Abstract

We present a method of reshaping light in three dimensions via phase modulation. The method calculates the target computer-generated hologram individually and adds to it an appropriate transfer function to translate the reconstruction to any location in space. We are able to simultaneously generate independently controlled arbitrary patterns at different positions using a single laser beam.

© 2014 Optical Society of America

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  1. F. Gonte, A. Courteville, and R. Dandliker, Opt. Eng. 41, 1073 (2002).
    [CrossRef]
  2. E. Alon, V. Stojanovic, J. M. Kahn, S. Boyd, and M. Horowitz, in IEEE Global Telecommunications Conference, 2004 (IEEE, 2004), Vol. 2, pp. 1023–1029.
  3. E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
    [CrossRef]
  4. J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
    [CrossRef]
  5. D. G. Grier and Y. Roichman, Appl. Opt. 45, 880 (2006).
    [CrossRef]
  6. G. Bautista, M. J. Romero, G. Tapang, and V. R. Daria, Opt. Commun. 282, 3746 (2009).
    [CrossRef]
  7. J. Xia and H. Yin, Opt. Eng. 48, 20502 (2009).
    [CrossRef]
  8. R. Gerchberg and W. Saxton, Optik 35, 237 (1972).
  9. T. Haist, M. Schönleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
    [CrossRef]
  10. G. Sinclair, J. Leach, P. Jordan, G. Gibson, E. Yao, Z. Laczik, M. Padgett, and J. Courtial, Opt. Express 12, 1665 (2004).
    [CrossRef]
  11. F. Belloni and S. Monneret, Appl. Opt. 46, 4587 (2007).
    [CrossRef]
  12. H. E. Hwang, H. T. Chang, and W. N. Lie, Opt. Lett. 34, 3917 (2009).
    [CrossRef]
  13. H. T. Chang, H. E. Hwang, and C. L. Lee, Opt. Commun. 284, 4146 (2011).
    [CrossRef]
  14. J. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005).
  15. D. Palima and V. R. Daria, Appl. Opt. 46, 4197 (2007).
    [CrossRef]

2011

H. T. Chang, H. E. Hwang, and C. L. Lee, Opt. Commun. 284, 4146 (2011).
[CrossRef]

2009

G. Bautista, M. J. Romero, G. Tapang, and V. R. Daria, Opt. Commun. 282, 3746 (2009).
[CrossRef]

J. Xia and H. Yin, Opt. Eng. 48, 20502 (2009).
[CrossRef]

H. E. Hwang, H. T. Chang, and W. N. Lie, Opt. Lett. 34, 3917 (2009).
[CrossRef]

2007

2006

2004

2002

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

F. Gonte, A. Courteville, and R. Dandliker, Opt. Eng. 41, 1073 (2002).
[CrossRef]

2001

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

1997

T. Haist, M. Schönleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
[CrossRef]

1972

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

Alon, E.

E. Alon, V. Stojanovic, J. M. Kahn, S. Boyd, and M. Horowitz, in IEEE Global Telecommunications Conference, 2004 (IEEE, 2004), Vol. 2, pp. 1023–1029.

Bautista, G.

G. Bautista, M. J. Romero, G. Tapang, and V. R. Daria, Opt. Commun. 282, 3746 (2009).
[CrossRef]

Belloni, F.

Boyd, S.

E. Alon, V. Stojanovic, J. M. Kahn, S. Boyd, and M. Horowitz, in IEEE Global Telecommunications Conference, 2004 (IEEE, 2004), Vol. 2, pp. 1023–1029.

Chang, H. T.

H. T. Chang, H. E. Hwang, and C. L. Lee, Opt. Commun. 284, 4146 (2011).
[CrossRef]

H. E. Hwang, H. T. Chang, and W. N. Lie, Opt. Lett. 34, 3917 (2009).
[CrossRef]

Courteville, A.

F. Gonte, A. Courteville, and R. Dandliker, Opt. Eng. 41, 1073 (2002).
[CrossRef]

Courtial, J.

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

Dandliker, R.

F. Gonte, A. Courteville, and R. Dandliker, Opt. Eng. 41, 1073 (2002).
[CrossRef]

Daria, V. R.

G. Bautista, M. J. Romero, G. Tapang, and V. R. Daria, Opt. Commun. 282, 3746 (2009).
[CrossRef]

D. Palima and V. R. Daria, Appl. Opt. 46, 4197 (2007).
[CrossRef]

Dearing, M. T.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Dufresne, E. R.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Gerchberg, R.

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

Gibson, G.

Gonte, F.

F. Gonte, A. Courteville, and R. Dandliker, Opt. Eng. 41, 1073 (2002).
[CrossRef]

Goodman, J.

J. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005).

Grier, D. G.

D. G. Grier and Y. Roichman, Appl. Opt. 45, 880 (2006).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Haist, T.

T. Haist, M. Schönleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
[CrossRef]

Horowitz, M.

E. Alon, V. Stojanovic, J. M. Kahn, S. Boyd, and M. Horowitz, in IEEE Global Telecommunications Conference, 2004 (IEEE, 2004), Vol. 2, pp. 1023–1029.

Hwang, H. E.

H. T. Chang, H. E. Hwang, and C. L. Lee, Opt. Commun. 284, 4146 (2011).
[CrossRef]

H. E. Hwang, H. T. Chang, and W. N. Lie, Opt. Lett. 34, 3917 (2009).
[CrossRef]

Jordan, P.

Kahn, J. M.

E. Alon, V. Stojanovic, J. M. Kahn, S. Boyd, and M. Horowitz, in IEEE Global Telecommunications Conference, 2004 (IEEE, 2004), Vol. 2, pp. 1023–1029.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

Laczik, Z.

Leach, J.

Lee, C. L.

H. T. Chang, H. E. Hwang, and C. L. Lee, Opt. Commun. 284, 4146 (2011).
[CrossRef]

Lie, W. N.

Monneret, S.

Padgett, M.

Palima, D.

Roichman, Y.

Romero, M. J.

G. Bautista, M. J. Romero, G. Tapang, and V. R. Daria, Opt. Commun. 282, 3746 (2009).
[CrossRef]

Saxton, W.

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

Schönleber, M.

T. Haist, M. Schönleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
[CrossRef]

Sheets, S. A.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Sinclair, G.

Spalding, G. C.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Stojanovic, V.

E. Alon, V. Stojanovic, J. M. Kahn, S. Boyd, and M. Horowitz, in IEEE Global Telecommunications Conference, 2004 (IEEE, 2004), Vol. 2, pp. 1023–1029.

Tapang, G.

G. Bautista, M. J. Romero, G. Tapang, and V. R. Daria, Opt. Commun. 282, 3746 (2009).
[CrossRef]

Tiziani, H. J.

T. Haist, M. Schönleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
[CrossRef]

Xia, J.

J. Xia and H. Yin, Opt. Eng. 48, 20502 (2009).
[CrossRef]

Yao, E.

Yin, H.

J. Xia and H. Yin, Opt. Eng. 48, 20502 (2009).
[CrossRef]

Appl. Opt.

Opt. Commun.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

G. Bautista, M. J. Romero, G. Tapang, and V. R. Daria, Opt. Commun. 282, 3746 (2009).
[CrossRef]

T. Haist, M. Schönleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
[CrossRef]

H. T. Chang, H. E. Hwang, and C. L. Lee, Opt. Commun. 284, 4146 (2011).
[CrossRef]

Opt. Eng.

F. Gonte, A. Courteville, and R. Dandliker, Opt. Eng. 41, 1073 (2002).
[CrossRef]

J. Xia and H. Yin, Opt. Eng. 48, 20502 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

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

Rev. Sci. Instrum.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Other

E. Alon, V. Stojanovic, J. M. Kahn, S. Boyd, and M. Horowitz, in IEEE Global Telecommunications Conference, 2004 (IEEE, 2004), Vol. 2, pp. 1023–1029.

J. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic diagram of the algorithm to generate an arbitrary light field situated at an arbitrary 3D location. The algorithm is repeated for other patterns. For multiple targets, the hologram is the phase of the superposed inputs.

Fig. 2.
Fig. 2.

Optical setup for holographic reconstruction of the target light fields.

Fig. 3.
Fig. 3.

Numerical simulation of generation or arbitrary light fields using our proposed method. The hologram window size is 20 mm, while the reconstruction window size is around 7.3 mm.

Fig. 4.
Fig. 4.

Experimental generation or arbitrary light fields using our proposed method. The size is around 4.8 mm.

Fig. 5.
Fig. 5.

Plot of the NMSE versus z. The NMSE changes slightly with axial position from the focus.

Fig. 6.
Fig. 6.

Independent control of the generated light fields along the transverse direction. The letters Y, N, and C were moved to different locations, while the letter S was held in place.

Tables (1)

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Table 1. Summary of Positions for the Experimental Targetsa

Equations (6)

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

U(x,y,z)=F1{A(fx,fy)exp(ikz1λ2fx2λ2fy2)},
A(fx,fy)=a(fx,fy)exp(iϕGS(fx,fy)),
U(x,y,z)=F1{a(fx,fy)exp(iϕGS(fx,fy))exp(ikz1λ2fx2λ2fy2)}.
Htranslate=exp(i2π(fxΔx+fyΔy)).
u(fx,fy)=a(fx,fy)exp(i(ϕGS+ϕtransfer+ϕtranslate)).
uinput=i=1Nui(fx,fy),

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