Abstract

We discuss a phase synthetic hologram, for encoding arbitrary complex fields, whose design is based on a sinusoidal phase grating with a spatially modulated phase depth. An important feature of the hologram is that it encodes the complex field at the zero diffraction order of the carrier grating. The smoothness of this sinusoidal carrier grating facilitates the implementation of the hologram with a pixelated spatial light modulator. We take advantage of the hologram reconstruction at the zero-diffraction order for the simultaneous generation of a collection of complex beams.

© 2009 Optical Society of America

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References

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  1. J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-554 (2000).
    [CrossRef]
  2. T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, "Novel Optical Trap of Atoms with a Doughnut Beam," Phys. Rev. Lett. 78, 4713-4716 (1997).
    [CrossRef]
  3. A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, "Observation of topological transformations of optical vortices in two-dimensional photonic lattices," Opt. Express 14, 8318-8327, (2006).
    [CrossRef]
  4. D. Sánchez-de-la-Llave, V. Arrizón, and L. A. Gonzalez, "Isotropic edge enhancement filter implemented with a phase-only spatial light modulator," Proc. SPIE 4471, 114-123 (2001).
    [CrossRef]
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    [CrossRef]
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2007 (2)

2006 (1)

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, "Observation of topological transformations of optical vortices in two-dimensional photonic lattices," Opt. Express 14, 8318-8327, (2006).
[CrossRef]

2005 (1)

2003 (1)

2002 (1)

2001 (1)

D. Sánchez-de-la-Llave, V. Arrizón, and L. A. Gonzalez, "Isotropic edge enhancement filter implemented with a phase-only spatial light modulator," Proc. SPIE 4471, 114-123 (2001).
[CrossRef]

2000 (2)

M. A. A. Neil, T. Wilson, and R. Juškaitis, "A wavefront generator for complex pupil function synthesis and point spread function engineering," J. Microsc. 197, 219-223 (2000).
[CrossRef] [PubMed]

J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-554 (2000).
[CrossRef]

1999 (1)

1997 (3)

1994 (1)

Apolinar-Iribe, A.

Arlt, J.

J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-554 (2000).
[CrossRef]

Arrizón, V.

Bernet, S.

Bezryadina, A.

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, "Observation of topological transformations of optical vortices in two-dimensional photonic lattices," Opt. Express 14, 8318-8327, (2006).
[CrossRef]

Campos, J.

Carrada, R.

Chavez-Cerda, S.

Chen, Z.

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, "Observation of topological transformations of optical vortices in two-dimensional photonic lattices," Opt. Express 14, 8318-8327, (2006).
[CrossRef]

Cohn, R. W.

Cottrell, D. M.

Davis, J. A.

Desyatnikov, A. S.

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, "Observation of topological transformations of optical vortices in two-dimensional photonic lattices," Opt. Express 14, 8318-8327, (2006).
[CrossRef]

Dholakia, K.

J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-554 (2000).
[CrossRef]

Fürhapter, S.

Gómez-Sarabia, C. M.

Gonzalez, L. A.

D. Sánchez-de-la-Llave, V. Arrizón, and L. A. Gonzalez, "Isotropic edge enhancement filter implemented with a phase-only spatial light modulator," Proc. SPIE 4471, 114-123 (2001).
[CrossRef]

González, L. A.

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, "Novel Optical Trap of Atoms with a Doughnut Beam," Phys. Rev. Lett. 78, 4713-4716 (1997).
[CrossRef]

Hitomi, T.

J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-554 (2000).
[CrossRef]

Jesacher, A.

Juškaitis, R.

M. A. A. Neil, T. Wilson, and R. Juškaitis, "A wavefront generator for complex pupil function synthesis and point spread function engineering," J. Microsc. 197, 219-223 (2000).
[CrossRef] [PubMed]

Kettunen, V.

Kivshar, Y. S.

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, "Observation of topological transformations of optical vortices in two-dimensional photonic lattices," Opt. Express 14, 8318-8327, (2006).
[CrossRef]

Korneev, N.

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, "Novel Optical Trap of Atoms with a Doughnut Beam," Phys. Rev. Lett. 78, 4713-4716 (1997).
[CrossRef]

Levi, U.

Liang, M.

Marom, E.

Mendlovic, D.

Moreno, I.

Neil, M. A. A.

M. A. A. Neil, T. Wilson, and R. Juškaitis, "A wavefront generator for complex pupil function synthesis and point spread function engineering," J. Microsc. 197, 219-223 (2000).
[CrossRef] [PubMed]

Neshev, D. N.

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, "Observation of topological transformations of optical vortices in two-dimensional photonic lattices," Opt. Express 14, 8318-8327, (2006).
[CrossRef]

Noponen, E.

Ritsch-Marte, M.

Ruiz, U.

Sánchez-de-la-Llave, D.

D. Sánchez-de-la-Llave, V. Arrizón, and L. A. Gonzalez, "Isotropic edge enhancement filter implemented with a phase-only spatial light modulator," Proc. SPIE 4471, 114-123 (2001).
[CrossRef]

Sasada, H.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, "Novel Optical Trap of Atoms with a Doughnut Beam," Phys. Rev. Lett. 78, 4713-4716 (1997).
[CrossRef]

Shabtay, G.

Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, "Novel Optical Trap of Atoms with a Doughnut Beam," Phys. Rev. Lett. 78, 4713-4716 (1997).
[CrossRef]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, "Novel Optical Trap of Atoms with a Doughnut Beam," Phys. Rev. Lett. 78, 4713-4716 (1997).
[CrossRef]

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, "Novel Optical Trap of Atoms with a Doughnut Beam," Phys. Rev. Lett. 78, 4713-4716 (1997).
[CrossRef]

Turunen, J.

Vahimaa, P.

Vysloukh, V.

Wilson, T.

M. A. A. Neil, T. Wilson, and R. Juškaitis, "A wavefront generator for complex pupil function synthesis and point spread function engineering," J. Microsc. 197, 219-223 (2000).
[CrossRef] [PubMed]

Young, J.

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, "Observation of topological transformations of optical vortices in two-dimensional photonic lattices," Opt. Express 14, 8318-8327, (2006).
[CrossRef]

Yzuel, M. J.

Zalevsky, Z.

Appl. Opt. (3)

Appl. Phys. B (1)

J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-554 (2000).
[CrossRef]

J. Microsc. (1)

M. A. A. Neil, T. Wilson, and R. Juškaitis, "A wavefront generator for complex pupil function synthesis and point spread function engineering," J. Microsc. 197, 219-223 (2000).
[CrossRef] [PubMed]

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

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, "Novel Optical Trap of Atoms with a Doughnut Beam," Phys. Rev. Lett. 78, 4713-4716 (1997).
[CrossRef]

Proc. SPIE (1)

D. Sánchez-de-la-Llave, V. Arrizón, and L. A. Gonzalez, "Isotropic edge enhancement filter implemented with a phase-only spatial light modulator," Proc. SPIE 4471, 114-123 (2001).
[CrossRef]

Other (1)

W. J. Dallas, "Computer-generated holograms" in The Computer in Optical Research, B. R. Frieden, ed., (Springer-Verlag, Berlin. 1980), pp. 4156-4165.

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Figures (7)

Fig. 1.
Fig. 1.

(a). Modulus and (b). phase of the complex field s1(x,y), and (c). modulus of its Fourier spectrum.

Fig. 2.
Fig. 2.

Fourier spectrum modulus of the SPH that encodes the field s1(x,y): (a) central section and several high orders of the spectrum, (b) close view of the central spectrum region, and (c) central spectrum region for a modified SPH, with new carrier frequencies u0=v0=Δu/4+Δu/32.

Fig. 3.
Fig. 3.

Amplitude profiles along the horizontal axis of the weak spots in the Fourier spectra corresponding to (a) the encoded field s1(x,y), (b) the SPH with carrier frequencies u0=v0=Δu/4, and (c) the SPH with carrier frequencies u0=v0=Δu/4+Δu/32.

Fig. 4.
Fig. 4.

Modulus of (a) the complex field s2(x,y), (b) modulus of its Fourier spectrum, and (c) Fourier spectrum modulus of the SPH that encodes the field s2(x,y).

Fig. 5.
Fig. 5.

(a). Modules of the complex field s3(x,y), and (b) of its Fourier spectrum. (c) Fourier spectrum modulus of the SPH that encodes the field s3(x,y).

Fig. 6.
Fig. 6.

Optical setup for experimental generation of multiple beams with a SPH.

Fig. 7.
Fig. 7.

Modules of experimentally generated complex fields (a) s2 (x,y) and (b) s3 (x,y).

Equations (9)

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s x y = a x y exp [ x y ] ,
h x y = h a x y exp [ x y ] ,
h a x y = exp { if ( a ) sin [ 2 π ( u 0 x + v 0 y ) ] } .
h a x y = q = J q [ f ( a ) ] exp [ i 2 π ( q u 0 x + q v 0 y ) ] ,
J 0 [ f ( a x y ) ] = a x y ,
h x y = exp [ x y ] exp { if ( a ) sin [ 2 π ( u 0 x + v 0 y ) ] } .
s 1 x y = c J 1 ( 2 π ρ 0 r ) exp ( ) [ cos ( 2 π ξ 0 y ) + b cos ( 2 π η 0 x ) ] .
s 2 x y = c [ J 1 ( 2 π ρ 0 r ) cos ( 2 π ξ 0 y + θ ) + b cos ( 2 π η 0 x ) ] .
s 3 x y = c [ J 0 ( 2 π ρ 0 r ) cos ( 2 π ξ 0 y ) + b cos ( 2 π η 0 x ) ] .

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