Abstract

Propagation time through standard (solid core) optical fibers changes with the temperature at a rate of 40 ps/km/K. The thermo-optic effect in silica glass accounts for about 95% of this change, and thus, hollow-core fibers, in which the majority of optical power propagates through an air rather than a glass core, can have this sensitivity greatly reduced. To date, we have demonstrated a sensitivity as low as 2 ps/km/K, this value being limited by thermally induced fiber elongation. In this paper, we predict and experimentally demonstrate that the thermal sensitivity of the propagation time can be reduced to zero (or even made negative) in hollow-core photonic bandgap fibers by compensating the thermally induced fiber elongation with an equal and opposite thermally induced group velocity change (i.e., by making the light travel faster through the elongated fiber). This represents the ultimate fiber solution for many propagation time-sensitive applications.

© 2017 Optical Society of America

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2016 (2)

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

J. Flury, “Relativistic geodesy,” J. Phys. 723, 012051 (2016).

2015 (2)

R. Slavík, G. Marra, E. Numkam Kokoua, N. Baddela, N. V. Wheeler, M. Petrovich, F. Poletti, and D. J. Richardson, “Ultralow thermal sensitivity of phase and propagation delay in hollow core optical fibres,” Sci. Rep. 5, 15447 (2015).
[Crossref]

E. R. Numkam Fokoua, S. R. Sandoghchi, Y. Chen, G. T. Jasion, N. V. Wheeler, N. K. Baddela, J. R. Hayes, M. N. Petrovich, D. J. Richardson, and F. Poletti, “Accurate modelling of fabricated hollow-core photonic bandgap fibers,” Opt. Express 23, 23117–23132 (2015).
[Crossref]

2013 (2)

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. Baddela, E. Numkam-Fokuoa, J. R. Hayes, D. R. Gray, Z. Li, R. Slavík, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7, 279–284 (2013).
[Crossref]

L. Olanterä, C. Sigaud, J. Troska, F. Vasey, M. N. Petrovich, F. Poletti, N. V. Wheeler, J. P. Wooler, and D. J. Richardson, “Gamma irradiation of minimal latency hollow-core photonic bandgap fibres,” J. Instrum. 8, C12010 (2013).

2011 (1)

2010 (1)

2009 (2)

2008 (2)

2005 (1)

2004 (3)

2003 (1)

2002 (2)

1996 (1)

1986 (1)

N. C. Frateschi and A. R. B. De Castro, “Perturbation theory for the wave equation and the “effective refractive index” approach,” IEEE J. Quantum Electron. QE-22, 12–15 (1986).
[Crossref]

1967 (1)

Abgrall, M.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Al-Masoudi, A.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Amezcua-Correa, R.

Amy-Klein, A.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Arsov, V.

F. Loehl, V. Arsov, M. Felber, K. Hacker, B. Lorbeer, F. Ludwig, K. Matthiesen, H. Schlarb, B. Schmidt, A. Winter, S. Schulz, J. Zemella, J. Szewinski, and W. Jalmuzna, “Measurement and stabilization of the bunch arrival time at FLASH,” in Proceedings of the 11th European Particle Accelerator Conference (EPAC), Genoa, Italy, 2008, paper THCP158.

Baddela, N.

R. Slavík, G. Marra, E. Numkam Kokoua, N. Baddela, N. V. Wheeler, M. Petrovich, F. Poletti, and D. J. Richardson, “Ultralow thermal sensitivity of phase and propagation delay in hollow core optical fibres,” Sci. Rep. 5, 15447 (2015).
[Crossref]

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. Baddela, E. Numkam-Fokuoa, J. R. Hayes, D. R. Gray, Z. Li, R. Slavík, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7, 279–284 (2013).
[Crossref]

Baddela, N. K.

Bilicki, S.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Bird, D. M.

Birks, T. A.

Bock, M. K.

M. Bousonville, M. K. Bock, M. Felber, T. Ladwig, T. Lamb, H. Schlarb, S. Schulz, C. Sydlo, S. Hunziker, P. Kownacki, and S. Jablonski, “New phase stable optical fiber,” in Proceedings of Beam Instrumentation Workshop (BIW), Virginia, USA, April 15–19, 2012, paper MOPG033.

Bookjans, E.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Bousonville, M.

M. Bousonville, M. K. Bock, M. Felber, T. Ladwig, T. Lamb, H. Schlarb, S. Schulz, C. Sydlo, S. Hunziker, P. Kownacki, and S. Jablonski, “New phase stable optical fiber,” in Proceedings of Beam Instrumentation Workshop (BIW), Virginia, USA, April 15–19, 2012, paper MOPG033.

Bouwmans, G.

Broderick, N. G. R.

Camisard, E.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Chardonnet, C.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Chen, Y.

Chiodo, N.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Costa, M.

M. Koivisto, M. Costa, J. Werner, K. Heiska, J. Talvitie, K. Leppänen, V. Koivunen, and M. Valkama, “Joint device positioning and clock synchronization in 5G ultra-dense networks,” arXiv: 1604.03322v1 (2016).

Cranch, G. A.

Dangui, V.

De Castro, A. R. B.

N. C. Frateschi and A. R. B. De Castro, “Perturbation theory for the wave equation and the “effective refractive index” approach,” IEEE J. Quantum Electron. QE-22, 12–15 (1986).
[Crossref]

Denker, H.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Digonnet, M. J. F.

Dörscher, S.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Engeness, T. D.

Felber, M.

M. Bousonville, M. K. Bock, M. Felber, T. Ladwig, T. Lamb, H. Schlarb, S. Schulz, C. Sydlo, S. Hunziker, P. Kownacki, and S. Jablonski, “New phase stable optical fiber,” in Proceedings of Beam Instrumentation Workshop (BIW), Virginia, USA, April 15–19, 2012, paper MOPG033.

F. Loehl, V. Arsov, M. Felber, K. Hacker, B. Lorbeer, F. Ludwig, K. Matthiesen, H. Schlarb, B. Schmidt, A. Winter, S. Schulz, J. Zemella, J. Szewinski, and W. Jalmuzna, “Measurement and stabilization of the bunch arrival time at FLASH,” in Proceedings of the 11th European Particle Accelerator Conference (EPAC), Genoa, Italy, 2008, paper THCP158.

Fink, Y.

Flury, J.

J. Flury, “Relativistic geodesy,” J. Phys. 723, 012051 (2016).

Frateschi, N. C.

N. C. Frateschi and A. R. B. De Castro, “Perturbation theory for the wave equation and the “effective refractive index” approach,” IEEE J. Quantum Electron. QE-22, 12–15 (1986).
[Crossref]

Gerome, F.

Gray, D. R.

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. Baddela, E. Numkam-Fokuoa, J. R. Hayes, D. R. Gray, Z. Li, R. Slavík, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7, 279–284 (2013).
[Crossref]

Grebing, C.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Grosche, G.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

G. Grosche, O. Terra, K. Predehl, R. Holzwarth, B. Lipphardt, F. Vogt, U. Sterr, and H. Schnatz, “Optical frequency transfer via 146  km fiber link with 10-19 relative accuracy,” Opt. Lett. 34, 2270–2272 (2009).
[Crossref]

Hacker, K.

F. Loehl, V. Arsov, M. Felber, K. Hacker, B. Lorbeer, F. Ludwig, K. Matthiesen, H. Schlarb, B. Schmidt, A. Winter, S. Schulz, J. Zemella, J. Szewinski, and W. Jalmuzna, “Measurement and stabilization of the bunch arrival time at FLASH,” in Proceedings of the 11th European Particle Accelerator Conference (EPAC), Genoa, Italy, 2008, paper THCP158.

Häfner, S.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Hand, D. P.

Hayes, J. R.

E. R. Numkam Fokoua, S. R. Sandoghchi, Y. Chen, G. T. Jasion, N. V. Wheeler, N. K. Baddela, J. R. Hayes, M. N. Petrovich, D. J. Richardson, and F. Poletti, “Accurate modelling of fabricated hollow-core photonic bandgap fibers,” Opt. Express 23, 23117–23132 (2015).
[Crossref]

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. Baddela, E. Numkam-Fokuoa, J. R. Hayes, D. R. Gray, Z. Li, R. Slavík, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7, 279–284 (2013).
[Crossref]

Hedley, T. D.

Heiska, K.

M. Koivisto, M. Costa, J. Werner, K. Heiska, J. Talvitie, K. Leppänen, V. Koivunen, and M. Valkama, “Joint device positioning and clock synchronization in 5G ultra-dense networks,” arXiv: 1604.03322v1 (2016).

Holzwarth, R.

Hunziker, S.

M. Bousonville, M. K. Bock, M. Felber, T. Ladwig, T. Lamb, H. Schlarb, S. Schulz, C. Sydlo, S. Hunziker, P. Kownacki, and S. Jablonski, “New phase stable optical fiber,” in Proceedings of Beam Instrumentation Workshop (BIW), Virginia, USA, April 15–19, 2012, paper MOPG033.

Ibanescu, M.

Jablonski, S.

M. Bousonville, M. K. Bock, M. Felber, T. Ladwig, T. Lamb, H. Schlarb, S. Schulz, C. Sydlo, S. Hunziker, P. Kownacki, and S. Jablonski, “New phase stable optical fiber,” in Proceedings of Beam Instrumentation Workshop (BIW), Virginia, USA, April 15–19, 2012, paper MOPG033.

Jacobs, S. A.

Jalmuzna, W.

F. Loehl, V. Arsov, M. Felber, K. Hacker, B. Lorbeer, F. Ludwig, K. Matthiesen, H. Schlarb, B. Schmidt, A. Winter, S. Schulz, J. Zemella, J. Szewinski, and W. Jalmuzna, “Measurement and stabilization of the bunch arrival time at FLASH,” in Proceedings of the 11th European Particle Accelerator Conference (EPAC), Genoa, Italy, 2008, paper THCP158.

Jasion, G. T.

Jiang, H.

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed., (Princeton University, 2008), p. 20.

Johnson, S. G.

Jones, J. D. C.

Kéfélian, F.

Kim, H. K.

Kino, G. S.

Knight, J. C.

Koczwara, A.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Koivisto, M.

M. Koivisto, M. Costa, J. Werner, K. Heiska, J. Talvitie, K. Leppänen, V. Koivunen, and M. Valkama, “Joint device positioning and clock synchronization in 5G ultra-dense networks,” arXiv: 1604.03322v1 (2016).

Koivunen, V.

M. Koivisto, M. Costa, J. Werner, K. Heiska, J. Talvitie, K. Leppänen, V. Koivunen, and M. Valkama, “Joint device positioning and clock synchronization in 5G ultra-dense networks,” arXiv: 1604.03322v1 (2016).

Koke, S.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Koshiba, M.

Kownacki, P.

M. Bousonville, M. K. Bock, M. Felber, T. Ladwig, T. Lamb, H. Schlarb, S. Schulz, C. Sydlo, S. Hunziker, P. Kownacki, and S. Jablonski, “New phase stable optical fiber,” in Proceedings of Beam Instrumentation Workshop (BIW), Virginia, USA, April 15–19, 2012, paper MOPG033.

Kuhl, A.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Ladwig, T.

M. Bousonville, M. K. Bock, M. Felber, T. Ladwig, T. Lamb, H. Schlarb, S. Schulz, C. Sydlo, S. Hunziker, P. Kownacki, and S. Jablonski, “New phase stable optical fiber,” in Proceedings of Beam Instrumentation Workshop (BIW), Virginia, USA, April 15–19, 2012, paper MOPG033.

Lamb, T.

M. Bousonville, M. K. Bock, M. Felber, T. Ladwig, T. Lamb, H. Schlarb, S. Schulz, C. Sydlo, S. Hunziker, P. Kownacki, and S. Jablonski, “New phase stable optical fiber,” in Proceedings of Beam Instrumentation Workshop (BIW), Virginia, USA, April 15–19, 2012, paper MOPG033.

Le Coq, Y.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Le Targat, R.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Legero, T.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Lemonde, P.

Leon-Saval, S. G.

Leppänen, K.

M. Koivisto, M. Costa, J. Werner, K. Heiska, J. Talvitie, K. Leppänen, V. Koivunen, and M. Valkama, “Joint device positioning and clock synchronization in 5G ultra-dense networks,” arXiv: 1604.03322v1 (2016).

Li, D.

K. Zhang and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics, 2nd ed., (Springer, 2008), p. 313.

Li, Z.

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. Baddela, E. Numkam-Fokuoa, J. R. Hayes, D. R. Gray, Z. Li, R. Slavík, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7, 279–284 (2013).
[Crossref]

Lipphardt, B.

Lisdat, C.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Lodewyck, J.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Loehl, F.

F. Loehl, V. Arsov, M. Felber, K. Hacker, B. Lorbeer, F. Ludwig, K. Matthiesen, H. Schlarb, B. Schmidt, A. Winter, S. Schulz, J. Zemella, J. Szewinski, and W. Jalmuzna, “Measurement and stabilization of the bunch arrival time at FLASH,” in Proceedings of the 11th European Particle Accelerator Conference (EPAC), Genoa, Italy, 2008, paper THCP158.

Lopez, O.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Lorbeer, B.

F. Loehl, V. Arsov, M. Felber, K. Hacker, B. Lorbeer, F. Ludwig, K. Matthiesen, H. Schlarb, B. Schmidt, A. Winter, S. Schulz, J. Zemella, J. Szewinski, and W. Jalmuzna, “Measurement and stabilization of the bunch arrival time at FLASH,” in Proceedings of the 11th European Particle Accelerator Conference (EPAC), Genoa, Italy, 2008, paper THCP158.

Lours, M.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Ludwig, F.

F. Loehl, V. Arsov, M. Felber, K. Hacker, B. Lorbeer, F. Ludwig, K. Matthiesen, H. Schlarb, B. Schmidt, A. Winter, S. Schulz, J. Zemella, J. Szewinski, and W. Jalmuzna, “Measurement and stabilization of the bunch arrival time at FLASH,” in Proceedings of the 11th European Particle Accelerator Conference (EPAC), Genoa, Italy, 2008, paper THCP158.

Maleki, L.

Mangan, B. J.

Marra, G.

R. Slavík, G. Marra, E. Numkam Kokoua, N. Baddela, N. V. Wheeler, M. Petrovich, F. Poletti, and D. J. Richardson, “Ultralow thermal sensitivity of phase and propagation delay in hollow core optical fibres,” Sci. Rep. 5, 15447 (2015).
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Matthiesen, K.

F. Loehl, V. Arsov, M. Felber, K. Hacker, B. Lorbeer, F. Ludwig, K. Matthiesen, H. Schlarb, B. Schmidt, A. Winter, S. Schulz, J. Zemella, J. Szewinski, and W. Jalmuzna, “Measurement and stabilization of the bunch arrival time at FLASH,” in Proceedings of the 11th European Particle Accelerator Conference (EPAC), Genoa, Italy, 2008, paper THCP158.

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed., (Princeton University, 2008), p. 20.

Meynadier, F.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Miller, G. A.

Mortensen, N. A.

Nicolodi, D.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Nielsen, M. D.

Numkam Fokoua, E. R.

Numkam Kokoua, E.

R. Slavík, G. Marra, E. Numkam Kokoua, N. Baddela, N. V. Wheeler, M. Petrovich, F. Poletti, and D. J. Richardson, “Ultralow thermal sensitivity of phase and propagation delay in hollow core optical fibres,” Sci. Rep. 5, 15447 (2015).
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Numkam-Fokuoa, E.

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. Baddela, E. Numkam-Fokuoa, J. R. Hayes, D. R. Gray, Z. Li, R. Slavík, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7, 279–284 (2013).
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Olanterä, L.

L. Olanterä, C. Sigaud, J. Troska, F. Vasey, M. N. Petrovich, F. Poletti, N. V. Wheeler, J. P. Wooler, and D. J. Richardson, “Gamma irradiation of minimal latency hollow-core photonic bandgap fibres,” J. Instrum. 8, C12010 (2013).

Owens, J. C.

Petrovich, M.

R. Slavík, G. Marra, E. Numkam Kokoua, N. Baddela, N. V. Wheeler, M. Petrovich, F. Poletti, and D. J. Richardson, “Ultralow thermal sensitivity of phase and propagation delay in hollow core optical fibres,” Sci. Rep. 5, 15447 (2015).
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Petrovich, M. N.

E. R. Numkam Fokoua, S. R. Sandoghchi, Y. Chen, G. T. Jasion, N. V. Wheeler, N. K. Baddela, J. R. Hayes, M. N. Petrovich, D. J. Richardson, and F. Poletti, “Accurate modelling of fabricated hollow-core photonic bandgap fibers,” Opt. Express 23, 23117–23132 (2015).
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L. Olanterä, C. Sigaud, J. Troska, F. Vasey, M. N. Petrovich, F. Poletti, N. V. Wheeler, J. P. Wooler, and D. J. Richardson, “Gamma irradiation of minimal latency hollow-core photonic bandgap fibres,” J. Instrum. 8, C12010 (2013).

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. Baddela, E. Numkam-Fokuoa, J. R. Hayes, D. R. Gray, Z. Li, R. Slavík, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7, 279–284 (2013).
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M. N. Petrovich, F. Poletti, A. van Brakel, and D. J. Richardson, “Robustly single mode hollow core photonic bandgap fiber,” Opt. Express 16, 4337–4346 (2008).
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Poletti, F.

R. Slavík, G. Marra, E. Numkam Kokoua, N. Baddela, N. V. Wheeler, M. Petrovich, F. Poletti, and D. J. Richardson, “Ultralow thermal sensitivity of phase and propagation delay in hollow core optical fibres,” Sci. Rep. 5, 15447 (2015).
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E. R. Numkam Fokoua, S. R. Sandoghchi, Y. Chen, G. T. Jasion, N. V. Wheeler, N. K. Baddela, J. R. Hayes, M. N. Petrovich, D. J. Richardson, and F. Poletti, “Accurate modelling of fabricated hollow-core photonic bandgap fibers,” Opt. Express 23, 23117–23132 (2015).
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F. Poletti, N. V. Wheeler, M. N. Petrovich, N. Baddela, E. Numkam-Fokuoa, J. R. Hayes, D. R. Gray, Z. Li, R. Slavík, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7, 279–284 (2013).
[Crossref]

L. Olanterä, C. Sigaud, J. Troska, F. Vasey, M. N. Petrovich, F. Poletti, N. V. Wheeler, J. P. Wooler, and D. J. Richardson, “Gamma irradiation of minimal latency hollow-core photonic bandgap fibres,” J. Instrum. 8, C12010 (2013).

F. Poletti, “Hollow core fiber with an octave spanning bandgap,” Opt. Lett. 35, 2837–2839 (2010).
[Crossref]

M. N. Petrovich, F. Poletti, A. van Brakel, and D. J. Richardson, “Robustly single mode hollow core photonic bandgap fiber,” Opt. Express 16, 4337–4346 (2008).
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Pottage, J. M.

Pottie, P.-E.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Predehl, K.

Quintin, N.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Raupach, S. M. F.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Richardson, D. J.

R. Slavík, G. Marra, E. Numkam Kokoua, N. Baddela, N. V. Wheeler, M. Petrovich, F. Poletti, and D. J. Richardson, “Ultralow thermal sensitivity of phase and propagation delay in hollow core optical fibres,” Sci. Rep. 5, 15447 (2015).
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E. R. Numkam Fokoua, S. R. Sandoghchi, Y. Chen, G. T. Jasion, N. V. Wheeler, N. K. Baddela, J. R. Hayes, M. N. Petrovich, D. J. Richardson, and F. Poletti, “Accurate modelling of fabricated hollow-core photonic bandgap fibers,” Opt. Express 23, 23117–23132 (2015).
[Crossref]

L. Olanterä, C. Sigaud, J. Troska, F. Vasey, M. N. Petrovich, F. Poletti, N. V. Wheeler, J. P. Wooler, and D. J. Richardson, “Gamma irradiation of minimal latency hollow-core photonic bandgap fibres,” J. Instrum. 8, C12010 (2013).

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. Baddela, E. Numkam-Fokuoa, J. R. Hayes, D. R. Gray, Z. Li, R. Slavík, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7, 279–284 (2013).
[Crossref]

M. N. Petrovich, F. Poletti, A. van Brakel, and D. J. Richardson, “Robustly single mode hollow core photonic bandgap fiber,” Opt. Express 16, 4337–4346 (2008).
[Crossref]

Robyr, J.-L.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Saitoh, K.

Sandoghchi, S. R.

Santarelli, G.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

F. Kéfélian, H. Jiang, P. Lemonde, and G. Santarelli, “Ultralow-frequency-noise stabilization of a laser by locking to an optical fiber-delay line,” Opt. Lett. 34, 914–916 (2009).
[Crossref]

Schlarb, H.

M. Bousonville, M. K. Bock, M. Felber, T. Ladwig, T. Lamb, H. Schlarb, S. Schulz, C. Sydlo, S. Hunziker, P. Kownacki, and S. Jablonski, “New phase stable optical fiber,” in Proceedings of Beam Instrumentation Workshop (BIW), Virginia, USA, April 15–19, 2012, paper MOPG033.

F. Loehl, V. Arsov, M. Felber, K. Hacker, B. Lorbeer, F. Ludwig, K. Matthiesen, H. Schlarb, B. Schmidt, A. Winter, S. Schulz, J. Zemella, J. Szewinski, and W. Jalmuzna, “Measurement and stabilization of the bunch arrival time at FLASH,” in Proceedings of the 11th European Particle Accelerator Conference (EPAC), Genoa, Italy, 2008, paper THCP158.

Schmidt, B.

F. Loehl, V. Arsov, M. Felber, K. Hacker, B. Lorbeer, F. Ludwig, K. Matthiesen, H. Schlarb, B. Schmidt, A. Winter, S. Schulz, J. Zemella, J. Szewinski, and W. Jalmuzna, “Measurement and stabilization of the bunch arrival time at FLASH,” in Proceedings of the 11th European Particle Accelerator Conference (EPAC), Genoa, Italy, 2008, paper THCP158.

Schnatz, H.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

G. Grosche, O. Terra, K. Predehl, R. Holzwarth, B. Lipphardt, F. Vogt, U. Sterr, and H. Schnatz, “Optical frequency transfer via 146  km fiber link with 10-19 relative accuracy,” Opt. Lett. 34, 2270–2272 (2009).
[Crossref]

Schulz, S.

F. Loehl, V. Arsov, M. Felber, K. Hacker, B. Lorbeer, F. Ludwig, K. Matthiesen, H. Schlarb, B. Schmidt, A. Winter, S. Schulz, J. Zemella, J. Szewinski, and W. Jalmuzna, “Measurement and stabilization of the bunch arrival time at FLASH,” in Proceedings of the 11th European Particle Accelerator Conference (EPAC), Genoa, Italy, 2008, paper THCP158.

M. Bousonville, M. K. Bock, M. Felber, T. Ladwig, T. Lamb, H. Schlarb, S. Schulz, C. Sydlo, S. Hunziker, P. Kownacki, and S. Jablonski, “New phase stable optical fiber,” in Proceedings of Beam Instrumentation Workshop (BIW), Virginia, USA, April 15–19, 2012, paper MOPG033.

Shephard, J. D.

Shi, C.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Sigaud, C.

L. Olanterä, C. Sigaud, J. Troska, F. Vasey, M. N. Petrovich, F. Poletti, N. V. Wheeler, J. P. Wooler, and D. J. Richardson, “Gamma irradiation of minimal latency hollow-core photonic bandgap fibres,” J. Instrum. 8, C12010 (2013).

Skorobogatiy, M.

Slavík, R.

R. Slavík, G. Marra, E. Numkam Kokoua, N. Baddela, N. V. Wheeler, M. Petrovich, F. Poletti, and D. J. Richardson, “Ultralow thermal sensitivity of phase and propagation delay in hollow core optical fibres,” Sci. Rep. 5, 15447 (2015).
[Crossref]

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. Baddela, E. Numkam-Fokuoa, J. R. Hayes, D. R. Gray, Z. Li, R. Slavík, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7, 279–284 (2013).
[Crossref]

Soljacic, M.

St.J. Russell, P.

Stefani, F.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Sterr, U.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

G. Grosche, O. Terra, K. Predehl, R. Holzwarth, B. Lipphardt, F. Vogt, U. Sterr, and H. Schnatz, “Optical frequency transfer via 146  km fiber link with 10-19 relative accuracy,” Opt. Lett. 34, 2270–2272 (2009).
[Crossref]

Sydlo, C.

M. Bousonville, M. K. Bock, M. Felber, T. Ladwig, T. Lamb, H. Schlarb, S. Schulz, C. Sydlo, S. Hunziker, P. Kownacki, and S. Jablonski, “New phase stable optical fiber,” in Proceedings of Beam Instrumentation Workshop (BIW), Virginia, USA, April 15–19, 2012, paper MOPG033.

Szewinski, J.

F. Loehl, V. Arsov, M. Felber, K. Hacker, B. Lorbeer, F. Ludwig, K. Matthiesen, H. Schlarb, B. Schmidt, A. Winter, S. Schulz, J. Zemella, J. Szewinski, and W. Jalmuzna, “Measurement and stabilization of the bunch arrival time at FLASH,” in Proceedings of the 11th European Particle Accelerator Conference (EPAC), Genoa, Italy, 2008, paper THCP158.

Talvitie, J.

M. Koivisto, M. Costa, J. Werner, K. Heiska, J. Talvitie, K. Leppänen, V. Koivunen, and M. Valkama, “Joint device positioning and clock synchronization in 5G ultra-dense networks,” arXiv: 1604.03322v1 (2016).

Terra, O.

Troska, J.

L. Olanterä, C. Sigaud, J. Troska, F. Vasey, M. N. Petrovich, F. Poletti, N. V. Wheeler, J. P. Wooler, and D. J. Richardson, “Gamma irradiation of minimal latency hollow-core photonic bandgap fibres,” J. Instrum. 8, C12010 (2013).

Valkama, M.

M. Koivisto, M. Costa, J. Werner, K. Heiska, J. Talvitie, K. Leppänen, V. Koivunen, and M. Valkama, “Joint device positioning and clock synchronization in 5G ultra-dense networks,” arXiv: 1604.03322v1 (2016).

van Brakel, A.

Vasey, F.

L. Olanterä, C. Sigaud, J. Troska, F. Vasey, M. N. Petrovich, F. Poletti, N. V. Wheeler, J. P. Wooler, and D. J. Richardson, “Gamma irradiation of minimal latency hollow-core photonic bandgap fibres,” J. Instrum. 8, C12010 (2013).

Vogt, F.

Weisberg, O.

Werner, J.

M. Koivisto, M. Costa, J. Werner, K. Heiska, J. Talvitie, K. Leppänen, V. Koivunen, and M. Valkama, “Joint device positioning and clock synchronization in 5G ultra-dense networks,” arXiv: 1604.03322v1 (2016).

Wheeler, N. V.

R. Slavík, G. Marra, E. Numkam Kokoua, N. Baddela, N. V. Wheeler, M. Petrovich, F. Poletti, and D. J. Richardson, “Ultralow thermal sensitivity of phase and propagation delay in hollow core optical fibres,” Sci. Rep. 5, 15447 (2015).
[Crossref]

E. R. Numkam Fokoua, S. R. Sandoghchi, Y. Chen, G. T. Jasion, N. V. Wheeler, N. K. Baddela, J. R. Hayes, M. N. Petrovich, D. J. Richardson, and F. Poletti, “Accurate modelling of fabricated hollow-core photonic bandgap fibers,” Opt. Express 23, 23117–23132 (2015).
[Crossref]

L. Olanterä, C. Sigaud, J. Troska, F. Vasey, M. N. Petrovich, F. Poletti, N. V. Wheeler, J. P. Wooler, and D. J. Richardson, “Gamma irradiation of minimal latency hollow-core photonic bandgap fibres,” J. Instrum. 8, C12010 (2013).

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. Baddela, E. Numkam-Fokuoa, J. R. Hayes, D. R. Gray, Z. Li, R. Slavík, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7, 279–284 (2013).
[Crossref]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed., (Princeton University, 2008), p. 20.

Winter, A.

F. Loehl, V. Arsov, M. Felber, K. Hacker, B. Lorbeer, F. Ludwig, K. Matthiesen, H. Schlarb, B. Schmidt, A. Winter, S. Schulz, J. Zemella, J. Szewinski, and W. Jalmuzna, “Measurement and stabilization of the bunch arrival time at FLASH,” in Proceedings of the 11th European Particle Accelerator Conference (EPAC), Genoa, Italy, 2008, paper THCP158.

Wiotte, F.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Wooler, J. P.

L. Olanterä, C. Sigaud, J. Troska, F. Vasey, M. N. Petrovich, F. Poletti, N. V. Wheeler, J. P. Wooler, and D. J. Richardson, “Gamma irradiation of minimal latency hollow-core photonic bandgap fibres,” J. Instrum. 8, C12010 (2013).

Yao, X. S.

Zemella, J.

F. Loehl, V. Arsov, M. Felber, K. Hacker, B. Lorbeer, F. Ludwig, K. Matthiesen, H. Schlarb, B. Schmidt, A. Winter, S. Schulz, J. Zemella, J. Szewinski, and W. Jalmuzna, “Measurement and stabilization of the bunch arrival time at FLASH,” in Proceedings of the 11th European Particle Accelerator Conference (EPAC), Genoa, Italy, 2008, paper THCP158.

Zhang, K.

K. Zhang and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics, 2nd ed., (Springer, 2008), p. 313.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

N. C. Frateschi and A. R. B. De Castro, “Perturbation theory for the wave equation and the “effective refractive index” approach,” IEEE J. Quantum Electron. QE-22, 12–15 (1986).
[Crossref]

J. Instrum. (1)

L. Olanterä, C. Sigaud, J. Troska, F. Vasey, M. N. Petrovich, F. Poletti, N. V. Wheeler, J. P. Wooler, and D. J. Richardson, “Gamma irradiation of minimal latency hollow-core photonic bandgap fibres,” J. Instrum. 8, C12010 (2013).

J. Opt. Soc. Am. B (2)

J. Phys. (1)

J. Flury, “Relativistic geodesy,” J. Phys. 723, 012051 (2016).

Nat. Commun. (1)

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. M. F. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kuhl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref]

Nat. Photonics (1)

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. Baddela, E. Numkam-Fokuoa, J. R. Hayes, D. R. Gray, Z. Li, R. Slavík, and D. J. Richardson, “Towards high-capacity fibre-optic communications at the speed of light in vacuum,” Nat. Photonics 7, 279–284 (2013).
[Crossref]

Opt. Express (8)

K. Saitoh and M. Koshiba, “Leakage loss and group velocity dispersion in air-core photonic bandgap fibers,” Opt. Express 11, 3100–3109 (2003).
[Crossref]

T. A. Birks, D. M. Bird, T. D. Hedley, J. M. Pottage, and P. St.J. Russell, “Scaling laws and vector effects in bandgap-guiding fibres,” Opt. Express 12, 69–74 (2004).
[Crossref]

M. Skorobogatiy, S. A. Jacobs, S. G. Johnson, and Y. Fink, “Geometric variations in high index-contrast waveguides, coupled mode theory in curvilinear coordinates,” Opt. Express 10, 1227–1243 (2002).
[Crossref]

J. D. Shephard, J. D. C. Jones, D. P. Hand, G. Bouwmans, J. C. Knight, P. St.J. Russell, and B. J. Mangan, “High energy nanosecond laser pulses delivered single-mode through hollow-core PBG fibers,” Opt. Express 12, 717–723 (2004).
[Crossref]

V. Dangui, H. K. Kim, M. J. F. Digonnet, and G. S. Kino, “Phase sensitivity of temperature of the fundamental mode in air-guiding photonic-bandgap fibers,” Opt. Express 13, 6669–6684 (2005).
[Crossref]

R. Amezcua-Correa, F. Gerome, S. G. Leon-Saval, N. G. R. Broderick, T. A. Birks, and J. C. Knight, “Control of surface modes in low loss hollow-core photonic bandgap fibers,” Opt. Express 16, 1142–1149 (2008).
[Crossref]

M. N. Petrovich, F. Poletti, A. van Brakel, and D. J. Richardson, “Robustly single mode hollow core photonic bandgap fiber,” Opt. Express 16, 4337–4346 (2008).
[Crossref]

E. R. Numkam Fokoua, S. R. Sandoghchi, Y. Chen, G. T. Jasion, N. V. Wheeler, N. K. Baddela, J. R. Hayes, M. N. Petrovich, D. J. Richardson, and F. Poletti, “Accurate modelling of fabricated hollow-core photonic bandgap fibers,” Opt. Express 23, 23117–23132 (2015).
[Crossref]

Opt. Lett. (5)

Sci. Rep. (1)

R. Slavík, G. Marra, E. Numkam Kokoua, N. Baddela, N. V. Wheeler, M. Petrovich, F. Poletti, and D. J. Richardson, “Ultralow thermal sensitivity of phase and propagation delay in hollow core optical fibres,” Sci. Rep. 5, 15447 (2015).
[Crossref]

Other (7)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed., (Princeton University, 2008), p. 20.

American Institute of Physics Handbook (McGraw-Hill, 1957).

M. Koivisto, M. Costa, J. Werner, K. Heiska, J. Talvitie, K. Leppänen, V. Koivunen, and M. Valkama, “Joint device positioning and clock synchronization in 5G ultra-dense networks,” arXiv: 1604.03322v1 (2016).

F. Loehl, V. Arsov, M. Felber, K. Hacker, B. Lorbeer, F. Ludwig, K. Matthiesen, H. Schlarb, B. Schmidt, A. Winter, S. Schulz, J. Zemella, J. Szewinski, and W. Jalmuzna, “Measurement and stabilization of the bunch arrival time at FLASH,” in Proceedings of the 11th European Particle Accelerator Conference (EPAC), Genoa, Italy, 2008, paper THCP158.

M. Bousonville, M. K. Bock, M. Felber, T. Ladwig, T. Lamb, H. Schlarb, S. Schulz, C. Sydlo, S. Hunziker, P. Kownacki, and S. Jablonski, “New phase stable optical fiber,” in Proceedings of Beam Instrumentation Workshop (BIW), Virginia, USA, April 15–19, 2012, paper MOPG033.

K. Zhang and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics, 2nd ed., (Springer, 2008), p. 313.

https://doi.org/10.5258/SOTON/D0073 .

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Figures (13)

Fig. 1.
Fig. 1. Principle of our compensation method. (a) A temperature increase makes the HC-PBGF longer by ΔL. Simultaneously, the glass refractive index and the fiber cross-section dimensions increase, modifying ng. We target conditions for which ng decreases with temperature (making the light travel faster), compensating for the fiber elongation. (b) Sketch of typical transmission and ng characteristics of an HC-PBGF at two temperatures. Increasing the temperature shifts the bandgap position to longer wavelengths [Eq. (7)], resulting in dng/dT>0 at shorter wavelengths and dng/dT<0 at longer wavelengths. The magnitude of this change is given by the gradient of the group delay, i.e., the chromatic dispersion. At a specific wavelength, the decrease in ng exactly compensates for the fiber elongation.

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Fig. 2.
Fig. 2. Structure used to model thermal effects in a realistic fiber comprising a finite-thickness silica jacket and a coating layer.

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Fig. 3.
Fig. 3. Simulated thermal coefficient of delay in an uncoated 7-cell HC-PBGF using finite element simulation (black solid), Eq. (9) (blue dashed–dotted), and Eq. (13) (red dashed); air-filling fraction is 0.975.

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Fig. 4.
Fig. 4. Simulated contributions to the thermal coefficient of delay in an uncoated 7-cell HC-PBGF. These include the transverse (black, solid) and longitudinal (green, dashed) thermal expansion, photo-elastic effect (dashed–dotted, blue), and thermo-optic effect (red, dotted). The air-filling fraction is 0.975.

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Fig. 5.
Fig. 5. Effect of polymer coating on the thermal coefficient of delay: 7-cell uncoated HC-PBGF with air-filling fraction of 0.975 (for reference, solid blue). Finite element full simulation results considering 45 μm acrylate coating and HC-PBGF with 40 μm (green, dotted) or 70 μm (red, dashed) silica jacket. Approximation using Eq. (14) (black, solid).

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Fig. 6.
Fig. 6. Thermal coefficient of delay as function of the core size: 3 (blue, dashed), 7 (black, solid), 19 (green, dashed–dotted), and 37-cell fibers (red, short dashed–dotted); the air-filling fraction is kept constant at 0.975. The spectral width over which the |TCD|≤0.2  ps/km/K is also shown.

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Fig. 7.
Fig. 7. Thermal coefficient of delay in 7-cell HC-PBGFs with different air-filling fraction d/Λ values: 0.95 (orange, dotted), 0.96 (blue, long dashed), 0.97 (solid, black), 0.98 (red, short dashed), and 0.99 (green, dashed–dotted). |TCD|≤0.2  ps/km/K spectral width is also shown. The cladding pitch for each fiber was scaled so as to obtain a photonic bandgap centered at 1.55 μm.

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Fig. 8.
Fig. 8. Transmission characteristics of the 7-cell HC-PBGF used. Theoretical curve (red, dashed) shows the fraction of the guided mode power carried in the core. This calculation was performed using data from a scanning electron micrograph of the fiber cross section, as described in Ref. [27]. The measured transmission is shown in solid black.

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Fig. 9.
Fig. 9. (a) Micrographs of the manufactured fiber. (b) The experimental setup. The 2.8 m long sample under test is placed on a hot plate (between two metallic sheets) and connected within a balanced interferometer. The spectral phase is recorded for various fiber temperatures. BS: Beam splitter.

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Fig. 10.
Fig. 10. Spectral phase (normalized to 1 m of fiber length) measured at 29°C. Each point corresponds to one interference maxima or minima in the measured spectrogram.

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Fig. 11.
Fig. 11. Normalized propagation delay evaluated from phase responses measured at 29°C (a) and its change as the fiber sample was heated to 47°C, 65°C, and 82°C (b).

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Fig. 12.
Fig. 12. TCD as a function of the wavelength: theoretical [including the acrylate jacket, Eq. (14)] and experimental results.

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Fig. 13.
Fig. 13. Dispersion evaluated from delay (experimental data shown in Fig. 12). The experimental values are solid black; the calculated values are dashed red.

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Equations (15)

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

τ=ngLc,
TCD=1LdτdT=1c(ng1LdLdT+dngdT)=1c(εzzng+dngdT),
εzz=1LdLdT
1ngdngdT=−εzz.
kΛ(nglass2−nair2)1/2
1λ0ΔλΔT=1ΛΔΛΔT+nglassnglass2−1ΔnΔT.
ΔλΔT=23.2  pm/K.
dngdT=−dngdλΔλΔT=−cDΔλΔT,
TCD=αngc−DΔλΔT.
Δβexp=αΔT(ω∂β∂ω−β),
Δβn=∬E*Δε(x,y)k02Edxdy2β∬E*Edxdy,
Δβn=k02βnglassΔnΔTη(λ)ΔT,
TCD=α∂β∂ω−αλD+∂∂ω(ΔnΔTk02βnglassη(λ)).
TCD=εzz∂β∂ω−α¯λD+∂∂ω((ΔnΔT)¯k02βnglassη(λ)),
n2−1n2+2=∑n0i2−1n0i2+2ρiρ0i,

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