Abstract

We present a powerful approach towards full understanding of laser light propagation through multimode optical fibres and control of the light at the fibre output. Transmission of light within a multimode fibre introduces randomization of laser beam amplitude, phase and polarization. We discuss the importance of each of these factors and introduce an experimental geometry allowing full analysis of the light transmission through the multimode fibre and subsequent beam-shaping using a single spatial light modulator. We show that using this approach one can generate an arbitrary output optical field within the accessible field of view and range of spatial frequencies given by fibre core diameter and numerical aperture, respectively, that contains over 80% of the total available power. We also show that this technology has applications in biophotonics. As an example, we demonstrate the manipulation of colloidal microparticles.

© 2011 OSA

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References

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  1. I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
  3. I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
    [CrossRef] [PubMed]
  4. I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
    [CrossRef] [PubMed]
  5. T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
    [CrossRef]
  6. A. J. Thompson, C. Paterson, M. A. A. Neil, C. Dunsby, and P. M. W. French, “Adaptive phase compensation for ultracompact laser scanning endomicroscopy,” Opt. Lett. 36, 1707–1709 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
  16. W. Wadsworth, R. Percival, G. Bouwmans, J. Knight, T. Birks, T. Hedley, and P. S. Russell, “Very high numerical aperture fibers,” Photon. Technol. Lett.16, 843–845 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
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2011 (4)

A. J. Thompson, C. Paterson, M. A. A. Neil, C. Dunsby, and P. M. W. French, “Adaptive phase compensation for ultracompact laser scanning endomicroscopy,” Opt. Lett. 36, 1707–1709 (2011).
[CrossRef] [PubMed]

R. D. Leonardo and S. Bianchi, “Hologram transmission through multi-mode optical fibers,” Opt. Express 19, 247–254 (2011).
[CrossRef] [PubMed]

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[CrossRef]

T. Čižmár, O. Brzobohatý, K. Dholakia, and P. Zemánek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[CrossRef]

2010 (1)

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[CrossRef]

2009 (3)

2008 (3)

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281, 3071–3080 (2008).
[CrossRef]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
[CrossRef] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
[CrossRef] [PubMed]

2007 (3)

2004 (1)

2001 (1)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

1994 (1)

1993 (1)

1986 (1)

1972 (1)

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

Ananthakrishnan, R.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

Ashkin, A.

Bellanger, C.

Bernet, S.

Bianchi, S.

Birks, T.

W. Wadsworth, R. Percival, G. Bouwmans, J. Knight, T. Birks, T. Hedley, and P. S. Russell, “Very high numerical aperture fibers,” Photon. Technol. Lett.16, 843–845 (2004).
[CrossRef]

Bjorkholm, J. E.

Bouwmans, G.

W. Wadsworth, R. Percival, G. Bouwmans, J. Knight, T. Birks, T. Hedley, and P. S. Russell, “Very high numerical aperture fibers,” Photon. Technol. Lett.16, 843–845 (2004).
[CrossRef]

Bragheri, F.

C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I. Cristiani, “Miniaturized all-fibre probe for three-dimensional optical trapping and manipulation,” Nat. Photonics 1, 723–727 (2007).
[CrossRef]

Brignon, A.

Brzobohatý, O.

T. Čižmár, O. Brzobohatý, K. Dholakia, and P. Zemánek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[CrossRef]

Chu, S.

Cižmár, T.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[CrossRef]

T. Čižmár, O. Brzobohatý, K. Dholakia, and P. Zemánek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[CrossRef]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[CrossRef]

T. Čižmár and K. Dholakia, “Tunable Bessel light modes: engineering the axial propagation,” Opt. Express 17, 15558–15570 (2009).
[CrossRef] [PubMed]

Constable, A.

Cristiani, I.

C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I. Cristiani, “Miniaturized all-fibre probe for three-dimensional optical trapping and manipulation,” Nat. Photonics 1, 723–727 (2007).
[CrossRef]

Cunningham, C.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

Daria, V. R.

De Angelis, F.

C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I. Cristiani, “Miniaturized all-fibre probe for three-dimensional optical trapping and manipulation,” Nat. Photonics 1, 723–727 (2007).
[CrossRef]

Dholakia, K.

T. Čižmár, O. Brzobohatý, K. Dholakia, and P. Zemánek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[CrossRef]

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[CrossRef]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[CrossRef]

T. Čižmár and K. Dholakia, “Tunable Bessel light modes: engineering the axial propagation,” Opt. Express 17, 15558–15570 (2009).
[CrossRef] [PubMed]

Di Fabrizio, E.

C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I. Cristiani, “Miniaturized all-fibre probe for three-dimensional optical trapping and manipulation,” Nat. Photonics 1, 723–727 (2007).
[CrossRef]

Di Leonardo, R.

Dong, B. Z.

Druon, F.

Dunsby, C.

Dziedzic, J. M.

Ersoy, O. K.

French, P. M. W.

Georges, P.

Gerchberg, R.

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Glückstad, J.

Gu, B. Y.

Guck, J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

Hanna, M.

Hedley, T.

W. Wadsworth, R. Percival, G. Bouwmans, J. Knight, T. Birks, T. Hedley, and P. S. Russell, “Very high numerical aperture fibers,” Photon. Technol. Lett.16, 843–845 (2004).
[CrossRef]

Huignard, J. P.

Ianni, F.

Kas, J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

Kim, J.

Knight, J.

W. Wadsworth, R. Percival, G. Bouwmans, J. Knight, T. Birks, T. Hedley, and P. S. Russell, “Very high numerical aperture fibers,” Photon. Technol. Lett.16, 843–845 (2004).
[CrossRef]

Lagendijk, A.

Leonardo, R. D.

Liberale, C.

C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I. Cristiani, “Miniaturized all-fibre probe for three-dimensional optical trapping and manipulation,” Nat. Photonics 1, 723–727 (2007).
[CrossRef]

Mahmood, H.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

Mazilu, M.

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[CrossRef]

Minzioni, P.

C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I. Cristiani, “Miniaturized all-fibre probe for three-dimensional optical trapping and manipulation,” Nat. Photonics 1, 723–727 (2007).
[CrossRef]

Moon, T.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

Mosk, A. P.

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
[CrossRef] [PubMed]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
[CrossRef] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281, 3071–3080 (2008).
[CrossRef]

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

Neil, M. A. A.

Paterson, C.

Paurisse, M.

Percival, R.

W. Wadsworth, R. Percival, G. Bouwmans, J. Knight, T. Birks, T. Hedley, and P. S. Russell, “Very high numerical aperture fibers,” Photon. Technol. Lett.16, 843–845 (2004).
[CrossRef]

Pitzek, M.

Ritsch-Marte, M.

Rodrigo, P. J.

Ruocco, G.

Russell, P. S.

W. Wadsworth, R. Percival, G. Bouwmans, J. Knight, T. Birks, T. Hedley, and P. S. Russell, “Very high numerical aperture fibers,” Photon. Technol. Lett.16, 843–845 (2004).
[CrossRef]

Saxton, W.

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Steiger, R.

Thalhammer, G.

Thompson, A. J.

van Putten, E. G.

Vellekoop, I. M.

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
[CrossRef] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281, 3071–3080 (2008).
[CrossRef]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
[CrossRef] [PubMed]

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

Wadsworth, W.

W. Wadsworth, R. Percival, G. Bouwmans, J. Knight, T. Birks, T. Hedley, and P. S. Russell, “Very high numerical aperture fibers,” Photon. Technol. Lett.16, 843–845 (2004).
[CrossRef]

Yang, G. Z.

Zemánek, P.

T. Čižmár, O. Brzobohatý, K. Dholakia, and P. Zemánek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[CrossRef]

Zhuang, J. Y.

Appl. Opt. (1)

Biophys. J. (1)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

Laser Phys. Lett. (1)

T. Čižmár, O. Brzobohatý, K. Dholakia, and P. Zemánek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[CrossRef]

Nat. Photonics (3)

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[CrossRef]

C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I. Cristiani, “Miniaturized all-fibre probe for three-dimensional optical trapping and manipulation,” Nat. Photonics 1, 723–727 (2007).
[CrossRef]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[CrossRef]

Opt. Commun. (1)

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281, 3071–3080 (2008).
[CrossRef]

Opt. Express (6)

Opt. Lett. (5)

Optik (1)

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Phys. Rev. Lett. (2)

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101, 120601 (2008).
[CrossRef] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

Other (1)

W. Wadsworth, R. Percival, G. Bouwmans, J. Knight, T. Birks, T. Hedley, and P. S. Russell, “Very high numerical aperture fibers,” Photon. Technol. Lett.16, 843–845 (2004).
[CrossRef]

Supplementary Material (2)

» Media 1: MOV (28 KB)     
» Media 2: MOV (1180 KB)     

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Figures (10)

Fig. 1
Fig. 1

Principle of the optimization procedure. a-d - standard method [5] applied for the optimization of multimode optical fibre; e-g - enhanced approach allowing full systematic transformation analysis including phase, amplitude and polarization. Using an external reference eliminates problem with ‘blind spots’ and crucially provides the missing phase and polarization calibration of output modes.

Fig. 2
Fig. 2

The experimental geometry allowing generating of individual input modes in both polarization states and feedback loop stabilizing the phase relation between multimode optical fibre path and the external reference pathway. L1-L8 - lenses, M1-M5 - mirrors, PBS - polarizing beam-splitter, NPBS - non-polarizing beam-splitter, PBD - polarizing beam displacer, λ/2 - half-wave plates, MO1 and MO2 - microscope objectives.

Fig. 3
Fig. 3

Example of modulation functions corresponding to single output mode. These functions are results of the optimization procedure analyzing intensity signal for one CCD pixel. The complex transformation contains a series of such four functions for every output mode.

Fig. 4
Fig. 4

Example of an output mode generated within the experimental geometry. The mode for (u,v,w) = (60, 60, s) was recorded by CCD while applying phase only modulation arg [ M k , l 60 , 60 , s ] at the SLM, where M k , l 60 , 60 , s was designed following equation 1. We show both CCD output polarization regions as well as the optimal fit with the expected intensity distribution of Airy disc.

Fig. 8
Fig. 8

Generation of output modes using internal reference mode. First two columns show output mode intensities and their histograms for single input polarizations (equation 3). The third column shows data for phase only superposition of input polarizations (equation 4). Last column shows results for complex superposition of input polarizations (equation 1).

Fig. 9
Fig. 9

Generation of output modes using external reference mode. Figure is organized the same way as fig. 8

Fig. 10
Fig. 10

Simultaneous generation of two output modes with tunable power ratio. a - numerical simulation for phase only (solid lines) and complex (dashed) superposition of output modes. Analytical functions for this dependencies are derived in [8]. b - c experimental results for the case of output modes combined by phase-only superposition (equation 6) where individual modes were generated by: b, - single polarization (equation 3); c, - phase-only superposition of input polarizations (equation 4) and d, - complex superposition of input polarizations (equation 1). Subplot d shows the optimal case of both, the input polarizations and the output modes combined by complex superposition (equations 1 and 5).

Fig. 5
Fig. 5

Simultaneous generation of output modes by complex superposition and G-S algorithm. Top: CCD frames showing different numbers of modes. Bottom: total power in output modes and averaged power per mode for the cases of complex superposition and G-S algorithm. Solid lines show the expected behaviour, considering that the total power distributed between individual modes is conserved.

Fig. 6
Fig. 6

G-S algorithm based beam shaping of the output of a multimode fibre. The target distribution is formed by modes with minimal mutual distance of 4 CCD pixels, that corresponds to 2.7 μm at fibre output facet, or 0.2× the size of the measured output mode diameter (central core of the fitted Airy disk). Output modes are strongly influenced by unwanted interference effects when combined by complex superposition (equation 5) - iteration 0. The G-S algorithm gradually improves the amplitude distribution as it converges after around 100 iterations. Results for every iteration are presented in (Media 1).

Fig. 7
Fig. 7

2-D optical manipulation of 16 polystyrene micro-particles each of 3μm in diameter. Both the trapping beams (output modes) and the white-light illumination are delivered by the multimode optical fibre. See also (Media 2), that is 3× faster than real-time.

Equations (9)

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

M k , l u , v , w = A k , l , s u , v , w e [ i ( P k , l , s u , v , w + G s ) ] + A k , l , p u , v , w e [ i ( P k , l , p u , v , w + G p ) ] .
M k , l u , v , w = A k , l , s u , v , w e [ i ( P k , l , s u , v , w + G s ) ] ,
M k , l u , v , w = e [ i ( P k , l , s u , v , w + G s ) ] + e [ i ( P k , l , p u , v , w + G p ) ] ,
M k , l N = q = 1 N a q M k , l u q , v q , w q ,
M k , l N = q = 1 N a q e i arg [ M k , l u q , v q , w q ] .
t M ̄ k , l N = e i arg [ t 1 M k , l N ] ,
t c q = k , l t M ̄ k , l N M k , l u q , v q , w q ,
t c ̄ q = a q e i arg [ t c q ] ,
t M k , l N = q = 1 N t c ̄ q M k , l u q , v q , w q .

Metrics