Abstract

We demonstrate that a structured light intensity pattern can be produced at the output of a multi-mode optical fiber by shaping the wavefront of the input beam with a spatial light modulator. We also find the useful property that, as in the case for free space propagation, output intensities can be easily superimposed by taking the argument of the complex superposition of corresponding phase-only holograms. An analytical expression is derived, relating output intensities ratios to hologram weights in the superposition.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2010 (5)

S. Bianchi and R. Di Leonardo "Real-time optical micro-manipulation using optimized holograms generated on the GPU," Comput. Phys. Commun. 181, 1444-1448 (2010).
[CrossRef]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, "Exploiting disorder for perfect focusing," Nat. Photonics 4, 320-322 (2010).
[CrossRef]

T. Cizmar, M. Mazilu, and K. Dholakia, "In situ wavefront correction and its application to micromanipulation," Nat. Photonics 4, 388-394 (2010).
[CrossRef]

I. M. Vellekoop, and C. M. Aegerter, "Scattered light fluorescence microscopy: imaging through turbid layers," Opt. Lett. 35, 1245-1247 (2010).
[CrossRef] [PubMed]

M. Paurisse, M. Hanna, F. Druon, and P. Georges, "Wavefront control of a multicore ytterbium-doped pulse fiber amplifier by digital holography," Opt. Lett. 35, 1428-1430 (2010).
[CrossRef] [PubMed]

2009 (2)

2008 (1)

2007 (4)

2006 (4)

2003 (1)

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

1999 (1)

1996 (1)

1993 (1)

1972 (1)

R. W. Gerchberg, and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 237-246 (1972).

Aegerter, C. M.

Anderson, D. Z.

Bellanger, C.

Bernet, S.

Bianchi, S.

S. Bianchi and R. Di Leonardo "Real-time optical micro-manipulation using optimized holograms generated on the GPU," Comput. Phys. Commun. 181, 1444-1448 (2010).
[CrossRef]

Bolshtyansky, M. A.

Brignon, A.

Cizmar, T.

T. Cizmar, M. Mazilu, and K. Dholakia, "In situ wavefront correction and its application to micromanipulation," Nat. Photonics 4, 388-394 (2010).
[CrossRef]

Clark, R. L.

Cole, D. G.

Colineau, J.

Constable, A.

Cooper, J.

Dholakia, K.

Di Leonardo, R.

Droun, F.

Druon, F.

Fürhapter, S.

Garcés-Chávez, V.

Gardel, E.

Georges, P.

Gerber, G.

Gerchberg, R. W.

R. W. Gerchberg, and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 237-246 (1972).

Gibson, G.

Grier, D.

Grier, D. G.

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

Haist, T.

Hanna, M.

Herrington, C. S.

Huignard, J. P.

Ianni, F.

Jesacher, A.

Jess, P. R. T.

Kemmer, R.

Kim, J.

Lagendijk, A.

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, "Exploiting disorder for perfect focusing," Nat. Photonics 4, 320-322 (2010).
[CrossRef]

Leach, J.

Leng, Y.

Li, X.

Lucensoli, A.

Maurer, C.

Mazilu, M.

Mervis, J.

Mosk, A. P.

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, "Exploiting disorder for perfect focusing," Nat. Photonics 4, 320-322 (2010).
[CrossRef]

I. M. Vellekoop, and A. P. Mosk, "Focusing coherent light through opaque strongly scattering media," Opt. Lett. 32, 2309-2311 (2007).
[CrossRef] [PubMed]

Padgett, M. J.

Paterson, L.

Paurisse, M.

Pfeifer, T.

Prentiss, M.

Reicherter, M.

Riches, A.

Ritsch-Marte, M.

Roichman, Y.

Rozzi, T.

Ruocco, G.

Saxton, W. O.

R. W. Gerchberg, and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 237-246 (1972).

Schwaighofer, A.

Sibbett, W.

Smith, D.

Spielmann, C.

Spitzenpfeil, R.

Tiziani, H. J.

Vellekoop, I. M.

Wagemann, E. U.

Waldron, A.

Walter, D.

Winterfeldt, C.

Wu, Y.

Wulff, K. D.

Xi, J.

Zarinetchi, F.

Zel’dovich, B. Y.

Appl. Opt. (2)

Comput. Phys. Commun. (1)

S. Bianchi and R. Di Leonardo "Real-time optical micro-manipulation using optimized holograms generated on the GPU," Comput. Phys. Commun. 181, 1444-1448 (2010).
[CrossRef]

Nat. Photonics (2)

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, "Exploiting disorder for perfect focusing," Nat. Photonics 4, 320-322 (2010).
[CrossRef]

T. Cizmar, M. Mazilu, and K. Dholakia, "In situ wavefront correction and its application to micromanipulation," Nat. Photonics 4, 388-394 (2010).
[CrossRef]

Nature (1)

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

Opt. Express (7)

A. Jesacher, A. Schwaighofer, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, "Wavefront correction of spatial light modulators using an optical vortex image," Opt. Express 15, 5801-5808 (2007).
[CrossRef] [PubMed]

K. D. Wulff, D. G. Cole, R. L. Clark, R. Di Leonardo, J. Leach, J. Cooper, G. Gibson, and M. J. Padgett, "Aberration correction in holographic optical tweezers," Opt. Express 14, 4169-4174 (2006).
[CrossRef] [PubMed]

Y. Wu, Y. Leng, J. Xi, and X. Li, "Scanning all-fiber-optic endomicroscopy system for 3D nonlinear optical imaging of biological tissues," Opt. Express 17, 7907-7915 (2009).
[CrossRef] [PubMed]

M. Paurisse, M. Hanna, F. Droun, P. Georges, C. Bellanger, A. Brignon, and J. P. Huignard, "Phase and amplitude control of a multimode fiber beam by use of digital holography," Opt. Express 17, 13000-13008 (2009).
[CrossRef] [PubMed]

D. Walter, T. Pfeifer, C. Winterfeldt, R. Kemmer, R. Spitzenpfeil, G. Gerber, and C. Spielmann, "Adaptive spatial control of fiber modes and their excitation for high-harmonic generation," Opt. Express 14, 3433-3442 (2006).
[CrossRef] [PubMed]

P. R. T. Jess, V. Garcés-Chávez, D. Smith, M. Mazilu, L. Paterson, A. Riches, C. S. Herrington, W. Sibbett, and K. Dholakia, "Dual beam fibre trap for Raman micro-spectroscopy of single cells," Opt. Express 14, 5779-5791 (2006).
[CrossRef] [PubMed]

R. Di Leonardo, F. Ianni, and G. Ruocco, "Computer generation of optimal holograms for optical trap arrays," Opt. Express 15, 1913-1922 (2007).
[CrossRef] [PubMed]

Opt. Lett. (7)

Optik (Stuttg.) (1)

R. W. Gerchberg, and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 237-246 (1972).

Other (2)

B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics, (John Wiley & Sons, 1991).
[CrossRef]

G. C. Spalding, J. Courtial, and R. Di Leonardo, "Holographic optical tweezers," in Structured Light and Its Applications, D. L. Andrews, ed. (Academic Press, 2008) pp. 139-168.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic view of the experimental setup. L1-L4 planoconvex lenses; L5, L6 fiber collimators; P polaroid; D iris diaphragm.

Fig. 2
Fig. 2

Single spot optimization. Power on the target spot (normalized to total output power) is plotted as a function of iteration step for four optimization runs (colored solid lines). An average over the four runs is displayed as a black solid line and clearly evidences a convergence after 2000 iterations.

Fig. 3
Fig. 3

a) Random speckle pattern on the fiber output without phase modulation. b) Detail of the full 768x768 optimized phase modulation. The linear grating, shifting the beam away from the zero order, has been subtracted. c) When applying the optimized phase modulation a single spot appears on the fiber output. d) Intensity profile across the target spot with (black line) and without (blue line) phase modulation.

Fig. 4
Fig. 4

Multiple target optimization. Incoming light is modulated so that the light that comes out of the multimode fiber is concentrated onto 17 spots arranged to form the letters “cnr”.

Fig. 5
Fig. 5

An holographic movie of a spinning square can be delivered through a 2 meters long multimode fiber by modulating the incoming beam with a time sequence of phase masks.

Fig. 6
Fig. 6

Normalized intensities (vA,B(x)2/vA,B(0)2)on the two target spots A (red dots) and B (black dots) as a function of the weight x that the hologram ϕA has in the superposition. The theoretical prediction given by equation 6 is also shown as solid lines. Gray dashed line is the expectation for full phase and amplitude modulation.

Equations (6)

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

ϕ j * = arg [ ( 1 ξ ) exp [ i ϕ j n 1 ] + ξ exp [ i ( k r j + θ ) ] ]
u j AB = x exp [ i ϕ j A ] + 1 x exp [ i ϕ j B ]
v A = j G j A u j
v A ( x ) = j G j A u j A B | u j A B | j g j A x + 1 x exp [ i θ j ] | x + 1 x exp [ i θ j ] |
v A ( x ) v A ( 0 ) 1 2 π 0 2 π a + b exp [ i θ ] | a + b exp [ i θ ] | d θ = 1 π 0 π a + b cos θ a 2 + b 2 + 2 a b cos θ d θ =
= a b a π E [ 4 a b ( a b ) 2 ] a + b a π k [ 4 a b ( a b ) 2 ]

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