Abstract

Light propagation in multimode fibers is typically assumed to be extremely sensitive to changes in geometry. We study here a particular configuration where an S-shaped bend is translated between two sections of fiber. In this sliding bend configuration, we show that nearly constant propagation characteristics can be obtained in certain fibers. Several fibers were tested using a bend with a peak radius of curvature of 25 mm. We found large differences in bending behavior between fibers of varying core diameters and numerical apertures. Fibers with a large numerical aperture are found to be more stable. In several fibers, the bend can be translated over a distance of 25 mm with a limited impact on imaging performance. The experimental results are confirmed using simulations. Our findings shed a new light on bending sensitivity in multimode fibers, and open up more possibilities for their use as imaging devices.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2017 (1)

2016 (2)

2015 (8)

2014 (1)

2013 (4)

2012 (3)

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]

T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (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)

2007 (1)

1997 (1)

1996 (1)

1983 (1)

A. Friesem, U. Levy, and Y. Silberberg, “Parallel transmission of images through single optical fibers,” Proc. IEEE 71(2), 208–221 (1983).
[Crossref]

1982 (1)

1976 (1)

1971 (1)

1967 (1)

E. Spitz and A. Werts, ““Transmission des images à travers une fibre optique,” Comptes Rendus Hebd,” Séances Académie Sci. Sér. B 264, 1015–1018 (1967).

1961 (1)

Al-Mohy, A. H.

A. H. Al-Mohy and N. J. Higham, “Computing the action of the matrix exponential, with an application to exponential integrators,” SIAM J. Sci. Comput. 33(2), 488–511 (2011).
[Crossref]

Anderson, D. Z.

Andresen, E. R.

Bianchi, S.

Bolshtyansky, M. A.

Bossy, E.

Bouwmans, G.

Caravaca-Aguirre, A. M.

Choi, W.

D. Kim, J. Moon, M. Kim, T. D. Yang, J. Kim, E. Chung, and W. Choi, “Toward a miniature endomicroscope: pixelation-free and diffraction-limited imaging through a fiber bundle,” Opt. Lett. 39(7), 1921–1924 (2014).
[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]

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]

Chung, E.

Cižmár, T.

M. Plöschner, T. Tyc, and T. Čižmár, “Seeing through chaos in multimode fibres,” Nat. Photonics 9(8), 529–535 (2015).
[Crossref]

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

Conkey, D. B.

Cossart, R.

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.

Dunning, G. J.

Dunsby, C.

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.

French, P. M.

French, P. M. W.

Friesem, A.

A. Friesem, U. Levy, and Y. Silberberg, “Parallel transmission of images through single optical fibers,” Proc. IEEE 71(2), 208–221 (1983).
[Crossref]

Gloge, D.

Goorden, S. A.

Goy, A.

Gu, R. Y.

Higham, N. J.

A. H. Al-Mohy and N. J. Higham, “Computing the action of the matrix exponential, with an application to exponential integrators,” SIAM J. Sci. Comput. 33(2), 488–511 (2011).
[Crossref]

Huignard, J.-P.

Kahn, J. M.

Kim, D.

Kim, J.

Kim, M.

D. Kim, J. Moon, M. Kim, T. D. Yang, J. Kim, E. Chung, and W. Choi, “Toward a miniature endomicroscope: pixelation-free and diffraction-limited imaging through a fiber bundle,” Opt. Lett. 39(7), 1921–1924 (2014).
[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]

Kim, Y.

Knight, J. C.

Laporte, G. P. J.

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]

Levy, U.

A. Friesem, U. Levy, and Y. Silberberg, “Parallel transmission of images through single optical fibers,” Proc. IEEE 71(2), 208–221 (1983).
[Crossref]

Lind, R. C.

Loterie, D.

Mahalati, R. N.

Mitchell, C.

Monneret, S.

Moon, J.

Morales-Delgado, E. E.

Moser, C.

G. P. J. Laporte, N. Stasio, C. Moser, and D. Psaltis, “Enhanced resolution in a multimode fiber imaging system,” Opt. Express 23(21), 27484–27493 (2015).
[Crossref] [PubMed]

E. E. Morales-Delgado, D. Psaltis, and C. Moser, “Two-photon imaging through a multimode fiber,” Opt. Express 23(25), 32158–32170 (2015).
[Crossref] [PubMed]

N. Stasio, A. Shibukawa, I. N. Papadopoulos, S. Farahi, O. Simandoux, J.-P. Huignard, E. Bossy, C. Moser, and D. Psaltis, “Towards new applications using capillary waveguides,” Biomed. Opt. Express 6(12), 4619–4631 (2015).
[Crossref] [PubMed]

D. Loterie, S. A. Goorden, D. Psaltis, and C. Moser, “Confocal microscopy through a multimode fiber using optical correlation,” Opt. Lett. 40(24), 5754–5757 (2015).
[Crossref] [PubMed]

N. Stasio, D. B. Conkey, C. Moser, and D. Psaltis, “Light control in a multicore fiber using the memory effect,” Opt. Express 23(23), 30532–30544 (2015).
[Crossref] [PubMed]

D. Loterie, S. Farahi, I. Papadopoulos, A. Goy, D. Psaltis, and C. Moser, “Digital confocal microscopy through a multimode fiber,” Opt. Express 23(18), 23845–23858 (2015).
[Crossref] [PubMed]

S. Farahi, D. Ziegler, I. N. Papadopoulos, D. Psaltis, and C. Moser, “Dynamic bending compensation while focusing through a multimode fiber,” Opt. Express 21(19), 22504–22514 (2013).
[Crossref] [PubMed]

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]

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]

Neil, M. A.

Neil, M. A. A.

Niv, E.

Papadopoulos, I.

Papadopoulos, I. N.

Paterson, C.

Piestun, R.

Plöschner, M.

M. Plöschner, T. Tyc, and T. Čižmár, “Seeing through chaos in multimode fibres,” Nat. Photonics 9(8), 529–535 (2015).
[Crossref]

Psaltis, D.

G. P. J. Laporte, N. Stasio, C. Moser, and D. Psaltis, “Enhanced resolution in a multimode fiber imaging system,” Opt. Express 23(21), 27484–27493 (2015).
[Crossref] [PubMed]

E. E. Morales-Delgado, D. Psaltis, and C. Moser, “Two-photon imaging through a multimode fiber,” Opt. Express 23(25), 32158–32170 (2015).
[Crossref] [PubMed]

N. Stasio, A. Shibukawa, I. N. Papadopoulos, S. Farahi, O. Simandoux, J.-P. Huignard, E. Bossy, C. Moser, and D. Psaltis, “Towards new applications using capillary waveguides,” Biomed. Opt. Express 6(12), 4619–4631 (2015).
[Crossref] [PubMed]

D. Loterie, S. A. Goorden, D. Psaltis, and C. Moser, “Confocal microscopy through a multimode fiber using optical correlation,” Opt. Lett. 40(24), 5754–5757 (2015).
[Crossref] [PubMed]

N. Stasio, D. B. Conkey, C. Moser, and D. Psaltis, “Light control in a multicore fiber using the memory effect,” Opt. Express 23(23), 30532–30544 (2015).
[Crossref] [PubMed]

D. Loterie, S. Farahi, I. Papadopoulos, A. Goy, D. Psaltis, and C. Moser, “Digital confocal microscopy through a multimode fiber,” Opt. Express 23(18), 23845–23858 (2015).
[Crossref] [PubMed]

S. Farahi, D. Ziegler, I. N. Papadopoulos, D. Psaltis, and C. Moser, “Dynamic bending compensation while focusing through a multimode fiber,” Opt. Express 21(19), 22504–22514 (2013).
[Crossref] [PubMed]

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]

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]

Rigneault, H.

Schermer, R. T.

Shibukawa, A.

Silberberg, Y.

A. Friesem, U. Levy, and Y. Silberberg, “Parallel transmission of images through single optical fibers,” Proc. IEEE 71(2), 208–221 (1983).
[Crossref]

Simandoux, O.

Sivankutty, S.

Snitzer, E.

Spitz, E.

E. Spitz and A. Werts, ““Transmission des images à travers une fibre optique,” Comptes Rendus Hebd,” Séances Académie Sci. Sér. B 264, 1015–1018 (1967).

Stasio, N.

Stone, J. M.

Thompson, A. J.

Tyc, T.

M. Plöschner, T. Tyc, and T. Čižmár, “Seeing through chaos in multimode fibres,” Nat. Photonics 9(8), 529–535 (2015).
[Crossref]

Warren, S. C.

Werts, A.

E. Spitz and A. Werts, ““Transmission des images à travers une fibre optique,” Comptes Rendus Hebd,” Séances Académie Sci. Sér. B 264, 1015–1018 (1967).

Yang, T. D.

D. Kim, J. Moon, M. Kim, T. D. Yang, J. Kim, E. Chung, and W. Choi, “Toward a miniature endomicroscope: pixelation-free and diffraction-limited imaging through a fiber bundle,” Opt. Lett. 39(7), 1921–1924 (2014).
[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]

Yariv, A.

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]

Zel’dovich, B. Y.

Ziegler, D.

Appl. Opt. (2)

Biomed. Opt. Express (2)

J. Opt. Soc. Am. (2)

Nat. Commun. (1)

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

Nat. Photonics (1)

M. Plöschner, T. Tyc, and T. Čižmár, “Seeing through chaos in multimode fibres,” Nat. Photonics 9(8), 529–535 (2015).
[Crossref]

Opt. Express (14)

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]

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

G. P. J. Laporte, N. Stasio, C. Moser, and D. Psaltis, “Enhanced resolution in a multimode fiber imaging system,” Opt. Express 23(21), 27484–27493 (2015).
[Crossref] [PubMed]

E. E. Morales-Delgado, D. Psaltis, and C. Moser, “Two-photon imaging through a multimode fiber,” Opt. Express 23(25), 32158–32170 (2015).
[Crossref] [PubMed]

R. T. Schermer, “Mode scalability in bent optical fibers,” Opt. Express 15(24), 15674–15701 (2007).
[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]

D. Loterie, S. Farahi, I. Papadopoulos, A. Goy, D. Psaltis, and C. Moser, “Digital confocal microscopy through a multimode fiber,” Opt. Express 23(18), 23845–23858 (2015).
[Crossref] [PubMed]

S. Sivankutty, E. R. Andresen, R. Cossart, G. Bouwmans, S. Monneret, and H. Rigneault, “Ultra-thin rigid endoscope: two-photon imaging through a graded-index multi-mode fiber,” Opt. Express 24(2), 825–841 (2016).
[Crossref] [PubMed]

N. Stasio, D. B. Conkey, C. Moser, and D. Psaltis, “Light control in a multicore fiber using the memory effect,” Opt. Express 23(23), 30532–30544 (2015).
[Crossref] [PubMed]

S. Farahi, D. Ziegler, I. N. Papadopoulos, D. Psaltis, and C. Moser, “Dynamic bending compensation while focusing through a multimode fiber,” Opt. Express 21(19), 22504–22514 (2013).
[Crossref] [PubMed]

A. M. Caravaca-Aguirre and R. Piestun, “Single multimode fiber endoscope,” Opt. Express 25(3), 1656 (2017).
[Crossref]

A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express 21(10), 12881–12887 (2013).
[Crossref] [PubMed]

R. Y. Gu, R. N. Mahalati, and J. M. Kahn, “Design of flexible multi-mode fiber endoscope,” Opt. Express 23(21), 26905–26918 (2015).
[Crossref] [PubMed]

S. C. Warren, Y. Kim, J. M. Stone, C. Mitchell, J. C. Knight, M. A. A. Neil, C. Paterson, P. M. W. French, and C. Dunsby, “Adaptive multiphoton endomicroscopy through a dynamically deformed multicore optical fiber using proximal detection,” Opt. Express 24(19), 21474–21484 (2016).
[Crossref] [PubMed]

Opt. Lett. (6)

Phys. Rev. Lett. (1)

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]

Proc. IEEE (1)

A. Friesem, U. Levy, and Y. Silberberg, “Parallel transmission of images through single optical fibers,” Proc. IEEE 71(2), 208–221 (1983).
[Crossref]

Séances Académie Sci. Sér. B (1)

E. Spitz and A. Werts, ““Transmission des images à travers une fibre optique,” Comptes Rendus Hebd,” Séances Académie Sci. Sér. B 264, 1015–1018 (1967).

SIAM J. Sci. Comput. (1)

A. H. Al-Mohy and N. J. Higham, “Computing the action of the matrix exponential, with an application to exponential integrators,” SIAM J. Sci. Comput. 33(2), 488–511 (2011).
[Crossref]

Other (2)

D. Loterie, S. Farahi, D. Psaltis, and C. Moser, “Complex pattern projection through a multimode fiber,” in Adaptive Optics and Wavefront Control for Biological Systems (2015), Vol. 9335, p. 93350I.

P. J. Schreier and L. L. Scharf, “Correlation analysis,” in Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals (Cambridge University Press, 2010), pp. 85–88.

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Figures (6)

Fig. 1
Fig. 1

Experimental geometry for imaging during translation of a bend in the fiber. Collimated laser light is modulated by a spatial light modulator, and relayed via a lens (L2) and a microscope objective (MO2) to a multimode fiber. The fiber (represented in light blue) passes through a sliding jacket (represented in white) that allows an S-bend with constant shape to be translated between the two ends of the fiber. The output of the fiber is relayed by a microscope objective (MO1) and a lens (L1) to a camera, where a holographic recording can be made by using an off-axis reference beam. The bend has a peak curvature of 40 m−1 and the overall length of the fiber is approximately 250 mm.

Fig. 2
Fig. 2

Shape of the bend used in our experiments.

Fig. 3
Fig. 3

Autocorrelation of the output as the bend is translated, for a random input. (a) Experimental autocorrelation of the speckle pattern at the output of the fiber as the bend is translated. (b) Simulated autocorrelation for the step index fibers. Refer to Table 1 for the fiber specifications.

Fig. 4
Fig. 4

Change in intensity of a focused spot due to the translation of the bend. (a) Experiments and (b) simulations for the intensity of a spot created in the middle of the fiber's core. (c) Experiments and (d) simulations for a spot created half-way between the center and the edge of the fiber core. Refer to Table 1 for the specifications of the various fibers.

Fig. 5
Fig. 5

Patterns at the tip of a fiber. (a) Spots before translating the bend and (b) after 25 mm translation. The average full width at half maximum of the spots is 480 nm. The inset is a zoom on the center of the spot grid. (c) Line before translating the bend and (d) after 25 mm translation, showing the extent of the central region of the core where bending resilience is lower. The patterns shown here were made via fiber S5 (70 μm core, NA 0.64). The boundary of the core is indicated with a dashed circle. The scale bars are 10 μm.

Fig. 6
Fig. 6

Simulations for a U-shaped bend. (a) U-shaped bend having the same absolute curvature at every point as the bend in Fig. 2, except the curvature is everywhere positive. (b) Autocorrelation trace versus horizontal translation of the bend. (c) Intensity of a spot created in the center of the fiber core and (d) intensity of an off-center spot versus translation of the bend.

Tables (1)

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Table 1 List of fibers and nominal specifications.

Equations (4)

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ρ= | f,g | f g = | k=1 N f k g k * | k=1 N | f k | 2 k=1 N | g k | 2
E n (r,ϕ,z,t)=( E r,n (r) E ϕ,n (r) E z,n (r) ) e i ν n ϕ e i β n z e iωt
B nm = β n δ nm ( n core k 0 ρ/ξ ) E n | x | E m
E n | x | E m = E n * (x,y)x E m (x,y)dxdy

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