. 43, 1409 (1996).
[CrossRef]

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M. Honkanen, V. Kettunen, J. Tervo, and J. Turunen, J. Mod. Opt. 47, 2351 (2000).

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J. Eickmans, T. Bieringer, S. Kostromine, H. Berneth, and R. Thoma, Jpn. J. Appl. Ph. 38, 1835 (1999).
[CrossRef]

Thomas, J.

S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, Nature 451, 694 (2008).
[CrossRef] [PubMed]

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S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, Nature 451, 694 (2008).
[CrossRef] [PubMed]

Turunen, J.

M. Honkanen, V. Kettunen, J. Tervo, and J. Turunen, J. Mod. Opt. 47, 2351 (2000).

Voorakaranam, R.

S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, Nature 451, 694 (2008).
[CrossRef] [PubMed]

Wang, P.

S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, Nature 451, 694 (2008).
[CrossRef] [PubMed]

Wyrowski, F.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, F. Wyrowski, and R. Chaussee, J. Mod. Opt. 43, 1409 (1996).
[CrossRef]

Yamamoto, M.

S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, Nature 451, 694 (2008).
[CrossRef] [PubMed]

Appl. Opt.

J. Mod. Opt.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, F. Wyrowski, and R. Chaussee, J. Mod. Opt. 43, 1409 (1996).
[CrossRef]

M. Honkanen, V. Kettunen, J. Tervo, and J. Turunen, J. Mod. Opt. 47, 2351 (2000).

Jpn. J. Appl. Ph.

J. Eickmans, T. Bieringer, S. Kostromine, H. Berneth, and R. Thoma, Jpn. J. Appl. Ph. 38, 1835 (1999).
[CrossRef]

Nature

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

S. Tay, P.-A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, Nature 451, 694 (2008).
[CrossRef] [PubMed]

Nature Photonics

D. N. Christodoulides, Nature Photonics 2, 652 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Science

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Other

L. Nikolova and P. S. Ramanujam, Polarization Holography (Cambridge U. Press, 2009).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Setup for the generation of amplitude and phase holograms. L 1 , write laser ( 532 nm ) ; BS, beam stop; BEO, beam-expanding optics; NPBS, nonpolarizing beam splitter; SLM, spatial light modulator; QWP, quarter-wave plate; IO, imaging objective; PS, polymer sample; C, camera; L 2 , control laser ( 670 nm ) ; PD, photodiode.

Fig. 2
Fig. 2

Generation of gratings for different exposure times. (a) Time dependence of the polarization orientation ρ in a single SLM pixel and measured diffracted intensity during the writing of a grating for a given time period in every pixel. T S , time interval of static polarization; T M , time of modulation; period T P = T S + T M was chosen to be 120 s . (b) Time-dependent diffracted intensities for various ratios of T S T P with T P 5.3 s during exposure. (c) Diffracted intensities after 10 min exposure as a function of the T S T P ratio.

Fig. 3
Fig. 3

CGHs with circular amplitude and spiral phase: (a) desired phase (top) and amplitude (bottom); (b) interferogram 140 mm behind CGH (spiral phase from 0 to 6 π ) with tilted reference beam (top), reconstructed phase and amplitude in the plane of the CGH (scale bar is 200 μ m ); (c) interferogram (top), reconstructed phase, and amplitude for CGH with a circular amplitude and spiral phase ranging from 0 to 8 π .

Fig. 4
Fig. 4

CGH with two regions of different nonzero amplitude and changing spiral phase pattern with opposite sense of rotation. (a) Desired amplitude and phase. (b) Measured amplitude and phase using lensless digital holography. (c) Radial amplitude profile of the measured and desired amplitude (in arbitrary units).

Equations (1)

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E out rcp = 1 2 sin ( δ 2 )     exp ( i ( 2 ρ + π 2 ) )     [ 1 i ] .

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