Abstract

A phase-only hologram applies a modal transformation to an optical transverse spatial mode via phase encoding and intensity masking. Accurate control of the optical field crucially depends on the method employed to encode the hologram. In this Letter, we present a method to encode the amplitude and the phase of an optical field into a phase-only hologram, which allows the exact control of spatial transverse modes. Any intensity masking method modulates the amplitude and alters the phase of the optical field. Our method consists in correcting for this unwanted phase alteration by modifying the phase encryption accordingly. We experimentally verify the accuracy of our method by applying it to the generation and detection of transverse spatial modes in mutually unbiased bases of dimension two and three.

© 2013 Optical Society of America

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References

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2011

M. Wieśniak, T. Paterek, and A. Zeilinger, New J. Phys. 13, 053047 (2011).
[CrossRef]

2009

2008

S. Franke-Arnold, L. Allen, and M. Padgett, Laser Photon. Rev. 2, 299 (2008).
[CrossRef]

2007

2005

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, New J. Phys. 7, 55 (2005).
[CrossRef]

2004

2001

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

1999

1995

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

1992

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

1990

J. A. Neff, R. A. Athale, and S. H. Lee, Proc. IEEE 78, 826 (1990).
[CrossRef]

1989

W. K. Wootters and B. D. Fields, Ann. Phys. 191, 363 (1989).
[CrossRef]

1971

Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, Laser Photon. Rev. 2, 299 (2008).
[CrossRef]

Ando, T.

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Arrizón, V.

Athale, R. A.

J. A. Neff, R. A. Athale, and S. H. Lee, Proc. IEEE 78, 826 (1990).
[CrossRef]

Barnett, S. M.

Bazhenov, V. Yu.

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Campos, J.

Cardano, F.

V. D’Ambrosio, F. Cardano, E. Karimi, E. Nagali, E. Santamato, L. Marrucci, and F. Sciarrino, arXiv:1304.4081.

Carrada, R.

Cottrell, D. M.

Courtial, J.

D’Ambrosio, V.

V. D’Ambrosio, F. Cardano, E. Karimi, E. Nagali, E. Santamato, L. Marrucci, and F. Sciarrino, arXiv:1304.4081.

Davis, J. A.

Dennis, M. R.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, New J. Phys. 7, 55 (2005).
[CrossRef]

Dholakia, K.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Fields, B. D.

W. K. Wootters and B. D. Fields, Ann. Phys. 191, 363 (1989).
[CrossRef]

Franke-Arnold, S.

Fukuchi, N.

Gibson, G.

González, L. A.

He, H.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

Heckenberg, N. R.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

Hell, W. S.

W. S. Hell, Science 316, 1153 (2007).
[CrossRef]

Inoue, T.

Jones, A. L.

Karimi, E.

V. D’Ambrosio, F. Cardano, E. Karimi, E. Nagali, E. Santamato, L. Marrucci, and F. Sciarrino, arXiv:1304.4081.

Kirk, J. P.

Leach, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, New J. Phys. 7, 55 (2005).
[CrossRef]

Lee, S. H.

J. A. Neff, R. A. Athale, and S. H. Lee, Proc. IEEE 78, 826 (1990).
[CrossRef]

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Marrucci, L.

V. D’Ambrosio, F. Cardano, E. Karimi, E. Nagali, E. Santamato, L. Marrucci, and F. Sciarrino, arXiv:1304.4081.

Matsumoto, N.

Moreno, I.

Nagali, E.

V. D’Ambrosio, F. Cardano, E. Karimi, E. Nagali, E. Santamato, L. Marrucci, and F. Sciarrino, arXiv:1304.4081.

Neff, J. A.

J. A. Neff, R. A. Athale, and S. H. Lee, Proc. IEEE 78, 826 (1990).
[CrossRef]

Ohtake, Y.

Padgett, M.

S. Franke-Arnold, L. Allen, and M. Padgett, Laser Photon. Rev. 2, 299 (2008).
[CrossRef]

Padgett, M. J.

Pasko, V.

Paterek, T.

M. Wieśniak, T. Paterek, and A. Zeilinger, New J. Phys. 13, 053047 (2011).
[CrossRef]

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Rubinsztein-Dunlop, H.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

Ruiz, U.

Santamato, E.

V. D’Ambrosio, F. Cardano, E. Karimi, E. Nagali, E. Santamato, L. Marrucci, and F. Sciarrino, arXiv:1304.4081.

Sciarrino, F.

V. D’Ambrosio, F. Cardano, E. Karimi, E. Nagali, E. Santamato, L. Marrucci, and F. Sciarrino, arXiv:1304.4081.

Sibbett, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Soskin, M. S.

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

Vasnetsov, M.

Vasnetsov, M. V.

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

Wiesniak, M.

M. Wieśniak, T. Paterek, and A. Zeilinger, New J. Phys. 13, 053047 (2011).
[CrossRef]

Wootters, W. K.

W. K. Wootters and B. D. Fields, Ann. Phys. 191, 363 (1989).
[CrossRef]

Yzuel, M. J.

Zeilinger, A.

M. Wieśniak, T. Paterek, and A. Zeilinger, New J. Phys. 13, 053047 (2011).
[CrossRef]

Ann. Phys.

W. K. Wootters and B. D. Fields, Ann. Phys. 191, 363 (1989).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Laser Photon. Rev.

S. Franke-Arnold, L. Allen, and M. Padgett, Laser Photon. Rev. 2, 299 (2008).
[CrossRef]

New J. Phys.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, New J. Phys. 7, 55 (2005).
[CrossRef]

M. Wieśniak, T. Paterek, and A. Zeilinger, New J. Phys. 13, 053047 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. IEEE

J. A. Neff, R. A. Athale, and S. H. Lee, Proc. IEEE 78, 826 (1990).
[CrossRef]

Science

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

W. S. Hell, Science 316, 1153 (2007).
[CrossRef]

Other

V. A. Soifer, eds., Methods for Computer Design of Diffractive Optical Elements (Wiley, 2002).

V. D’Ambrosio, F. Cardano, E. Karimi, E. Nagali, E. Santamato, L. Marrucci, and F. Sciarrino, arXiv:1304.4081.

The similarity is defined as S=((∑i,jPijPij′)2/∑i,jPij∑i,jPij′), where P and P′ stand for experimental and expected theoretical projection matrix.

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Figures (4)

Fig. 1.
Fig. 1.

Amplitude of the generated beam, after selection of the first order of diffraction, as a function of the normalized desired amplitude of Eq. (1). The solid-red curve corresponds to our exact hologram encryption method; the generated amplitude is equal to the desired amplitude. The blue dashed curve is based on the technique reported in [10].

Fig. 2.
Fig. 2.

Layout of the experimental setup used to encode and detect OAM qubit and qutrit states based on our new method. A HeNe laser beam illuminates SLM-A, which generates any of the MUBs. The 4f systems made of the lenses {L1,L2} image the plane of SLM-A to that of SLM-B with unit magnification. The SLM-B and a SMF act together as a mode projector on any of the MUBs states. We sequentially display all MUBs states on SLM-A and SLM-B, and acquire all combinations of projections. The last set of lenses, composed of {L3,L4, microscope objective}, take the far-field of SLM-B to the entrance facet of the SMF. The irises act as spatial filters which select the first order of diffraction of SLM-A and SLM-B. As SLMs are polarization sensitive, the polarizer (POL) and the half-wave plate (λ/2) optimize the diffraction efficiency.

Fig. 3.
Fig. 3.

Experimental projections between states in all MUBs in (a) d=2 and (b) d=3 OAM Hilbert subspaces, i.e., Pij=|αi|βj|2.

Fig. 4.
Fig. 4.

Qualitative comparison of the method of Davis et al. and our proposed improvement of their technique. The desired intensity profile purposely has small features to accentuate the difference between the two methods. The experimentally recorded images are taken in the far-field of a HOLOEYE SLM.

Equations (6)

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

E(r,z0)A(r,z0)eiΦ(r,z0),
T(m,n)=eiM(m,n)Mod(F(m,n)+2πm/Λ,2π).
T1(m,n)=sinc(πMπ)ei(F+πM),
M=1+1πsinc1(A)F=ΦπM,
{I}={|0,|1}{II}={|0+|12,|0|12}{III}={|0+i|12,|0i|12}.
{I}={|0,|1,|2}{II}={|0+|1+|23,|0+ω|1+ω2|23,|0+ω2|1+ω|23}{III}={|0+ω|1+ω|23,|0+ω2|1+|23,|0+|1+ω2|23}{IV}={|0+ω2|1+ω2|23,|0+ω|1+|23,|0+|1+ω|23},

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