Abstract

We present experimental and numerical studies on principal modes in a multimode fiber with mode coupling. By applying external stress to the fiber and gradually adjusting the stress, we have realized a transition from weak to strong mode coupling, which corresponds to the transition from single scattering to multiple scattering in mode space. Our experiments show that principal modes have distinct spatial and spectral characteristic in the weak and strong mode coupling regimes. We also investigate the bandwidth of the principal modes, in particular, the dependence of the bandwidth on the delay time, and the effects of the mode-dependent loss. By analyzing the path-length distributions, we discover two distinct mechanisms that are responsible for the bandwidth of principal modes in weak and strong mode coupling regimes. Their interplay leads to a non-monotonic transition of the average principal mode bandwidth from weak to strong mode coupling. Taking into account the mode-dependent loss in the fiber, our numerical results are in qualitative agreement with our experimental observations. Our study paves the way for exploring potential applications of principal modes in communication, imaging and spectroscopy.

© 2017 Optical Society of America

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2016 (5)

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117(8), 086803 (2016).
[Crossref] [PubMed]

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref] [PubMed]

W. Xiong, P. Ambichl, Y. Bromberg, B. Redding, S. Rotter, and H. Cao, “ Spatiotemporal control of light transmission through a multimode fiber with strong mode mixing,” Phys. Rev. Lett. 117, 053901 (2016).
[Crossref]

L. V. Amitonova, A. Descloux, J. Petschulat, M. H. Frosz, G. Ahmed, F. Babic, X. Jiang, A. P. Mosk, P. S. J. Russell, and P. W. H. Pinkse, “High-resolution wavefront shaping with a photonic crystal fiber for multimode fiber imaging,” Opt. Lett. 41(3), 497–500 (2016).
[Crossref] [PubMed]

S. F. Liew, B. Redding, M. A. Choma, H. D. Tagare, and H. Cao, “Broadband multimode fiber spectrometer,” Opt. Lett. 41(9), 2029–2032 (2016).
[Crossref] [PubMed]

2015 (9)

J. Carpenter, J. E. Benjamin, and J. Schröder, “Observation of Eisenbud-Wigner-Smith states as principal modes in multimode fibre,” Nat. Photon. 9, 751 (2015).
[Crossref]

G. Milione, D. A. Nolan, and R. R. Alfano, “Determining principal modes in a multimode optical fiber using the nide dependent signal delay method,” J. Opt. Soc. Am. B 32(1) 143–149 (2015).
[Crossref]

E. E. Morales-Delgado, S. Farahi, I. N. Papadppoulos, D. Psaltis, and C. Moser, “Delivery of focused short pulses through a multimode fiber,” Opt. Express 23(7), 9109–9120 (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]

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

Z. Shi and A. Z. Genack, “Dynamic and spectral properties of transmission eigenchannels in random media,” Phys. Rev. B 92(18), 184202 (2015).
[Crossref]

M. Davy, Z. Shi, J. Park, C. Tian, and A. Z. Genack, “Universal structure of transmission eigenchannels inside opaque media,” Nat. Commun. 6, 6893 (2015).
[Crossref] [PubMed]

R. Sarma, A. Yamilov, S. F. Liew, M. Guy, and H. Cao, “Control of mesoscopic transport by modifying transmission channels in opaque media,” Phys. Rev. B 92(21), 214206 (2015).
[Crossref]

D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep. 5, 10347 (2015).
[Crossref] [PubMed]

2014 (8)

B. Gérardin, J. Laurent, A. Derode, C. Prada, and A. Aubry, “Full transmission and reflection of waves propagating through a maze of disorder,” Phys. Rev. Lett. 113(17), 173901 (2014).
[Crossref] [PubMed]

S. M. Popoff, A. Goetschy, S. F. Liew, A. D. Stone, and H. Cao, “Coherent control of total transmission of light through disordered media,” Phys. Rev. Lett. 112(13), 133903 (2014).
[Crossref] [PubMed]

R. Barankov and J. Mertz, “High-throughput imaging of self-luminous objects through a single optical fibre,” Nat. Commun. 5, 5581 (2014).
[Crossref] [PubMed]

J. Doppler, J. A. Méndez-Bermúdez, J. Feist, O. Dietz, D. O. Krimer, N. M. Makarov, F. M. Izrailev, and S. Rotter, “Reflection resonances in surface-disordered waveguides: strong higher-order effects of the disorder,” New J. Phys. 16, 053026 (2014).
[Crossref]

D. A. Nolan, G. Milione, and R. R. Alfano, “Bandwidth analysis of the principal states superimposed from vortex modes propagating in an optical fiber,” Proc. SPIE 8999, 899911 (2014).
[Crossref]

B. Redding, S. M. Popoff, Y. Bromberg, M. A. Choma, and H. Cao, “Noise analysis of spectrometers based on speckle pattern reconstruction,” Appl. Opt. 53(3), 410–417 (2014).
[Crossref] [PubMed]

K. P. Ho and J. M. Kahn, “Linear propagation effects in mode-division multiplexing systems,” J. Lightwave Technol. 32(4), 614–628 (2014).
[Crossref]

B. Redding, M. Alam, M. Seifert, and H. Cao, “High-resolution and broadband all-fiber spectrometers,” Optica 1(3), 175–180 (2014).
[Crossref]

2013 (6)

B. Redding, S. M. Popoff, and H. Cao, “All-fiber spectrometer based on speckle pattern reconstruction,” Opt. Express 21(5), 6584–6600 (2013).
[Crossref] [PubMed]

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]

Z. Shi, M. Davy, J. Wang, and A. Z. Genack, “Focusing through random media in space and time: a transmission matrix approach,” Opt. Lett. 38(15), 2714–2716 (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,” Opt. Express 4(2), 260–270 (2013).
[Crossref]

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

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. K. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref]

2012 (11)

Z. Shi and A. Z. Genack, “Transmission eigenvalues and the bare conductance in the crossover to Anderson localization,” Phys. Rev. Lett. 108(4), 043901 (2012).
[Crossref] [PubMed]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. H. Park, and W Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photon. 6(9), 581–585 (2012).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photon. 6(5), 283–292 (2012).
[Crossref]

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

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

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

C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Stokes-space analysis of modal dispersion in fibers with multiple mode transmission,” Opt. Express 20(11), 11718–11733 (2012).
[Crossref] [PubMed]

A. A. Juarez, C. A. Bunge, S. Warm, and K. Petermann, “Perspectives of principal mode transmission in mode-division-multiplex operation,” Opt. Express 20(13), 13810–13824 (2012).
[Crossref] [PubMed]

B. Redding and H. Cao, “Using a multimode fiber as a high-resolution, low-loss spectrometer,” Opt. Lett. 37(16), 3384–3386 (2012).
[Crossref]

J. Aulbach, B. Gjonaj, P. Johnson, and A. Lagendijk, “Spatiotemporal focusing in opaque scattering media by wave front shaping with nonlinear feedback,” Opt. Express 20(28), 29237–29251 (2012).
[Crossref]

J. Carpenter, B. C. Thomsen, and T. D. Wiilkinson, “Degenerate Mode-Group Division Multiplexing,” J. Lightwave Technol. 30(24), 3946–3952 (2012).
[Crossref]

2011 (7)

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]

K. P. Ho and J. M. Kahn, “Statistics of group delays in multimode fiber with strong mode coupling,” J. Lightwave Technol. 29(21), 3119–3128 (2011).
[Crossref]

S. Rotter, P. Ambichl, and F. Libisch, “Generating particlelike scattering states in wave transport,” Phys. Rev. Lett. 106, 120602 (2011).
[Crossref] [PubMed]

W. Choi, A. P. Mosk, Q. H. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83(13), 134207 (2011).
[Crossref]

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

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref] [PubMed]

J. Aulbach, B. Gjonaj, P. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[Crossref] [PubMed]

2010 (1)

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101(12), 120601 (2008).
[Crossref] [PubMed]

2007 (1)

2005 (1)

2000 (1)

S. Rotter, J.-Z. Tang, L. Wirtz, J. Trost, and J. Burgdörfer, “Modular recursive Green’s function method for ballistic quantum transport,” Phys. Rev. B 62(3), 1950 (2000).
[Crossref]

1998 (1)

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281, 962–967 (1998).
[Crossref] [PubMed]

1990 (1)

R. A. Jalabert, H. U. Baranger, and A. D. Stone, “Conductance fluctuations in the ballistic regime: A probe of quantum chaos?” Phys. Rev. Lett. 65, 2442 (1990).
[Crossref] [PubMed]

1960 (1)

F. T. Smith, “Lifetime matrix in collision theory,” Phys. Rev. 118, 349 (1960).
[Crossref]

1955 (1)

E. P. Wigner, “Lower limit for the energy derivative of the scattering phase shift,” Phys. Rev. 98, 145 (1955).
[Crossref]

Ahmed, G.

Alam, M.

Alfano, R. R.

G. Milione, D. A. Nolan, and R. R. Alfano, “Determining principal modes in a multimode optical fiber using the nide dependent signal delay method,” J. Opt. Soc. Am. B 32(1) 143–149 (2015).
[Crossref]

D. A. Nolan, G. Milione, and R. R. Alfano, “Bandwidth analysis of the principal states superimposed from vortex modes propagating in an optical fiber,” Proc. SPIE 8999, 899911 (2014).
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Mao, W.

McCabe, D. J.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref] [PubMed]

Mecozzi, A.

Méndez-Bermúdez, J. A.

J. Doppler, J. A. Méndez-Bermúdez, J. Feist, O. Dietz, D. O. Krimer, N. M. Makarov, F. M. Izrailev, and S. Rotter, “Reflection resonances in surface-disordered waveguides: strong higher-order effects of the disorder,” New J. Phys. 16, 053026 (2014).
[Crossref]

Mertz, J.

R. Barankov and J. Mertz, “High-throughput imaging of self-luminous objects through a single optical fibre,” Nat. Commun. 5, 5581 (2014).
[Crossref] [PubMed]

Milione, G.

G. Milione, D. A. Nolan, and R. R. Alfano, “Determining principal modes in a multimode optical fiber using the nide dependent signal delay method,” J. Opt. Soc. Am. B 32(1) 143–149 (2015).
[Crossref]

D. A. Nolan, G. Milione, and R. R. Alfano, “Bandwidth analysis of the principal states superimposed from vortex modes propagating in an optical fiber,” Proc. SPIE 8999, 899911 (2014).
[Crossref]

Morales-Delgado, E. E.

Moser, C.

Mosk, A. P.

L. V. Amitonova, A. Descloux, J. Petschulat, M. H. Frosz, G. Ahmed, F. Babic, X. Jiang, A. P. Mosk, P. S. J. Russell, and P. W. H. Pinkse, “High-resolution wavefront shaping with a photonic crystal fiber for multimode fiber imaging,” Opt. Lett. 41(3), 497–500 (2016).
[Crossref] [PubMed]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photon. 6(5), 283–292 (2012).
[Crossref]

J. Aulbach, B. Gjonaj, P. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[Crossref] [PubMed]

W. Choi, A. P. Mosk, Q. H. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83(13), 134207 (2011).
[Crossref]

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101(12), 120601 (2008).
[Crossref] [PubMed]

Mounaix, M.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref] [PubMed]

Nelson, L. E.

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

Niv, E.

Nolan, D. A.

G. Milione, D. A. Nolan, and R. R. Alfano, “Determining principal modes in a multimode optical fiber using the nide dependent signal delay method,” J. Opt. Soc. Am. B 32(1) 143–149 (2015).
[Crossref]

D. A. Nolan, G. Milione, and R. R. Alfano, “Bandwidth analysis of the principal states superimposed from vortex modes propagating in an optical fiber,” Proc. SPIE 8999, 899911 (2014).
[Crossref]

Panicker, R. A.

Papadopoulos, I.

Papadopoulos, I. N.

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

Papadppoulos, I. N.

Park, J.

M. Davy, Z. Shi, J. Park, C. Tian, and A. Z. Genack, “Universal structure of transmission eigenchannels inside opaque media,” Nat. Commun. 6, 6893 (2015).
[Crossref] [PubMed]

Park, Q. H.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. H. Park, and W Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photon. 6(9), 581–585 (2012).
[Crossref]

W. Choi, A. P. Mosk, Q. H. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83(13), 134207 (2011).
[Crossref]

Park, Y. K.

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. K. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref]

Petermann, K.

Petrenko, S.

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117(8), 086803 (2016).
[Crossref] [PubMed]

Petschulat, J.

Piestun, R.

Pinkse, P. W. H.

Plöschner, M.

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

Popoff, S.

D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep. 5, 10347 (2015).
[Crossref] [PubMed]

Popoff, S. M.

B. Redding, S. M. Popoff, Y. Bromberg, M. A. Choma, and H. Cao, “Noise analysis of spectrometers based on speckle pattern reconstruction,” Appl. Opt. 53(3), 410–417 (2014).
[Crossref] [PubMed]

S. M. Popoff, A. Goetschy, S. F. Liew, A. D. Stone, and H. Cao, “Coherent control of total transmission of light through disordered media,” Phys. Rev. Lett. 112(13), 133903 (2014).
[Crossref] [PubMed]

B. Redding, S. M. Popoff, and H. Cao, “All-fiber spectrometer based on speckle pattern reconstruction,” Opt. Express 21(5), 6584–6600 (2013).
[Crossref] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref] [PubMed]

Prada, C.

B. Gérardin, J. Laurent, A. Derode, C. Prada, and A. Aubry, “Full transmission and reflection of waves propagating through a maze of disorder,” Phys. Rev. Lett. 113(17), 173901 (2014).
[Crossref] [PubMed]

Psaltis, D.

Redding, B.

Richardson, D. J.

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

Rotter, S.

W. Xiong, P. Ambichl, Y. Bromberg, B. Redding, S. Rotter, and H. Cao, “ Spatiotemporal control of light transmission through a multimode fiber with strong mode mixing,” Phys. Rev. Lett. 117, 053901 (2016).
[Crossref]

J. Doppler, J. A. Méndez-Bermúdez, J. Feist, O. Dietz, D. O. Krimer, N. M. Makarov, F. M. Izrailev, and S. Rotter, “Reflection resonances in surface-disordered waveguides: strong higher-order effects of the disorder,” New J. Phys. 16, 053026 (2014).
[Crossref]

S. Rotter, P. Ambichl, and F. Libisch, “Generating particlelike scattering states in wave transport,” Phys. Rev. Lett. 106, 120602 (2011).
[Crossref] [PubMed]

S. Rotter, J.-Z. Tang, L. Wirtz, J. Trost, and J. Burgdörfer, “Modular recursive Green’s function method for ballistic quantum transport,” Phys. Rev. B 62(3), 1950 (2000).
[Crossref]

Ruiz, U.

Russell, P. S. J.

Ryf, R.

N. K. Fontaine, R. Ryf, M. Hirano, and T. Sasaki, “Experimental investigation of crosstalk accumulation in a ring-core fiber,” Proc. IEEE Summer Topicals 2013, Waikoloa, HI, USA, paper TuC4.2.

Sarma, R.

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117(8), 086803 (2016).
[Crossref] [PubMed]

R. Sarma, A. Yamilov, S. F. Liew, M. Guy, and H. Cao, “Control of mesoscopic transport by modifying transmission channels in opaque media,” Phys. Rev. B 92(21), 214206 (2015).
[Crossref]

Sasaki, T.

N. K. Fontaine, R. Ryf, M. Hirano, and T. Sasaki, “Experimental investigation of crosstalk accumulation in a ring-core fiber,” Proc. IEEE Summer Topicals 2013, Waikoloa, HI, USA, paper TuC4.2.

Schröder, J.

J. Carpenter, J. E. Benjamin, and J. Schröder, “Observation of Eisenbud-Wigner-Smith states as principal modes in multimode fibre,” Nat. Photon. 9, 751 (2015).
[Crossref]

Seifert, M.

Shemirani, M. B.

Shi, Z.

Z. Shi and A. Z. Genack, “Dynamic and spectral properties of transmission eigenchannels in random media,” Phys. Rev. B 92(18), 184202 (2015).
[Crossref]

M. Davy, Z. Shi, J. Park, C. Tian, and A. Z. Genack, “Universal structure of transmission eigenchannels inside opaque media,” Nat. Commun. 6, 6893 (2015).
[Crossref] [PubMed]

Z. Shi, M. Davy, J. Wang, and A. Z. Genack, “Focusing through random media in space and time: a transmission matrix approach,” Opt. Lett. 38(15), 2714–2716 (2013).
[Crossref] [PubMed]

Z. Shi and A. Z. Genack, “Transmission eigenvalues and the bare conductance in the crossover to Anderson localization,” Phys. Rev. Lett. 108(4), 043901 (2012).
[Crossref] [PubMed]

Shtaif, M.

Silberberg, Y.

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

Smith, F. T.

F. T. Smith, “Lifetime matrix in collision theory,” Phys. Rev. 118, 349 (1960).
[Crossref]

Stone, A. D.

S. M. Popoff, A. Goetschy, S. F. Liew, A. D. Stone, and H. Cao, “Coherent control of total transmission of light through disordered media,” Phys. Rev. Lett. 112(13), 133903 (2014).
[Crossref] [PubMed]

R. A. Jalabert, H. U. Baranger, and A. D. Stone, “Conductance fluctuations in the ballistic regime: A probe of quantum chaos?” Phys. Rev. Lett. 65, 2442 (1990).
[Crossref] [PubMed]

Tagare, H. D.

Tajalli, A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref] [PubMed]

Tang, J.-Z.

S. Rotter, J.-Z. Tang, L. Wirtz, J. Trost, and J. Burgdörfer, “Modular recursive Green’s function method for ballistic quantum transport,” Phys. Rev. B 62(3), 1950 (2000).
[Crossref]

Thomsen, B. C.

Tian, C.

M. Davy, Z. Shi, J. Park, C. Tian, and A. Z. Genack, “Universal structure of transmission eigenchannels inside opaque media,” Nat. Commun. 6, 6893 (2015).
[Crossref] [PubMed]

Trost, J.

S. Rotter, J.-Z. Tang, L. Wirtz, J. Trost, and J. Burgdörfer, “Modular recursive Green’s function method for ballistic quantum transport,” Phys. Rev. B 62(3), 1950 (2000).
[Crossref]

Tyc, T.

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

Vellekoop, I. M.

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101(12), 120601 (2008).
[Crossref] [PubMed]

Volpe, G.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref] [PubMed]

D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep. 5, 10347 (2015).
[Crossref] [PubMed]

Walmsley, I. A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref] [PubMed]

Wang, J.

Warm, S.

Wigner, E. P.

E. P. Wigner, “Lower limit for the energy derivative of the scattering phase shift,” Phys. Rev. 98, 145 (1955).
[Crossref]

Wiilkinson, T. D.

Winzer, P. J.

Wirtz, L.

S. Rotter, J.-Z. Tang, L. Wirtz, J. Trost, and J. Burgdörfer, “Modular recursive Green’s function method for ballistic quantum transport,” Phys. Rev. B 62(3), 1950 (2000).
[Crossref]

Xiong, W.

W. Xiong, P. Ambichl, Y. Bromberg, B. Redding, S. Rotter, and H. Cao, “ Spatiotemporal control of light transmission through a multimode fiber with strong mode mixing,” Phys. Rev. Lett. 117, 053901 (2016).
[Crossref]

Yamilov, A.

R. Sarma, A. Yamilov, S. F. Liew, M. Guy, and H. Cao, “Control of mesoscopic transport by modifying transmission channels in opaque media,” Phys. Rev. B 92(21), 214206 (2015).
[Crossref]

Yamilov, A. G.

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117(8), 086803 (2016).
[Crossref] [PubMed]

Yang, T.

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

Yoon, C.

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

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. H. Park, and W Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photon. 6(9), 581–585 (2012).
[Crossref]

Yu, H.

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. K. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref]

Appl. Opt. (1)

J. Lightwave Technol. (4)

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

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

Lab Chip (1)

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

Nat. Commun. (4)

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

R. Barankov and J. Mertz, “High-throughput imaging of self-luminous objects through a single optical fibre,” Nat. Commun. 5, 5581 (2014).
[Crossref] [PubMed]

M. Davy, Z. Shi, J. Park, C. Tian, and A. Z. Genack, “Universal structure of transmission eigenchannels inside opaque media,” Nat. Commun. 6, 6893 (2015).
[Crossref] [PubMed]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[Crossref] [PubMed]

Nat. Photon. (6)

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

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

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. H. Park, and W Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photon. 6(9), 581–585 (2012).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photon. 6(5), 283–292 (2012).
[Crossref]

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

J. Carpenter, J. E. Benjamin, and J. Schröder, “Observation of Eisenbud-Wigner-Smith states as principal modes in multimode fibre,” Nat. Photon. 9, 751 (2015).
[Crossref]

New J. Phys. (1)

J. Doppler, J. A. Méndez-Bermúdez, J. Feist, O. Dietz, D. O. Krimer, N. M. Makarov, F. M. Izrailev, and S. Rotter, “Reflection resonances in surface-disordered waveguides: strong higher-order effects of the disorder,” New J. Phys. 16, 053026 (2014).
[Crossref]

Opt. Express (9)

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

E. E. Morales-Delgado, S. Farahi, I. N. Papadppoulos, D. Psaltis, and C. Moser, “Delivery of focused short pulses through a multimode fiber,” Opt. Express 23(7), 9109–9120 (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]

B. Redding, S. M. Popoff, and H. Cao, “All-fiber spectrometer based on speckle pattern reconstruction,” Opt. Express 21(5), 6584–6600 (2013).
[Crossref] [PubMed]

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]

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]

C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Stokes-space analysis of modal dispersion in fibers with multiple mode transmission,” Opt. Express 20(11), 11718–11733 (2012).
[Crossref] [PubMed]

A. A. Juarez, C. A. Bunge, S. Warm, and K. Petermann, “Perspectives of principal mode transmission in mode-division-multiplex operation,” Opt. Express 20(13), 13810–13824 (2012).
[Crossref] [PubMed]

J. Aulbach, B. Gjonaj, P. Johnson, and A. Lagendijk, “Spatiotemporal focusing in opaque scattering media by wave front shaping with nonlinear feedback,” Opt. Express 20(28), 29237–29251 (2012).
[Crossref]

Opt. Lett. (5)

Optica (1)

Phys. Rev. (2)

E. P. Wigner, “Lower limit for the energy derivative of the scattering phase shift,” Phys. Rev. 98, 145 (1955).
[Crossref]

F. T. Smith, “Lifetime matrix in collision theory,” Phys. Rev. 118, 349 (1960).
[Crossref]

Phys. Rev. B (4)

S. Rotter, J.-Z. Tang, L. Wirtz, J. Trost, and J. Burgdörfer, “Modular recursive Green’s function method for ballistic quantum transport,” Phys. Rev. B 62(3), 1950 (2000).
[Crossref]

W. Choi, A. P. Mosk, Q. H. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83(13), 134207 (2011).
[Crossref]

Z. Shi and A. Z. Genack, “Dynamic and spectral properties of transmission eigenchannels in random media,” Phys. Rev. B 92(18), 184202 (2015).
[Crossref]

R. Sarma, A. Yamilov, S. F. Liew, M. Guy, and H. Cao, “Control of mesoscopic transport by modifying transmission channels in opaque media,” Phys. Rev. B 92(21), 214206 (2015).
[Crossref]

Phys. Rev. Lett. (13)

R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of energy density inside a disordered medium by coupling to open or closed channels,” Phys. Rev. Lett. 117(8), 086803 (2016).
[Crossref] [PubMed]

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

J. Aulbach, B. Gjonaj, P. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[Crossref] [PubMed]

Z. Shi and A. Z. Genack, “Transmission eigenvalues and the bare conductance in the crossover to Anderson localization,” Phys. Rev. Lett. 108(4), 043901 (2012).
[Crossref] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Universal optimal transmission of light through disordered materials,” Phys. Rev. Lett. 101(12), 120601 (2008).
[Crossref] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref] [PubMed]

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. K. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref]

S. M. Popoff, A. Goetschy, S. F. Liew, A. D. Stone, and H. Cao, “Coherent control of total transmission of light through disordered media,” Phys. Rev. Lett. 112(13), 133903 (2014).
[Crossref] [PubMed]

B. Gérardin, J. Laurent, A. Derode, C. Prada, and A. Aubry, “Full transmission and reflection of waves propagating through a maze of disorder,” Phys. Rev. Lett. 113(17), 173901 (2014).
[Crossref] [PubMed]

S. Rotter, P. Ambichl, and F. Libisch, “Generating particlelike scattering states in wave transport,” Phys. Rev. Lett. 106, 120602 (2011).
[Crossref] [PubMed]

W. Xiong, P. Ambichl, Y. Bromberg, B. Redding, S. Rotter, and H. Cao, “ Spatiotemporal control of light transmission through a multimode fiber with strong mode mixing,” Phys. Rev. Lett. 117, 053901 (2016).
[Crossref]

R. A. Jalabert, H. U. Baranger, and A. D. Stone, “Conductance fluctuations in the ballistic regime: A probe of quantum chaos?” Phys. Rev. Lett. 65, 2442 (1990).
[Crossref] [PubMed]

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref] [PubMed]

Proc. SPIE (1)

D. A. Nolan, G. Milione, and R. R. Alfano, “Bandwidth analysis of the principal states superimposed from vortex modes propagating in an optical fiber,” Proc. SPIE 8999, 899911 (2014).
[Crossref]

Sci. Rep. (1)

D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep. 5, 10347 (2015).
[Crossref] [PubMed]

Science (1)

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281, 962–967 (1998).
[Crossref] [PubMed]

Other (3)

L. Eisenbud, Ph.D. thesis, Princeton, 1948.

M. Brack and R. K. Bhaduri, Semiclassical Physics (Addison-Wesley, 1997).

N. K. Fontaine, R. Ryf, M. Hirano, and T. Sasaki, “Experimental investigation of crosstalk accumulation in a ring-core fiber,” Proc. IEEE Summer Topicals 2013, Waikoloa, HI, USA, paper TuC4.2.

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Figures (9)

Fig. 1
Fig. 1

Experimental setup for measuring the field transmission matrix of a MMF. The continuous-wave output from a tunable laser source (Agilent 81940A) at wavelength ∼ 1550 nm is collimated (C1) and linearly polarized (PBS1). The beam is split into two arms by a beam splitter (BS1). In the fiber arm, light is modulated by the SLM in the reflection mode and then coupled to the MMF by a tube lens (L) and an objective (O). The output light from the MMF is collimated (C2) and linearly polarized (PBS2), before combining with the beam from the reference arm at a second beamsplitter (BS2). To match the optical path-length in the two arms, two mirrors (M1, M2) are inserted to the reference arm to adjust the path-length. BS2 is tilted to produce interference fringes of the two beams, which are recorded in the far field by a CCD camera.

Fig. 2
Fig. 2

Field transmission matrix of a MMF with weak (a,b) and strong mode coupling (c,d). The one-meter-long step-index fiber has a 50 μm core and a numerical aperture of 0.22. There are about 120 guided modes for one polarization, which are labeled by the propagation constant (from large to small). Amplitude (a,c) and phase (b,d) of the measured transmission matrix at λ = 1550 nm (ω = 194 THz) for one linear polarization. The transmission matrix is nearly diagonal in (a), indicating weak coupling among modes of similar propagation constants. In (c) all modes are coupled, although higher-order modes have more attenuation.

Fig. 3
Fig. 3

Experimental realization of PMs at λ = 1550 nm. Experimentally measured (a,b) and numerically calculated (c,d) amplitude and phase of the output field of a PM in the same fiber as in Fig. 2. The agreement confirms the accuracy of the transmission matrix measurement.

Fig. 4
Fig. 4

PMs in the weak mode coupling regime. (a–c) Spatial distribution of the far-field amplitude for three PMs in the weak mode coupling regime with short (a), medium (b) and long (c) delay time. (d–f) Decomposition of output fields in (a–c) by the LP modes. The PMs with short/medium/long delay time are composed mostly of low/medium/high-order LP modes. Ne is the mode participation number.

Fig. 5
Fig. 5

PMs in the strong mode coupling regime. (a–c) Spatial distribution of the far-field amplitude for three PMs in the strong mode coupling regime with short (a), medium (b) and long (c) delay time. (d–f) Modal decomposition of output fields in (a–c), revealing the PM is a superposition of many LP modes. Ne is the mode partition number.

Fig. 6
Fig. 6

Spectral decorrelation of PMs. (a,b) Spectral correlation function Cω) of the output field pattern, measured experimentally for three PMs with short delay time (red line), medium delay time (blue line) and long delay time (green line) in the MMF with weak (a) and strong (b) mode coupling. For comparison, Cω) for a random input is also shown (black dashed curve). Cω) is normalized to one at Δω = 0. The output field pattern for the PM with short delay time decorrelates more slowly with frequency than that with long delay time. (c,d) Normalized spectral correlation width of PMs vs. delay times in weak (c) and strong (d) mode coupling regime. The red, blue and green arrows indicate the PMs of which the three spectral correlation curves are plotted in (a) and (b).

Fig. 7
Fig. 7

Calculated PM bandwidths (upper row) and corresponding path-length distributions (lower row). The MMF is a step-index fiber with 50 μm core and 0.22 numerical aperture. The mode coupling strength (L/ℓ) is 0.2 in (a,d), 1.0 in (b,e), and 10 in (c,f). (a,b,c) PM bandwidths vs. delay times. The bandwidth is normalized to the average width of random inputs. The shortest delay time is set to be 0 and the difference between the shortest and longest delay time is normalized to 1. (d,e,f) The intensity distributions over the relative path-length of the PMs in (a,c,e) with the delay time = 0 (red solid line), 0.5 (blue dashed line) and 1 (green dotted line). In the weak mode coupling regime (a), the PM bandwidth is maximized at the shortest and longest delay time. In the strong mode coupling regime (c), the PM bandwidth is the largest at the medium delay time. (b) shows the transition between the two regimes.

Fig. 8
Fig. 8

Evolution of PM bandwidth with mode coupling strength. (a) With L fixed, the average bandwidth of all PMs (blue solid curve) first decreases with L/ℓ, reaches the minimum at L/ℓ ≃ 1, and then increases. For comparison (black dashed curve), the average bandwidth of random inputs increases monotonically with L/ℓ. (b) The normalized bandwidths (bandwidth enhancement ratio) of PMs decrease with L/ℓ and approaches a constant. (c) The difference between the maximum bandwidth and the minimum bandwidth (blue, solid line) exhibits a similar trend as the average bandwidth. The bandwidth difference is normalized by the average bandwidth to show the relative bandwidth fluctuation (black, dashed line).

Fig. 9
Fig. 9

Effects of MDL on PM bandwidths and path-length distributions. (a) Normalized bandwidths of PMs in the weak (a) and strong (c) mode coupling regimes with (red dots) or without (black crosses) MDL. (b,d) Calculated intensity distributions over the path-length of PMs in (a,c) with delay time = 0, 0.2 ns in (b) and 0, 0.12 ns in (d) with (red dashed) or without (black solid) MDL. In the weak coupling regime, the MDL reduces significantly the bandwidth of slow PMs (a) by broadening their path-length distributions (b). In the strong coupling regime, the MDL enhances the bandwidth of fast PMs (c) by narrowing their path-length distribution (d).

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