Abstract

We report the generation of continuous phase masks designed to generate a set of target diffraction orders with defined relative intensity weights. We apply a previously reported analytic calculation that requires resolving a single equation with a set of parameters defining the target diffraction orders. Then the same phase map is extended to other phase patterns such as vortex generating/sensing gratings. Results are demonstrated experimentally with a parallel-aligned spatial light modulator.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]

2012

J. Albero and I. Moreno, J. Opt. 14, 075704 (2012).
[CrossRef]

2010

L. A. Romero and F. M. Dickey, Prog. Opt. 54, 319 (2010).
[CrossRef]

Y. V. Miklyaev, W. Imgrunt, T. Bizjak, L. Aschke, V. N. Lissotschenko, V. S. Pavelyev, and D. G. Kachalov, Proc. SPIE 7640, 764024 (2010).
[CrossRef]

I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X.-C. Yuan, Opt. Lett. 35, 1536 (2010).
[CrossRef]

M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, Opt. Express 18, 12136 (2010).
[CrossRef]

2009

2007

2006

2003

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

1999

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, Opt. Eng. 38, 1051 (1999).
[CrossRef]

1998

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, Opt. Commun. 157, 13 (1998).
[CrossRef]

1997

1995

M. J. Padgett and L. Allen, Opt. Commun. 121, 36 (1995).
[CrossRef]

1992

1990

V. Yu Bazhenov, V. Vasnetsov, and M. S. Soskin, J. Exp. Theor. Phys. Lett. 52, 429 (1990).

1972

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

1971

H. Dammann and K. Görtler, Opt. Commun 3, 312 (1971).
[CrossRef]

Albero, J.

J. Albero and I. Moreno, J. Opt. 14, 075704 (2012).
[CrossRef]

Allen, L.

M. J. Padgett and L. Allen, Opt. Commun. 121, 36 (1995).
[CrossRef]

Amako, J.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, Opt. Eng. 38, 1051 (1999).
[CrossRef]

Andilla, J.

Aschke, L.

Y. V. Miklyaev, W. Imgrunt, T. Bizjak, L. Aschke, V. N. Lissotschenko, V. S. Pavelyev, and D. G. Kachalov, Proc. SPIE 7640, 764024 (2010).
[CrossRef]

Bengtsson, J.

Bizjak, T.

Y. V. Miklyaev, W. Imgrunt, T. Bizjak, L. Aschke, V. N. Lissotschenko, V. S. Pavelyev, and D. G. Kachalov, Proc. SPIE 7640, 764024 (2010).
[CrossRef]

Borghi, R.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, Opt. Commun. 157, 13 (1998).
[CrossRef]

Cincotti, G.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, Opt. Commun. 157, 13 (1998).
[CrossRef]

Cottrell, D. M.

Dammann, H.

H. Dammann and K. Görtler, Opt. Commun 3, 312 (1971).
[CrossRef]

Dändliker, R.

Davis, J. A.

Di Fabrizio, E.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, Opt. Commun. 157, 13 (1998).
[CrossRef]

Di Leonardo, R.

Dickey, F. M.

L. A. Romero and F. M. Dickey, Prog. Opt. 54, 319 (2010).
[CrossRef]

Gale, M. T.

Gentili, M.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, Opt. Commun. 157, 13 (1998).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Gori, F.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, Opt. Commun. 157, 13 (1998).
[CrossRef]

Görtler, K.

H. Dammann and K. Görtler, Opt. Commun 3, 312 (1971).
[CrossRef]

Grier, D.

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

Herzig, H. P.

Hirao, K.

Ianni, F.

Imgrunt, W.

Y. V. Miklyaev, W. Imgrunt, T. Bizjak, L. Aschke, V. N. Lissotschenko, V. S. Pavelyev, and D. G. Kachalov, Proc. SPIE 7640, 764024 (2010).
[CrossRef]

Kachalov, D. G.

Y. V. Miklyaev, W. Imgrunt, T. Bizjak, L. Aschke, V. N. Lissotschenko, V. S. Pavelyev, and D. G. Kachalov, Proc. SPIE 7640, 764024 (2010).
[CrossRef]

Lissotschenko, V. N.

Y. V. Miklyaev, W. Imgrunt, T. Bizjak, L. Aschke, V. N. Lissotschenko, V. S. Pavelyev, and D. G. Kachalov, Proc. SPIE 7640, 764024 (2010).
[CrossRef]

Martín-Badosa, E.

Miklyaev, Y. V.

Y. V. Miklyaev, W. Imgrunt, T. Bizjak, L. Aschke, V. N. Lissotschenko, V. S. Pavelyev, and D. G. Kachalov, Proc. SPIE 7640, 764024 (2010).
[CrossRef]

Mitry, M. J.

Miura, K.

Montes-Usategui, M.

Moreno, I.

Padgett, M. J.

M. J. Padgett and L. Allen, Opt. Commun. 121, 36 (1995).
[CrossRef]

Pascoguin, B. M. L.

Pavelyev, V. S.

Y. V. Miklyaev, W. Imgrunt, T. Bizjak, L. Aschke, V. N. Lissotschenko, V. S. Pavelyev, and D. G. Kachalov, Proc. SPIE 7640, 764024 (2010).
[CrossRef]

Pleguezuelos, E.

Prongué, D.

Romero, L. A.

L. A. Romero and F. M. Dickey, Prog. Opt. 54, 319 (2010).
[CrossRef]

Ruocco, G.

Sakakura, M.

Santarsiero, M.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, Opt. Commun. 157, 13 (1998).
[CrossRef]

Sawano, T.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Shimotsuma, Y.

Sonehara, T.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, Opt. Eng. 38, 1051 (1999).
[CrossRef]

Soskin, M. S.

V. Yu Bazhenov, V. Vasnetsov, and M. S. Soskin, J. Exp. Theor. Phys. Lett. 52, 429 (1990).

Tsai, P.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, Opt. Eng. 38, 1051 (1999).
[CrossRef]

Vasnetsov, V.

V. Yu Bazhenov, V. Vasnetsov, and M. S. Soskin, J. Exp. Theor. Phys. Lett. 52, 429 (1990).

Vicalvi, S.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, Opt. Commun. 157, 13 (1998).
[CrossRef]

Yu Bazhenov, V.

V. Yu Bazhenov, V. Vasnetsov, and M. S. Soskin, J. Exp. Theor. Phys. Lett. 52, 429 (1990).

Yuan, X.-C.

Zhang, N.

Appl. Opt.

J. Exp. Theor. Phys. Lett.

V. Yu Bazhenov, V. Vasnetsov, and M. S. Soskin, J. Exp. Theor. Phys. Lett. 52, 429 (1990).

J. Opt.

J. Albero and I. Moreno, J. Opt. 14, 075704 (2012).
[CrossRef]

Nature

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

Opt. Commun

H. Dammann and K. Görtler, Opt. Commun 3, 312 (1971).
[CrossRef]

Opt. Commun.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, Opt. Commun. 157, 13 (1998).
[CrossRef]

M. J. Padgett and L. Allen, Opt. Commun. 121, 36 (1995).
[CrossRef]

Opt. Eng.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, Opt. Eng. 38, 1051 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Proc. SPIE

Y. V. Miklyaev, W. Imgrunt, T. Bizjak, L. Aschke, V. N. Lissotschenko, V. S. Pavelyev, and D. G. Kachalov, Proc. SPIE 7640, 764024 (2010).
[CrossRef]

Prog. Opt.

L. A. Romero and F. M. Dickey, Prog. Opt. 54, 319 (2010).
[CrossRef]

Other

http://support.microsoft.com/kb/214115 .

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Figures (3)

Fig. 1.
Fig. 1.

Phase mapping to generate the optimal phase grating φ(x) from a linear blazed grating (ϕ(x)=2πx/p) of the same period p.

Fig. 2.
Fig. 2.

Experimental N=7 beam splitter (a) equi-energy spots and their profile, (b) detail of the phase grating encoded on the SLM to obtain Fig. 2(a) (c) phase profile corresponding to one period of Fig. 2(b), (d) spots with different energies and their profile, (e) detail of the phase grating encoded on the SLM to obtain the results in Fig. 2(d), and (f) phase profile corresponding to one period in Fig. 2(e).

Fig. 3.
Fig. 3.

Experimental N=7 vortex grating (a) equal energy distribution among diffraction orders and their profile, (b) phase grating encoded on the SLM to obtain Fig. 3(a), (c) compensated energy for equi-intense vortices and their profile, and (d) phase grating encoded on the SLM to obtain Fig. 3(c).

Equations (6)

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

exp[iφ(x)],
ak=12πππexp[iφ(x)]exp[ikx]dx,
exp[iφ(x)]=s(x)|s(x)|,
s(x)=k=mmμkexp[iαk]exp[ikx].
η=k=mm|ak|2k=|ak|2.
r|k|.

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