Abstract

Light propagation through multimode fibers suffers from spatial distortions that lead to a scrambled intensity profile. In previous work, the correction of such distortions using various wavefront control methods has been demonstrated in the continuous wave case. However, in the ultra-fast pulse regime, modal dispersion temporally broadens a pulse after propagation. Here, we present a method that compensates for spatial distortions and mitigates temporal broadening due to modal dispersion by a selective phase conjugation process in which only modes of similar group velocities are excited. The selectively excited modes are forced to follow certain paths through the multimode fiber and interfere constructively at the distal tip to form a focused spot with minimal temporal broadening. We demonstrate the delivery of focused 500 fs pulses through a 30 cm long step-index multimode fiber. The achieved pulse duration corresponds to approximately 1/30th of the duration obtained if modal dispersion was not controlled. Moreover, we measured a detailed two-dimensional map of the pulse duration at the output of the fiber and confirmed that the focused spot produces a two-photon absorption effect. This work opens new possibilities for ultra-thin multiphoton imaging through multimode fibers.

© 2015 Optical Society of America

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References

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2014 (1)

2013 (4)

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “High-resolution, lensless endoscope based on digital scanning through a multimode optical fiber,” Biomed. Opt. Express 4(2), 260–270 (2013).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

E. R. Andresen, G. Bouwmans, S. Monneret, and H. Rigneault, “Two-photon lensless endoscope,” Opt. Express 21(18), 20713–20721 (2013).
[Crossref] [PubMed]

2012 (4)

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12(3), 635–639 (2012).
[Crossref] [PubMed]

T. Cižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref] [PubMed]

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref] [PubMed]

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20(10), 10583–10590 (2012).
[Crossref] [PubMed]

2011 (4)

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett. 106(10), 103901 (2011).
[Crossref] [PubMed]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

R. Di Leonardo and S. Bianchi, “Hologram transmission through multi-mode optical fibers,” Opt. Express 19(1), 247–254 (2011).
[Crossref] [PubMed]

T. Čižmár and K. Dholakia, “Shaping the light transmission through a multimode optical fibre: complex transformation analysis and applications in biophotonics,” Opt. Express 19(20), 18871–18884 (2011).
[Crossref] [PubMed]

2006 (1)

H. Itoh, T. Urakami, S. Aoshima, and Y. Tsuchiya, “Femtosecond pulse delivery through long multimode fiber using adaptive pulse synthesis,” Jpn. J. Appl. Phys. 45(7), 5761–5763 (2006).
[Crossref]

2005 (1)

2003 (1)

1999 (1)

1995 (1)

1991 (1)

1987 (1)

1983 (1)

1979 (1)

1976 (1)

A. A. Yariv, “Three-dimensional pictorial transmission in optical fibers,” Appl. Phys. Lett. 28(2), 88–89 (1976).
[Crossref]

Andresen, E. R.

Aoshima, S.

H. Itoh, T. Urakami, S. Aoshima, and Y. Tsuchiya, “Femtosecond pulse delivery through long multimode fiber using adaptive pulse synthesis,” Jpn. J. Appl. Phys. 45(7), 5761–5763 (2006).
[Crossref]

Aulbach, J.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett. 106(10), 103901 (2011).
[Crossref] [PubMed]

Beckwith, P.

Bianchi, S.

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12(3), 635–639 (2012).
[Crossref] [PubMed]

R. Di Leonardo and S. Bianchi, “Hologram transmission through multi-mode optical fibers,” Opt. Express 19(1), 247–254 (2011).
[Crossref] [PubMed]

Bouwmans, G.

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Bromberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

Carpenter, J.

Choi, W.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref] [PubMed]

Choi, Y.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref] [PubMed]

Cižmár, T.

Dasari, R. R.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref] [PubMed]

Dholakia, K.

Di Leonardo, R.

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12(3), 635–639 (2012).
[Crossref] [PubMed]

R. Di Leonardo and S. Bianchi, “Hologram transmission through multi-mode optical fibers,” Opt. Express 19(1), 247–254 (2011).
[Crossref] [PubMed]

Eggleton, B. J.

Fainman, S.

Fang-Yen, C.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref] [PubMed]

Farahi, S.

Fekete, D.

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Fisher, R. A.

Forman, P. R.

Gjonaj, B.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett. 106(10), 103901 (2011).
[Crossref] [PubMed]

Hartmann, H. J.

Horowitz, M. A.

Huang, H.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Itoh, H.

H. Itoh, T. Urakami, S. Aoshima, and Y. Tsuchiya, “Femtosecond pulse delivery through long multimode fiber using adaptive pulse synthesis,” Jpn. J. Appl. Phys. 45(7), 5761–5763 (2006).
[Crossref]

Jahoda, F. C.

Johnson, P. M.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett. 106(10), 103901 (2011).
[Crossref] [PubMed]

Jüptner, W.

Kahn, J. M.

Katz, O.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

Kim, M.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref] [PubMed]

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Lagendijk, A.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett. 106(10), 103901 (2011).
[Crossref] [PubMed]

Lee, K. J.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref] [PubMed]

Luce, B.

Mason, B. L.

McMichael, I.

Monneret, S.

Moser, C.

Mosk, A. P.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett. 106(10), 103901 (2011).
[Crossref] [PubMed]

Nelson, L. E.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Omenetto, F.

Papadopoulos, I. N.

Pepper, D. M.

Pomarico, J.

Psaltis, D.

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Ren, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Richardson, D. J.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Rigneault, H.

Rokitski, R.

Schnars, U.

Schröder, J.

Shen, X.

Silberberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

Small, E.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

Suydam, B. R.

Taylor, A.

Tsuchiya, Y.

H. Itoh, T. Urakami, S. Aoshima, and Y. Tsuchiya, “Femtosecond pulse delivery through long multimode fiber using adaptive pulse synthesis,” Jpn. J. Appl. Phys. 45(7), 5761–5763 (2006).
[Crossref]

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Urakami, T.

H. Itoh, T. Urakami, S. Aoshima, and Y. Tsuchiya, “Femtosecond pulse delivery through long multimode fiber using adaptive pulse synthesis,” Jpn. J. Appl. Phys. 45(7), 5761–5763 (2006).
[Crossref]

Willner, A. E.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Yang, T. D.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref] [PubMed]

Yariv, A.

Yariv, A. A.

A. A. Yariv, “Three-dimensional pictorial transmission in optical fibers,” Appl. Phys. Lett. 28(2), 88–89 (1976).
[Crossref]

Yeh, P.

Yevick, D.

Yoon, C.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref] [PubMed]

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

A. A. Yariv, “Three-dimensional pictorial transmission in optical fibers,” Appl. Phys. Lett. 28(2), 88–89 (1976).
[Crossref]

Biomed. Opt. Express (1)

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (1)

H. Itoh, T. Urakami, S. Aoshima, and Y. Tsuchiya, “Femtosecond pulse delivery through long multimode fiber using adaptive pulse synthesis,” Jpn. J. Appl. Phys. 45(7), 5761–5763 (2006).
[Crossref]

Lab Chip (1)

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12(3), 635–639 (2012).
[Crossref] [PubMed]

Nat. Commun. (1)

T. Cižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref] [PubMed]

Nat. Photonics (2)

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibers,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
[Crossref]

Opt. Express (6)

Opt. Lett. (4)

Phys. Rev. Lett. (2)

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett. 109(20), 203901 (2012).
[Crossref] [PubMed]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of Light Transmission through Opaque Scattering Media in Space and Time,” Phys. Rev. Lett. 106(10), 103901 (2011).
[Crossref] [PubMed]

Science (1)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Other (1)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).

Supplementary Material (1)

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Figures (8)

Fig. 1
Fig. 1 Experimental Setup. Calibration step. The beam from the CPA unit is divided by a polarizing beam splitter PBS into a reference and an object beam. The object beam is coupled into the multimode fiber by a 20X microscope objective OBJ2. The output of the fiber is imaged on the infrared Camera 1 by a 20X microscope objective (OBJ1) and the lens (L1), f = 150 mm, where it is interfered with the reference beam obtained by reflection from the beam splitter BS1. For each delay τ, a digital hologram is recorded. Reconstruction step. The time-sampled field is reconstructed by the reference and phase conjugated using a spatial light modulator SLM. The reconstruction is imaged on the fiber by the lens L1 and the 20X microscope objective OBJ1. The reconstructed field counter-propagates generating the short focused spot on the distal side of the fiber. This spot is imaged on Camera 2 using a 4f system (OBJ2 and lens L2, f = 300 mm). Moreover, the spatio-temporal duration of the phase conjugated spot and its surrounding background is measured on each pixel of a silicon-based detector (Camera 3) using second order (interferometric) autocorrelation, by introducing on the reference the collinear time-delayed replicas required for this measurement, using the Michelson interferometer. The non-linearity in the second order autocorrelation is a two-photon process occurring in the silicon camera. The dashed polygon encloses a possible embodiment of an imaging device based on our method.
Fig. 2
Fig. 2 Propagation and characterization of an ultrashort pulse through a multimode fiber. (a) Optical intensity as seen on the proximal end (Camera 1) containing the superposition of the excited modes arriving at all times. (b) Normalized optical power of (a) over the whole area of the Camera 1 as a function of time. (c)-(f) Time-gated snapshots of the sampled field (Eq. (3)) taken at times τ 1 = 2.9 ps, τ 1 = 7.7 ps, τ 1 = 13.3 ps, and τ 1 = 15.1 ps respectively. Scale bars are 25 μm. Dashed circles indicate the edge of the multimode fiber core.
Fig. 3
Fig. 3 Spatio-temporal characterization of the reconstructed phase conjugated spot. (a)-(d) intensity of the spatial profile measured with Camera 2 and (e) temporal profile of the phase conjugated spots generated from the reconstructed holograms of Fig. 2(c)-2(f) taken at times: τ 1 = 2.9 ps, τ 1 = 7.7 ps, τ 1 = 13.3 ps and τ 1 = 15.1 ps respectively. τ 1 identifies the time at which the hologram was recorded and t is the time dependence of the intensity autocorrelation trace of the phase conjugated spot. (f) Size of the phase conjugated spot as a function of τ 1 . Points represent experimental data and the solid curve a polynomial fit.
Fig. 4
Fig. 4 Comparison between the excitation of a large number of modes and the selective DPC method. (a) Intensity when many fiber modes are excited. (b) Intensity of a phase conjugated spot generated using DPC. The size of the spot is 7 µm and is 16 times more intense that the background. (c) and (d) are the spatio-temporal maps of pulse duration when many fiber modes are excited and when DPC is performed respectively. (e) Envelope of the second order autocorrelation trace of the delivered pulse for the excitation of many fiber modes (black curve, averaged over the camera area) and for the DPC case (blue curve, averaged over the FWHM of the spot size). Dashed red lines are their respective Gaussian fit. The broad pulse (black curve) was scaled to enhance its visibility on the graph. Both pulses possess the same energy. Scale bars are 25 μm. Yellow circles on (a), (b), (c), and (d) indicate the edge of the core of the multimode fiber.
Fig. 5
Fig. 5 Two-photon measurement of the phase conjugated spot. (a) Two-photon signal versus normalized power produced by the phase conjugated spot measured on a silicon-based detector (Camera 3 in Fig. 1). Measured (black curve) and theoretical curve (dashed red curve). (b) Two-photon phase conjugated spot. The spot size is 5 µm. The contrast ratio between the maximum intensity to the average background is 270.
Fig. 6
Fig. 6 Scanning of the phase conjugated focus. The pulsed intensity focused can be generated at different locations. Scale bars are 25 µm.
Fig. 7
Fig. 7 Generation of two time multiplexed phase conjugated spots. The time envelope is measured by time-gated interferometry (solid curve). The phase conjugated pulses are centered at t = 2.9 ps and t = 7.7 ps respectively. Dashed curves: second order autocorrelation envelopes of phase conjugated pulses 1 and 2. Their pulse widths are 500 fs and 800 fs respectively.
Fig. 8
Fig. 8 Normalized peak intensity of the phase conjugated spot versus time τ 1 . Points represent experimental data and the solid lines represent their polynomial fit. The optimal time interval to phase conjugate can be therefore chosen based on the maximized intensity given by the data set.

Equations (4)

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E out (x,y,t)= m=1 M a m (t) ψ m (x,y) e j ϕ m (x,y,t) e j ω 0 t
E ref (x,y,tτ)= a ref (x,y,tτ) e j ω 0 (tτ)
E sampled (x,y, τ 1 )= m= M a m= M b a m ( τ 1 ) ψ m (x,y) e j ϕ m (x,y, τ 1 ) e j ω 0 τ 1
I peak = E spot σ s   σ t

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