Abstract

We demonstrate a numerical technique that can evaluate the core-to-core variations in propagation constant in multicore fiber. Using a Markov Chain Monte Carlo process, we replicate the interference patterns of light that has coupled between the cores during propagation. We describe the algorithm and verify its operation by successfully reconstructing target propagation constants in a fictional fiber. Then we carry out a reconstruction of the propagation constants in a real fiber containing 37 single-mode cores. We find that the range of fractional propagation constant variation across the cores is approximately ±2 × 10−5.

© 2014 Optical Society of America

Full Article  |  PDF Article
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References

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2014 (2)

K. Poulios, R. Keil, D. Fry, A. Meinecke, Jasmin D. F. Matthews, Jonathan C. A. Politi, M. Lobino, M. Gräfe, M. Heinrich, S. Nolte, A. Szameit, and J. L. O’Brien, “Quantum Walks of Correlated Photon Pairs in Two-Dimensional Waveguide Arrays,” Phys. Rev. Lett. 112, 143604 (2014). URL http://link.aps.org/doi/10.1103/PhysRevLett.112.143604 .
[Crossref] [PubMed]

E. Nazemosadat and A. Mafi, “Design considerations for multicore optical fibers in nonlinear switching and mode-locking applications,” J. Opt. Soc. Am. B 31(8), 1874–1878 (2014).
[Crossref]

2013 (3)

2012 (3)

2011 (5)

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(9), 1707–1709 (2011).
[Crossref] [PubMed]

K. Imamura, Y. Tsuchida, K. Mukasa, R. Sugizaki, K. Saitoh, and M. Koshiba, “Investigation on multi-core fibers with large Aeff and low micro bending loss,” Opt. Express 19(11), 10595–10603 (2011).
[Crossref] [PubMed]

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Multi-core fiber design and analysis: coupled-mode theory and coupled-power theory,” Opt. Express 19(26), B102–B111 (2011).
[Crossref]

J. Bland-Hawthorn, S. Ellis, S. Leon-Saval, R. Haynes, M. Roth, H.-G. Löhmannsröben, A. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[Crossref] [PubMed]

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011). URL http://stacks.iop.org/1367-2630/13/i=7/a=075003 .
[Crossref]

2010 (1)

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Worhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum Walks of Correlated Photons,” Science 329(5998), 1500–1503 (2010). http://www.sciencemag.org/cgi/reprint/329/5998/1500.pdf , URL http://www.sciencemag.org/cgi/content/abstract/329/5998/1500 .
[Crossref] [PubMed]

2009 (2)

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Expr. 6(2), 98–103 (2009).
[Crossref]

J. Bland-Hawthorn and P. Kern, “Astrophotonics: a new era for astronomical instruments,” Opt. Express 17(3), 1880–1884 (2009).
[Crossref] [PubMed]

2008 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simmulated annealing,” Science 220 (4598), 671–680 (1983).
[Crossref] [PubMed]

1953 (1)

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21(6), 1087–1092 (1953).
[Crossref]

Abe, Y.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) Crosstalk-managed Transmission with 91.4-b/s/Hz Aggregate Spectral Efficiency,” in European Conference and Exhibition on Optical Communication, p. Th.3.C.1 (Optical Society of America, 2012).

Abedin, K. S.

Ams, M.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011). URL http://stacks.iop.org/1367-2630/13/i=7/a=075003 .
[Crossref]

Andresen, E. R.

Armand, P.

Barthélémy, A.

Benoist, J.

Biggerstaff, D. N.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011). URL http://stacks.iop.org/1367-2630/13/i=7/a=075003 .
[Crossref]

Birks, T.

E. Lindley, S.-S. Min, S. Leon-Saval, N. Cvetojevic, N. Jovanovic, J. Bland-Hawthorn, J. Lawrence, I. Gris-Sanchez, T. Birks, R. Haynes, and D. Haynes, “Core-to-core uniformity improvement in multi-core fiber Bragg gratings,” in Proc. SPIE, vol. 9151, pp. 91,515F (2014). URL http://dx.doi.org/10.1117/12.2055623 .
[Crossref]

Birks, T. A.

T. A. Birks, B. J. Mangan, A. Díez, J. L. Cruz, and D. F. Murphy, ““Photonic lantern” spectral filters in multi-core fibre,” Opt. Express 20(13), 13996–14008 (2012).
[Crossref] [PubMed]

J. Bland-Hawthorn, S. Ellis, S. Leon-Saval, R. Haynes, M. Roth, H.-G. Löhmannsröben, A. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[Crossref] [PubMed]

Bland-Hawthorn, J.

J. Bland-Hawthorn, S. Ellis, S. Leon-Saval, R. Haynes, M. Roth, H.-G. Löhmannsröben, A. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[Crossref] [PubMed]

J. Bland-Hawthorn and P. Kern, “Astrophotonics: a new era for astronomical instruments,” Opt. Express 17(3), 1880–1884 (2009).
[Crossref] [PubMed]

E. Lindley, S.-S. Min, S. Leon-Saval, N. Cvetojevic, N. Jovanovic, J. Bland-Hawthorn, J. Lawrence, I. Gris-Sanchez, T. Birks, R. Haynes, and D. Haynes, “Core-to-core uniformity improvement in multi-core fiber Bragg gratings,” in Proc. SPIE, vol. 9151, pp. 91,515F (2014). URL http://dx.doi.org/10.1117/12.2055623 .
[Crossref]

Bouwmans, G.

Bromberg, Y.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Worhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum Walks of Correlated Photons,” Science 329(5998), 1500–1503 (2010). http://www.sciencemag.org/cgi/reprint/329/5998/1500.pdf , URL http://www.sciencemag.org/cgi/content/abstract/329/5998/1500 .
[Crossref] [PubMed]

Broome, M. A.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011). URL http://stacks.iop.org/1367-2630/13/i=7/a=075003 .
[Crossref]

Cheng, X.

D. Qian, E. Ip, M.-F. Huang, M. jun Li, A. Dogariu, S. Zhang, Y. Shao, Y.-K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto, and T. Wang, “1.05Pb/s Transmission with 109b/s/Hz Spectral Efficiency using Hybrid Single- and Few-Mode Cores,” in Frontiers in Optics 2012/Laser Science XXVIII, p. FW6C.3 (Optical Society of America, 2012).

Collier, A.

D. Qian, E. Ip, M.-F. Huang, M. jun Li, A. Dogariu, S. Zhang, Y. Shao, Y.-K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto, and T. Wang, “1.05Pb/s Transmission with 109b/s/Hz Spectral Efficiency using Hybrid Single- and Few-Mode Cores,” in Frontiers in Optics 2012/Laser Science XXVIII, p. FW6C.3 (Optical Society of America, 2012).

Cruz, J. L.

Cuby, J.-G.

J. Bland-Hawthorn, S. Ellis, S. Leon-Saval, R. Haynes, M. Roth, H.-G. Löhmannsröben, A. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[Crossref] [PubMed]

Cvetojevic, N.

E. Lindley, S.-S. Min, S. Leon-Saval, N. Cvetojevic, N. Jovanovic, J. Bland-Hawthorn, J. Lawrence, I. Gris-Sanchez, T. Birks, R. Haynes, and D. Haynes, “Core-to-core uniformity improvement in multi-core fiber Bragg gratings,” in Proc. SPIE, vol. 9151, pp. 91,515F (2014). URL http://dx.doi.org/10.1117/12.2055623 .
[Crossref]

Desfarges-Berthelemot, A.

Díez, A.

Dogariu, A.

D. Qian, E. Ip, M.-F. Huang, M. jun Li, A. Dogariu, S. Zhang, Y. Shao, Y.-K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto, and T. Wang, “1.05Pb/s Transmission with 109b/s/Hz Spectral Efficiency using Hybrid Single- and Few-Mode Cores,” in Frontiers in Optics 2012/Laser Science XXVIII, p. FW6C.3 (Optical Society of America, 2012).

Dunsby, C.

Ellis, S.

J. Bland-Hawthorn, S. Ellis, S. Leon-Saval, R. Haynes, M. Roth, H.-G. Löhmannsröben, A. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[Crossref] [PubMed]

Fedrizzi, A.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011). URL http://stacks.iop.org/1367-2630/13/i=7/a=075003 .
[Crossref]

Fini, J.

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nature Photon. 7(5), 354–362 (2013).
[Crossref]

Fini, J. M.

French, P. M. W.

Fry, D.

K. Poulios, R. Keil, D. Fry, A. Meinecke, Jasmin D. F. Matthews, Jonathan C. A. Politi, M. Lobino, M. Gräfe, M. Heinrich, S. Nolte, A. Szameit, and J. L. O’Brien, “Quantum Walks of Correlated Photon Pairs in Two-Dimensional Waveguide Arrays,” Phys. Rev. Lett. 112, 143604 (2014). URL http://link.aps.org/doi/10.1103/PhysRevLett.112.143604 .
[Crossref] [PubMed]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simmulated annealing,” Science 220 (4598), 671–680 (1983).
[Crossref] [PubMed]

Geng, Y.

D. Qian, E. Ip, M.-F. Huang, M. jun Li, A. Dogariu, S. Zhang, Y. Shao, Y.-K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto, and T. Wang, “1.05Pb/s Transmission with 109b/s/Hz Spectral Efficiency using Hybrid Single- and Few-Mode Cores,” in Frontiers in Optics 2012/Laser Science XXVIII, p. FW6C.3 (Optical Society of America, 2012).

Gillingham, P.

J. Bland-Hawthorn, S. Ellis, S. Leon-Saval, R. Haynes, M. Roth, H.-G. Löhmannsröben, A. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[Crossref] [PubMed]

Goggin, M. E.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011). URL http://stacks.iop.org/1367-2630/13/i=7/a=075003 .
[Crossref]

Goto, Y.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) Crosstalk-managed Transmission with 91.4-b/s/Hz Aggregate Spectral Efficiency,” in European Conference and Exhibition on Optical Communication, p. Th.3.C.1 (Optical Society of America, 2012).

Gräfe, M.

K. Poulios, R. Keil, D. Fry, A. Meinecke, Jasmin D. F. Matthews, Jonathan C. A. Politi, M. Lobino, M. Gräfe, M. Heinrich, S. Nolte, A. Szameit, and J. L. O’Brien, “Quantum Walks of Correlated Photon Pairs in Two-Dimensional Waveguide Arrays,” Phys. Rev. Lett. 112, 143604 (2014). URL http://link.aps.org/doi/10.1103/PhysRevLett.112.143604 .
[Crossref] [PubMed]

Gris-Sanchez, I.

E. Lindley, S.-S. Min, S. Leon-Saval, N. Cvetojevic, N. Jovanovic, J. Bland-Hawthorn, J. Lawrence, I. Gris-Sanchez, T. Birks, R. Haynes, and D. Haynes, “Core-to-core uniformity improvement in multi-core fiber Bragg gratings,” in Proc. SPIE, vol. 9151, pp. 91,515F (2014). URL http://dx.doi.org/10.1117/12.2055623 .
[Crossref]

Haynes, D.

E. Lindley, S.-S. Min, S. Leon-Saval, N. Cvetojevic, N. Jovanovic, J. Bland-Hawthorn, J. Lawrence, I. Gris-Sanchez, T. Birks, R. Haynes, and D. Haynes, “Core-to-core uniformity improvement in multi-core fiber Bragg gratings,” in Proc. SPIE, vol. 9151, pp. 91,515F (2014). URL http://dx.doi.org/10.1117/12.2055623 .
[Crossref]

Haynes, R.

J. Bland-Hawthorn, S. Ellis, S. Leon-Saval, R. Haynes, M. Roth, H.-G. Löhmannsröben, A. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[Crossref] [PubMed]

E. Lindley, S.-S. Min, S. Leon-Saval, N. Cvetojevic, N. Jovanovic, J. Bland-Hawthorn, J. Lawrence, I. Gris-Sanchez, T. Birks, R. Haynes, and D. Haynes, “Core-to-core uniformity improvement in multi-core fiber Bragg gratings,” in Proc. SPIE, vol. 9151, pp. 91,515F (2014). URL http://dx.doi.org/10.1117/12.2055623 .
[Crossref]

Heinrich, M.

K. Poulios, R. Keil, D. Fry, A. Meinecke, Jasmin D. F. Matthews, Jonathan C. A. Politi, M. Lobino, M. Gräfe, M. Heinrich, S. Nolte, A. Szameit, and J. L. O’Brien, “Quantum Walks of Correlated Photon Pairs in Two-Dimensional Waveguide Arrays,” Phys. Rev. Lett. 112, 143604 (2014). URL http://link.aps.org/doi/10.1103/PhysRevLett.112.143604 .
[Crossref] [PubMed]

Hirooka, T.

Horton, A.

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[Crossref] [PubMed]

Poulios, K.

K. Poulios, R. Keil, D. Fry, A. Meinecke, Jasmin D. F. Matthews, Jonathan C. A. Politi, M. Lobino, M. Gräfe, M. Heinrich, S. Nolte, A. Szameit, and J. L. O’Brien, “Quantum Walks of Correlated Photon Pairs in Two-Dimensional Waveguide Arrays,” Phys. Rev. Lett. 112, 143604 (2014). URL http://link.aps.org/doi/10.1103/PhysRevLett.112.143604 .
[Crossref] [PubMed]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Worhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum Walks of Correlated Photons,” Science 329(5998), 1500–1503 (2010). http://www.sciencemag.org/cgi/reprint/329/5998/1500.pdf , URL http://www.sciencemag.org/cgi/content/abstract/329/5998/1500 .
[Crossref] [PubMed]

Prieto, X.

D. Qian, E. Ip, M.-F. Huang, M. jun Li, A. Dogariu, S. Zhang, Y. Shao, Y.-K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto, and T. Wang, “1.05Pb/s Transmission with 109b/s/Hz Spectral Efficiency using Hybrid Single- and Few-Mode Cores,” in Frontiers in Optics 2012/Laser Science XXVIII, p. FW6C.3 (Optical Society of America, 2012).

Qian, D.

D. Qian, E. Ip, M.-F. Huang, M. jun Li, A. Dogariu, S. Zhang, Y. Shao, Y.-K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto, and T. Wang, “1.05Pb/s Transmission with 109b/s/Hz Spectral Efficiency using Hybrid Single- and Few-Mode Cores,” in Frontiers in Optics 2012/Laser Science XXVIII, p. FW6C.3 (Optical Society of America, 2012).

Quiquempois, Y.

Richardson, D.

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nature Photon. 7(5), 354–362 (2013).
[Crossref]

Rigaud, P.

Rigneault, H.

Rosenbluth, A. W.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21(6), 1087–1092 (1953).
[Crossref]

Rosenbluth, M. N.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21(6), 1087–1092 (1953).
[Crossref]

Roth, M.

J. Bland-Hawthorn, S. Ellis, S. Leon-Saval, R. Haynes, M. Roth, H.-G. Löhmannsröben, A. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[Crossref] [PubMed]

Ryder, S. D.

J. Bland-Hawthorn, S. Ellis, S. Leon-Saval, R. Haynes, M. Roth, H.-G. Löhmannsröben, A. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[Crossref] [PubMed]

Saitoh, K.

K. Imamura, Y. Tsuchida, K. Mukasa, R. Sugizaki, K. Saitoh, and M. Koshiba, “Investigation on multi-core fibers with large Aeff and low micro bending loss,” Opt. Express 19(11), 10595–10603 (2011).
[Crossref] [PubMed]

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Multi-core fiber design and analysis: coupled-mode theory and coupled-power theory,” Opt. Express 19(26), B102–B111 (2011).
[Crossref]

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Expr. 6(2), 98–103 (2009).
[Crossref]

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) Crosstalk-managed Transmission with 91.4-b/s/Hz Aggregate Spectral Efficiency,” in European Conference and Exhibition on Optical Communication, p. Th.3.C.1 (Optical Society of America, 2012).

Sano, A.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) Crosstalk-managed Transmission with 91.4-b/s/Hz Aggregate Spectral Efficiency,” in European Conference and Exhibition on Optical Communication, p. Th.3.C.1 (Optical Society of America, 2012).

Sasaki, Y.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) Crosstalk-managed Transmission with 91.4-b/s/Hz Aggregate Spectral Efficiency,” in European Conference and Exhibition on Optical Communication, p. Th.3.C.1 (Optical Society of America, 2012).

Shao, Y.

D. Qian, E. Ip, M.-F. Huang, M. jun Li, A. Dogariu, S. Zhang, Y. Shao, Y.-K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto, and T. Wang, “1.05Pb/s Transmission with 109b/s/Hz Spectral Efficiency using Hybrid Single- and Few-Mode Cores,” in Frontiers in Optics 2012/Laser Science XXVIII, p. FW6C.3 (Optical Society of America, 2012).

Shikama, K.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) Crosstalk-managed Transmission with 91.4-b/s/Hz Aggregate Spectral Efficiency,” in European Conference and Exhibition on Optical Communication, p. Th.3.C.1 (Optical Society of America, 2012).

Silberberg, Y.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Worhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum Walks of Correlated Photons,” Science 329(5998), 1500–1503 (2010). http://www.sciencemag.org/cgi/reprint/329/5998/1500.pdf , URL http://www.sciencemag.org/cgi/content/abstract/329/5998/1500 .
[Crossref] [PubMed]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory, (Chapman and Hall, London, 1983).

Stone, J. M.

Sugizaki, R.

Szameit, A.

K. Poulios, R. Keil, D. Fry, A. Meinecke, Jasmin D. F. Matthews, Jonathan C. A. Politi, M. Lobino, M. Gräfe, M. Heinrich, S. Nolte, A. Szameit, and J. L. O’Brien, “Quantum Walks of Correlated Photon Pairs in Two-Dimensional Waveguide Arrays,” Phys. Rev. Lett. 112, 143604 (2014). URL http://link.aps.org/doi/10.1103/PhysRevLett.112.143604 .
[Crossref] [PubMed]

Takara, H.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) Crosstalk-managed Transmission with 91.4-b/s/Hz Aggregate Spectral Efficiency,” in European Conference and Exhibition on Optical Communication, p. Th.3.C.1 (Optical Society of America, 2012).

Takenaga, K.

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Multi-core fiber design and analysis: coupled-mode theory and coupled-power theory,” Opt. Express 19(26), B102–B111 (2011).
[Crossref]

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) Crosstalk-managed Transmission with 91.4-b/s/Hz Aggregate Spectral Efficiency,” in European Conference and Exhibition on Optical Communication, p. Th.3.C.1 (Optical Society of America, 2012).

Taunay, T. F.

Teller, A. H.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21(6), 1087–1092 (1953).
[Crossref]

Teller, E.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21(6), 1087–1092 (1953).
[Crossref]

Thompson, A. J.

Thompson, M. G.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Worhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum Walks of Correlated Photons,” Science 329(5998), 1500–1503 (2010). http://www.sciencemag.org/cgi/reprint/329/5998/1500.pdf , URL http://www.sciencemag.org/cgi/content/abstract/329/5998/1500 .
[Crossref] [PubMed]

Tian, Y.

D. Qian, E. Ip, M.-F. Huang, M. jun Li, A. Dogariu, S. Zhang, Y. Shao, Y.-K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto, and T. Wang, “1.05Pb/s Transmission with 109b/s/Hz Spectral Efficiency using Hybrid Single- and Few-Mode Cores,” in Frontiers in Optics 2012/Laser Science XXVIII, p. FW6C.3 (Optical Society of America, 2012).

Trinh, C.

J. Bland-Hawthorn, S. Ellis, S. Leon-Saval, R. Haynes, M. Roth, H.-G. Löhmannsröben, A. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[Crossref] [PubMed]

Tsuchida, Y.

Tsujikawa, K.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) Crosstalk-managed Transmission with 91.4-b/s/Hz Aggregate Spectral Efficiency,” in European Conference and Exhibition on Optical Communication, p. Th.3.C.1 (Optical Society of America, 2012).

Twamley, J.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011). URL http://stacks.iop.org/1367-2630/13/i=7/a=075003 .
[Crossref]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simmulated annealing,” Science 220 (4598), 671–680 (1983).
[Crossref] [PubMed]

Wang, T.

D. Qian, E. Ip, M.-F. Huang, M. jun Li, A. Dogariu, S. Zhang, Y. Shao, Y.-K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto, and T. Wang, “1.05Pb/s Transmission with 109b/s/Hz Spectral Efficiency using Hybrid Single- and Few-Mode Cores,” in Frontiers in Optics 2012/Laser Science XXVIII, p. FW6C.3 (Optical Society of America, 2012).

White, A. G.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011). URL http://stacks.iop.org/1367-2630/13/i=7/a=075003 .
[Crossref]

Withford, M. J.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011). URL http://stacks.iop.org/1367-2630/13/i=7/a=075003 .
[Crossref]

Worhoff, K.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Worhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum Walks of Correlated Photons,” Science 329(5998), 1500–1503 (2010). http://www.sciencemag.org/cgi/reprint/329/5998/1500.pdf , URL http://www.sciencemag.org/cgi/content/abstract/329/5998/1500 .
[Crossref] [PubMed]

Yagi, T.

Yan, M. F.

Yoshida, M.

Zhang, S.

D. Qian, E. Ip, M.-F. Huang, M. jun Li, A. Dogariu, S. Zhang, Y. Shao, Y.-K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto, and T. Wang, “1.05Pb/s Transmission with 109b/s/Hz Spectral Efficiency using Hybrid Single- and Few-Mode Cores,” in Frontiers in Optics 2012/Laser Science XXVIII, p. FW6C.3 (Optical Society of America, 2012).

Zhang, Y.

D. Qian, E. Ip, M.-F. Huang, M. jun Li, A. Dogariu, S. Zhang, Y. Shao, Y.-K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto, and T. Wang, “1.05Pb/s Transmission with 109b/s/Hz Spectral Efficiency using Hybrid Single- and Few-Mode Cores,” in Frontiers in Optics 2012/Laser Science XXVIII, p. FW6C.3 (Optical Society of America, 2012).

Zhou, X.-Q.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Worhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum Walks of Correlated Photons,” Science 329(5998), 1500–1503 (2010). http://www.sciencemag.org/cgi/reprint/329/5998/1500.pdf , URL http://www.sciencemag.org/cgi/content/abstract/329/5998/1500 .
[Crossref] [PubMed]

Zhu, B.

IEICE Electron. Expr. (1)

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Expr. 6(2), 98–103 (2009).
[Crossref]

J. Chem. Phys. (1)

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21(6), 1087–1092 (1953).
[Crossref]

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

Nat. Commun. (1)

J. Bland-Hawthorn, S. Ellis, S. Leon-Saval, R. Haynes, M. Roth, H.-G. Löhmannsröben, A. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[Crossref] [PubMed]

Nature Photon. (1)

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nature Photon. 7(5), 354–362 (2013).
[Crossref]

New J. Phys. (1)

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011). URL http://stacks.iop.org/1367-2630/13/i=7/a=075003 .
[Crossref]

Opt. Express (9)

T. A. Birks, B. J. Mangan, A. Díez, J. L. Cruz, and D. F. Murphy, ““Photonic lantern” spectral filters in multi-core fibre,” Opt. Express 20(13), 13996–14008 (2012).
[Crossref] [PubMed]

T. Mansuryan, P. Rigaud, G. Bouwmans, V. Kermene, Y. Quiquempois, A. Desfarges-Berthelemot, P. Armand, J. Benoist, and A. Barthélémy, “Spatially dispersive scheme for transmission and synthesis of femtosecond pulses through a multicore fiber,” Opt. Express 20(22), 24769–24777 (2012).
[Crossref] [PubMed]

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

J. Bland-Hawthorn and P. Kern, “Astrophotonics: a new era for astronomical instruments,” Opt. Express 17(3), 1880–1884 (2009).
[Crossref] [PubMed]

K. Imamura, Y. Tsuchida, K. Mukasa, R. Sugizaki, K. Saitoh, and M. Koshiba, “Investigation on multi-core fibers with large Aeff and low micro bending loss,” Opt. Express 19(11), 10595–10603 (2011).
[Crossref] [PubMed]

J. M. Fini, B. Zhu, T. F. Taunay, M. F. Yan, and K. S. Abedin, “Crosstalk in multicore fibers with randomness: gradual drift vs. short-length variations,” Opt. Express 20(2), 949–959 (2012).
[Crossref] [PubMed]

M. Yoshida, T. Hirooka, M. Nakazawa, K. Imamura, R. Sugizaki, and T. Yagi, “Detailed comparison between mode couplings along multi-core fibers and structural irregularities using a synchronous multi-channel OTDR system with a high dynamic range,” Opt. Express 21(24), 29157–29164 (2013).
[Crossref]

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Multi-core fiber design and analysis: coupled-mode theory and coupled-power theory,” Opt. Express 19(26), B102–B111 (2011).
[Crossref]

J. M. Stone and J. C. Knight, “Visibly “white” light generation in uniform photonic crystal fiber using a microchip laser,” Opt. Express 16(4), 2670–2675 (2008).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

K. Poulios, R. Keil, D. Fry, A. Meinecke, Jasmin D. F. Matthews, Jonathan C. A. Politi, M. Lobino, M. Gräfe, M. Heinrich, S. Nolte, A. Szameit, and J. L. O’Brien, “Quantum Walks of Correlated Photon Pairs in Two-Dimensional Waveguide Arrays,” Phys. Rev. Lett. 112, 143604 (2014). URL http://link.aps.org/doi/10.1103/PhysRevLett.112.143604 .
[Crossref] [PubMed]

Science (2)

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Worhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum Walks of Correlated Photons,” Science 329(5998), 1500–1503 (2010). http://www.sciencemag.org/cgi/reprint/329/5998/1500.pdf , URL http://www.sciencemag.org/cgi/content/abstract/329/5998/1500 .
[Crossref] [PubMed]

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simmulated annealing,” Science 220 (4598), 671–680 (1983).
[Crossref] [PubMed]

Other (4)

E. Lindley, S.-S. Min, S. Leon-Saval, N. Cvetojevic, N. Jovanovic, J. Bland-Hawthorn, J. Lawrence, I. Gris-Sanchez, T. Birks, R. Haynes, and D. Haynes, “Core-to-core uniformity improvement in multi-core fiber Bragg gratings,” in Proc. SPIE, vol. 9151, pp. 91,515F (2014). URL http://dx.doi.org/10.1117/12.2055623 .
[Crossref]

A. W. Snyder and J. D. Love, Optical Waveguide Theory, (Chapman and Hall, London, 1983).

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) Crosstalk-managed Transmission with 91.4-b/s/Hz Aggregate Spectral Efficiency,” in European Conference and Exhibition on Optical Communication, p. Th.3.C.1 (Optical Society of America, 2012).

D. Qian, E. Ip, M.-F. Huang, M. jun Li, A. Dogariu, S. Zhang, Y. Shao, Y.-K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto, and T. Wang, “1.05Pb/s Transmission with 109b/s/Hz Spectral Efficiency using Hybrid Single- and Few-Mode Cores,” in Frontiers in Optics 2012/Laser Science XXVIII, p. FW6C.3 (Optical Society of America, 2012).

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Figures (4)

Fig. 1
Fig. 1 Dependence of the propagation constant of an individual core (a, b) and the coupling strength between two identical cores (c, d) on core radius. (b, d) show the fitted dependencies over the typical range of variation in a seen in our MCF. (e) Evolution of intensity for propagation in two coupled cores: identical cores with radii a0, propagation constants β0 and coupling g0 in black; identical cores with radii a0 + Δa, identical propagation constants β0 + Δβ, and modified coupling strength g0 − Δg in red; two different cores with different propagation constants β0 and β0 + Δβ but coupling g0 in blue. Parameters were a0 = 0.48 μm, a0 + Δa = 0.4824 μm, d = 8.0 μm, Δn = 0.02.
Fig. 2
Fig. 2 Typical performance of simulated reconstruction algorithm on one run. (a) Fit residual and (b) intermediate fractional values of Δβi as functions of iteration number. (c) Fractional values of target propagation constants {β′i} that we aimed to reconstruct. (d) Reconstructed fractional values of propagation constants { β i ( rec ) } .
Fig. 3
Fig. 3 Statistics of simulated reconstruction over 100 runs. (a) Raw reconstructed differences in βi for each of 100 runs. (b) Residual value of , with convergence cut-off illustrated by black line. (c) Reconstructed differences in βi for each of the 91 runs that satisfied convergence condition. (d) Mean reconstructed differences in βi (red) with error bars equal to the standard deviation of the values in (c), with target βi plotted in black.
Fig. 4
Fig. 4 (Top) Optical micrograph of the cleaved end face of the 37-core MCF illuminated from below, and schematic of the setup used to characterise the MCF. (Bottom) Results of reconstruction of 37-core MCF over 100 runs. (a) Raw reconstructed differences in βi for each of 100 runs. (b) Residual value of , with convergence cut-off illustrated by black line. (c) Reconstructed differences in βi for each of the 95 runs that satisfied convergence condition. (d) Mean reconstructed differences in βi (red) with error bars equal to the standard deviation of the values in (c). (e) Variations in βi plotted against position in the MCF structure; size of points represents certainty in reconstructed value.

Equations (7)

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d A d z = i MA
M = ( β 1 g 12 g 13 g 1 m g 21 β 2 g 23 g 2 m g 31 g 32 β 3 g 3 m g m 1 g m 2 g m 3 β m ) ,
g i j = 2 π λ 0 d x d y [ n ( x , y ) n ¯ i ] Ψ ¯ i ( ω , x , y ) Ψ ¯ j ( ω , x , y ) .
g 2 -core = 2 Δ n n core 1 a U 2 V 3 K 0 ( W d / a ) K 1 2 ( W ) ,
= 1 2 m k = 1 m i = 1 m | P ˜ out , i ( k ) P out , i ( k ) | .
P = c 1 n st exp ( Δ T ) , Δ > 0 .
T ( n ) = 1 2 m ( c 2 + exp [ ( n c 3 N ) 2 ] ) ,

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