Abstract

We report the importance of cross-phase modulation (XPM) on the coherence of a low-energy probe pulse co-propagating with a high-energy pump pulse that generates incoherent supercontinuum in all-normal dispersion (ANDi) fiber due to Raman amplification of quantum noise. By investigating numerous fiber and pulse parameters, we show consistently that for weak probe pulses, the XPM from the pump is the dominant influence on the degradation of the probe coherence. We show that the faster decoherence at the pump leading edge means that the probe coherence is reduced more significantly when the probe has a higher group velocity, i.e., when an orthogonally polarized probe is aligned to the fast (lower refractive index) axis of the fiber or when a co-polarized probe has a longer central wavelength. Simulations show that this effect occurs for both polarization-maintaining (PM) and non-PM ANDi fibers and can result in a probe decoherence rate that is higher than that of the pump. These previously unreported results extend our earlier scalar simulations showing incoherent supercontinuum within a single pulse.

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References

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2019 (1)

2018 (5)

D. Dobrakowski, A. Rampur, G. Stępniewski, A. Anuszkiewicz, J. Lisowska, D. Pysz, R. Kasztelanic, and M. Klimczak, “Development of highly nonlinear polarization-maintaining fibers with normal dispersion across entire transmission window,” J. Opt. 21, 015504 (2018).
[Crossref]

S. Xing, S. Kharitonov, J. Hu, and C.-S. Brès, “Linearly chirped mid-infrared supercontinuum in all-normal-dispersion chalcogenide photonic crystal fibers,” Opt. Express 26, 19627–19636 (2018).
[Crossref]

I. B. Gonzalo and O. Bang, “Role of the Raman gain in the noise dynamics of all-normal dispersion silica fiber supercontinuum generation,” J. Opt. Soc. Am. B 35, 2102–2110 (2018).
[Crossref]

I. B. Gonzalo, R. D. Engelsholm, M. P. Sørensen, and O. Bang, “Polarization noise places severe constraints on coherence of all-normal dispersion femtosecond supercontinuum generation,” Sci. Rep. 8, 6579 (2018).
[Crossref]

H. Timmers, A. Kowligy, A. Lind, F. C. Cruz, N. Nader, M. Silfies, G. Ycas, T. K. Allison, P. G. Schunemann, S. B. Papp, and S. A. Diddams, “Molecular fingerprinting with bright, broadband infrared frequency combs,” Optica 5, 727–732 (2018).
[Crossref]

2017 (4)

2016 (1)

2013 (2)

L. Shen, N. Healy, P. Mehta, T. D. Day, J. R. Sparks, J. V. Badding, and A. C. Peacock, “Nonlinear transmission properties of hydrogenated amorphous silicon core fibers towards the mid-infrared regime,” Opt. Express 21, 13075–13083 (2013).
[Crossref]

C. R. Head, H. Y. Chan, J. S. Feehan, D. P. Shepherd, S. Alam, A. C. Tropper, J. H. V. Price, and K. G. Wilcox, “Supercontinuum generation with GHz repetition rate femtosecond-pulse fiber-amplified VECSELs,” IEEE Photon. Technol. Lett. 25, 464–467 (2013).
[Crossref]

2012 (2)

J. H. V. Price, X. Feng, A. M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W. H. Loh, H. N. Rutt, and D. J. Richardson, “Supercontinuum generation in non-silica fibers,” Opt. Fiber Technol. 18, 327–344 (2012).
[Crossref]

A. A. Rieznik, A. M. Heidt, P. G. Konig, V. A. Bettachini, and D. F. Grosz, “Optimum integration procedures for supercontinuum simulation,” IEEE Photon. J. 4, 552–560 (2012).
[Crossref]

2011 (3)

2010 (2)

2009 (1)

2008 (1)

2007 (2)

2006 (2)

2005 (2)

2004 (2)

2002 (5)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref]

S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. 89, 273901 (2002).
[Crossref]

J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler, “All-optical switching based on cross-phase modulation in microstructure fiber,” IEEE Photon. Technol. Lett. 14, 77–79 (2002).
[Crossref]

J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27, 1180–1182 (2002).
[Crossref]

J. M. Dudley and S. Coen, “Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers,” IEEE J. Sel. Top. Quantum Electron 8, 651–659 (2002).
[Crossref]

2001 (2)

P. D. Drummond and J. F. Corney, “Quantum noise in optical fibers. I. Stochastic equations,” J. Opt. Soc. Am. B 18, 139–152 (2001).
[Crossref]

B.-E. Olsson and D. J. Blumenthal, “All-optical demultiplexing using fiber cross-phase modulation (XPM) and optical filtering,” IEEE Photon. Technol. Lett. 13, 875–877 (2001).
[Crossref]

2000 (1)

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (2000).
[Crossref]

1993 (2)

1992 (2)

1990 (1)

E. A. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, “Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
[Crossref]

1989 (2)

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Modulation instability induced by cross-phase modulation in optical fibers,” Phys. Rev. A 39, 3406–3413 (1989).
[Crossref]

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159–1166 (1989).
[Crossref]

1987 (1)

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[Crossref]

1986 (2)

1985 (1)

1979 (1)

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55µm,” Electron. Lett. 15, 106–108 (1979).
[Crossref]

1972 (1)

Agrawal, G. P.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Modulation instability induced by cross-phase modulation in optical fibers,” Phys. Rev. A 39, 3406–3413 (1989).
[Crossref]

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2006).

Alam, S.

C. R. Head, H. Y. Chan, J. S. Feehan, D. P. Shepherd, S. Alam, A. C. Tropper, J. H. V. Price, and K. G. Wilcox, “Supercontinuum generation with GHz repetition rate femtosecond-pulse fiber-amplified VECSELs,” IEEE Photon. Technol. Lett. 25, 464–467 (2013).
[Crossref]

Alfano, R. R.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Modulation instability induced by cross-phase modulation in optical fibers,” Phys. Rev. A 39, 3406–3413 (1989).
[Crossref]

Allison, T. K.

Anderson, D.

Andrejco, M. J.

Anuszkiewicz, A.

D. Dobrakowski, A. Rampur, G. Stępniewski, A. Anuszkiewicz, J. Lisowska, D. Pysz, R. Kasztelanic, and M. Klimczak, “Development of highly nonlinear polarization-maintaining fibers with normal dispersion across entire transmission window,” J. Opt. 21, 015504 (2018).
[Crossref]

K. Tarnowski, T. Martynkien, P. Mergo, K. Poturaj, A. Anuszkiewicz, P. Béjot, F. Billard, O. Faucher, B. Kibler, and W. Urbanczyk, “Polarized all-normal dispersion supercontinuum reaching 2.5 µm generated in a birefringent microstructured silica fiber,” Opt. Express 25, 27452–27463 (2017).
[Crossref]

Badding, J. V.

Baldeck, P. L.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Modulation instability induced by cross-phase modulation in optical fibers,” Phys. Rev. A 39, 3406–3413 (1989).
[Crossref]

Bang, O.

Bartelt, H.

Béjot, P.

Bettachini, V. A.

A. A. Rieznik, A. M. Heidt, P. G. Konig, V. A. Bettachini, and D. F. Grosz, “Optimum integration procedures for supercontinuum simulation,” IEEE Photon. J. 4, 552–560 (2012).
[Crossref]

Billard, F.

Birks, T. A.

Blumenthal, D. J.

B.-E. Olsson and D. J. Blumenthal, “All-optical demultiplexing using fiber cross-phase modulation (XPM) and optical filtering,” IEEE Photon. Technol. Lett. 13, 875–877 (2001).
[Crossref]

Bosman, G. W.

Bowen, P.

Brambilla, G.

J. H. V. Price, X. Feng, A. M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W. H. Loh, H. N. Rutt, and D. J. Richardson, “Supercontinuum generation in non-silica fibers,” Opt. Fiber Technol. 18, 327–344 (2012).
[Crossref]

Brès, C.-S.

Breuer, E. I.

Brocklesby, W. S.

Buczynski, R.

Chan, H. Y.

C. R. Head, H. Y. Chan, J. S. Feehan, D. P. Shepherd, S. Alam, A. C. Tropper, J. H. V. Price, and K. G. Wilcox, “Supercontinuum generation with GHz repetition rate femtosecond-pulse fiber-amplified VECSELs,” IEEE Photon. Technol. Lett. 25, 464–467 (2013).
[Crossref]

Chen, Y.

Cherif, R.

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. 89, 273901 (2002).
[Crossref]

J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27, 1180–1182 (2002).
[Crossref]

J. M. Dudley and S. Coen, “Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers,” IEEE J. Sel. Top. Quantum Electron 8, 651–659 (2002).
[Crossref]

Corney, J. F.

Cruz, F. C.

Day, T. D.

Desaix, M.

Dianov, E. M.

E. A. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, “Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
[Crossref]

Diddams, S. A.

Diouf, M.

Dobrakowski, D.

D. Dobrakowski, A. Rampur, G. Stępniewski, A. Anuszkiewicz, J. Lisowska, D. Pysz, R. Kasztelanic, and M. Klimczak, “Development of highly nonlinear polarization-maintaining fibers with normal dispersion across entire transmission window,” J. Opt. 21, 015504 (2018).
[Crossref]

Drummond, P. D.

Dudley, J. M.

E. Genier, P. Bowen, T. Sylvestre, J. M. Dudley, P. Moselund, and O. Bang, “Amplitude noise and coherence degradation of femtosecond supercontinuum generation in all-normal-dispersion fibers,” J. Opt. Soc. Am. B 36, A161–A167 (2019).
[Crossref]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

J. M. Dudley and S. Coen, “Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers,” IEEE J. Sel. Top. Quantum Electron 8, 651–659 (2002).
[Crossref]

J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27, 1180–1182 (2002).
[Crossref]

Engelsholm, R. D.

I. B. Gonzalo, R. D. Engelsholm, M. P. Sørensen, and O. Bang, “Polarization noise places severe constraints on coherence of all-normal dispersion femtosecond supercontinuum generation,” Sci. Rep. 8, 6579 (2018).
[Crossref]

Falk, P.

Faucher, O.

Feehan, J. S.

Feng, X.

J. H. V. Price, X. Feng, A. M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W. H. Loh, H. N. Rutt, and D. J. Richardson, “Supercontinuum generation in non-silica fibers,” Opt. Fiber Technol. 18, 327–344 (2012).
[Crossref]

Fermann, M. E.

Feurer, T.

Finot, C.

Fiorentino, M.

J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler, “All-optical switching based on cross-phase modulation in microstructure fiber,” IEEE Photon. Technol. Lett. 14, 77–79 (2002).
[Crossref]

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Fujimoto, J. G.

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J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
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[Crossref]

Gonzalo, I. B.

I. B. Gonzalo, R. D. Engelsholm, M. P. Sørensen, and O. Bang, “Polarization noise places severe constraints on coherence of all-normal dispersion femtosecond supercontinuum generation,” Sci. Rep. 8, 6579 (2018).
[Crossref]

I. B. Gonzalo and O. Bang, “Role of the Raman gain in the noise dynamics of all-normal dispersion silica fiber supercontinuum generation,” J. Opt. Soc. Am. B 35, 2102–2110 (2018).
[Crossref]

Gordon, J. P.

Grosz, D. F.

A. A. Rieznik, A. M. Heidt, P. G. Konig, V. A. Bettachini, and D. F. Grosz, “Optimum integration procedures for supercontinuum simulation,” IEEE Photon. J. 4, 552–560 (2012).
[Crossref]

Hänsch, T. W.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref]

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (2000).
[Crossref]

Hartung, A.

Harvey, J. D.

S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. 89, 273901 (2002).
[Crossref]

Haus, H. A.

Head, C. R.

C. R. Head, H. Y. Chan, J. S. Feehan, D. P. Shepherd, S. Alam, A. C. Tropper, J. H. V. Price, and K. G. Wilcox, “Supercontinuum generation with GHz repetition rate femtosecond-pulse fiber-amplified VECSELs,” IEEE Photon. Technol. Lett. 25, 464–467 (2013).
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Healy, N.

Heidt, A.

Heidt, A. M.

A. M. Heidt, J. S. Feehan, J. H. V. Price, and T. Feurer, “Limits of coherent supercontinuum generation in normal dispersion fibers,” J. Opt. Soc. Am. B 34, 764–775 (2017).
[Crossref]

J. H. V. Price, X. Feng, A. M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W. H. Loh, H. N. Rutt, and D. J. Richardson, “Supercontinuum generation in non-silica fibers,” Opt. Fiber Technol. 18, 327–344 (2012).
[Crossref]

A. A. Rieznik, A. M. Heidt, P. G. Konig, V. A. Bettachini, and D. F. Grosz, “Optimum integration procedures for supercontinuum simulation,” IEEE Photon. J. 4, 552–560 (2012).
[Crossref]

A. M. Heidt, A. Hartung, G. W. Bosman, P. Krok, E. G. Rohwer, H. Schwoerer, and H. Bartelt, “Coherent octave spanning near-infrared and visible supercontinuum generation in all-normal dispersion photonic crystal fibers,” Opt. Express 19, 3775–3787 (2011).
[Crossref]

A. M. Heidt, J. Rothhardt, A. Hartung, H. Bartelt, E. G. Rohwer, J. Limpert, and A. Tünnermann, “High quality sub-two cycle pulses from compression of supercontinuum generated in all-normal dispersion photonic crystal fiber,” Opt. Express 19, 13873–13879 (2011).
[Crossref]

A. M. Heidt, “Pulse preserving flat-top supercontinuum generation in all-normal dispersion photonic crystal fibers,” J. Opt. Soc. Am. B 27, 550–559 (2010).
[Crossref]

A. M. Heidt, “Efficient adaptive step size method for the simulation of supercontinuum generation in optical fibers,” J. Lightwave Technol. 27, 3984–3991 (2009).
[Crossref]

Holzwarth, R.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref]

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (2000).
[Crossref]

Hooper, L. E.

Horak, P.

J. H. V. Price, X. Feng, A. M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W. H. Loh, H. N. Rutt, and D. J. Richardson, “Supercontinuum generation in non-silica fibers,” Opt. Fiber Technol. 18, 327–344 (2012).
[Crossref]

Hosaka, T.

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55µm,” Electron. Lett. 15, 106–108 (1979).
[Crossref]

Hsiung, P.

Hu, J.

Hult, J.

Humbert, G.

Ibsen, M.

J. H. V. Price, X. Feng, A. M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W. H. Loh, H. N. Rutt, and D. J. Richardson, “Supercontinuum generation in non-silica fibers,” Opt. Fiber Technol. 18, 327–344 (2012).
[Crossref]

Ilday, F. Ö.

Ippen, E. P.

Johnson, A. M.

Kasztelanic, R.

D. Dobrakowski, A. Rampur, G. Stępniewski, A. Anuszkiewicz, J. Lisowska, D. Pysz, R. Kasztelanic, and M. Klimczak, “Development of highly nonlinear polarization-maintaining fibers with normal dispersion across entire transmission window,” J. Opt. 21, 015504 (2018).
[Crossref]

Kharitonov, S.

Kibler, B.

Klimczak, M.

D. Dobrakowski, A. Rampur, G. Stępniewski, A. Anuszkiewicz, J. Lisowska, D. Pysz, R. Kasztelanic, and M. Klimczak, “Development of highly nonlinear polarization-maintaining fibers with normal dispersion across entire transmission window,” J. Opt. 21, 015504 (2018).
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M. Klimczak, B. Siwicki, A. Heidt, and R. Buczyński, “Coherent supercontinuum generation in soft glass photonic crystal fibers,” Photon. Res. 5, 710–727 (2017).
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Knight, J. C.

Konig, P. G.

A. A. Rieznik, A. M. Heidt, P. G. Konig, V. A. Bettachini, and D. F. Grosz, “Optimum integration procedures for supercontinuum simulation,” IEEE Photon. J. 4, 552–560 (2012).
[Crossref]

Kopf, D.

Koshiba, M.

Kowligy, A.

Krok, P.

Kumar, P.

J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler, “All-optical switching based on cross-phase modulation in microstructure fiber,” IEEE Photon. Technol. Lett. 14, 77–79 (2002).
[Crossref]

Lederer, M. J.

Leon-Saval, S. G.

Limpert, J.

Lind, A.

Lisak, M.

Lisowska, J.

D. Dobrakowski, A. Rampur, G. Stępniewski, A. Anuszkiewicz, J. Lisowska, D. Pysz, R. Kasztelanic, and M. Klimczak, “Development of highly nonlinear polarization-maintaining fibers with normal dispersion across entire transmission window,” J. Opt. 21, 015504 (2018).
[Crossref]

Loh, W. H.

J. H. V. Price, X. Feng, A. M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W. H. Loh, H. N. Rutt, and D. J. Richardson, “Supercontinuum generation in non-silica fibers,” Opt. Fiber Technol. 18, 327–344 (2012).
[Crossref]

Mamyshev, P. V.

E. A. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, “Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
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Martynkien, T.

Mehta, P.

Mergo, P.

Mitschke, F. M.

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T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55µm,” Electron. Lett. 15, 106–108 (1979).
[Crossref]

Miyashita, T.

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55µm,” Electron. Lett. 15, 106–108 (1979).
[Crossref]

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Moselund, P.

Mosley, P. J.

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Newbury, N. R.

Nishizawa, N.

Olsson, B.-E.

B.-E. Olsson and D. J. Blumenthal, “All-optical demultiplexing using fiber cross-phase modulation (XPM) and optical filtering,” IEEE Photon. Technol. Lett. 13, 875–877 (2001).
[Crossref]

Papp, S. B.

Peacock, A. C.

Petropoulos, P.

J. H. V. Price, X. Feng, A. M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W. H. Loh, H. N. Rutt, and D. J. Richardson, “Supercontinuum generation in non-silica fibers,” Opt. Fiber Technol. 18, 327–344 (2012).
[Crossref]

Petrovich, M.

J. H. V. Price, X. Feng, A. M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W. H. Loh, H. N. Rutt, and D. J. Richardson, “Supercontinuum generation in non-silica fibers,” Opt. Fiber Technol. 18, 327–344 (2012).
[Crossref]

Pilipetskii, A. N.

E. A. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, “Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
[Crossref]

Poletti, F.

J. H. V. Price, X. Feng, A. M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W. H. Loh, H. N. Rutt, and D. J. Richardson, “Supercontinuum generation in non-silica fibers,” Opt. Fiber Technol. 18, 327–344 (2012).
[Crossref]

Ponzo, G.

J. H. V. Price, X. Feng, A. M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W. H. Loh, H. N. Rutt, and D. J. Richardson, “Supercontinuum generation in non-silica fibers,” Opt. Fiber Technol. 18, 327–344 (2012).
[Crossref]

Poturaj, K.

Price, J. H. V.

A. M. Heidt, J. S. Feehan, J. H. V. Price, and T. Feurer, “Limits of coherent supercontinuum generation in normal dispersion fibers,” J. Opt. Soc. Am. B 34, 764–775 (2017).
[Crossref]

J. S. Feehan, F. Ö. Ilday, W. S. Brocklesby, and J. H. V. Price, “Simulations and experiments showing the origin of multiwavelength mode locking in femtosecond, Yb-fiber lasers,” J. Opt. Soc. Am. B 33, 1668–1676 (2016).
[Crossref]

C. R. Head, H. Y. Chan, J. S. Feehan, D. P. Shepherd, S. Alam, A. C. Tropper, J. H. V. Price, and K. G. Wilcox, “Supercontinuum generation with GHz repetition rate femtosecond-pulse fiber-amplified VECSELs,” IEEE Photon. Technol. Lett. 25, 464–467 (2013).
[Crossref]

J. H. V. Price, X. Feng, A. M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W. H. Loh, H. N. Rutt, and D. J. Richardson, “Supercontinuum generation in non-silica fibers,” Opt. Fiber Technol. 18, 327–344 (2012).
[Crossref]

Provost, L.

Pysz, D.

D. Dobrakowski, A. Rampur, G. Stępniewski, A. Anuszkiewicz, J. Lisowska, D. Pysz, R. Kasztelanic, and M. Klimczak, “Development of highly nonlinear polarization-maintaining fibers with normal dispersion across entire transmission window,” J. Opt. 21, 015504 (2018).
[Crossref]

Quiroga-Teixeiro, M. L.

Rampur, A.

D. Dobrakowski, A. Rampur, G. Stępniewski, A. Anuszkiewicz, J. Lisowska, D. Pysz, R. Kasztelanic, and M. Klimczak, “Development of highly nonlinear polarization-maintaining fibers with normal dispersion across entire transmission window,” J. Opt. 21, 015504 (2018).
[Crossref]

Richardson, D. J.

J. H. V. Price, X. Feng, A. M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W. H. Loh, H. N. Rutt, and D. J. Richardson, “Supercontinuum generation in non-silica fibers,” Opt. Fiber Technol. 18, 327–344 (2012).
[Crossref]

Rieznik, A. A.

A. A. Rieznik, A. M. Heidt, P. G. Konig, V. A. Bettachini, and D. F. Grosz, “Optimum integration procedures for supercontinuum simulation,” IEEE Photon. J. 4, 552–560 (2012).
[Crossref]

Rohwer, E. G.

Rothhardt, J.

Russell, P. S. J.

Rutt, H. N.

J. H. V. Price, X. Feng, A. M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W. H. Loh, H. N. Rutt, and D. J. Richardson, “Supercontinuum generation in non-silica fibers,” Opt. Fiber Technol. 18, 327–344 (2012).
[Crossref]

Saghaei, H.

Saitoh, K.

Salem, A. B.

Schunemann, P. G.

Schwoerer, H.

Sharping, J. E.

J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler, “All-optical switching based on cross-phase modulation in microstructure fiber,” IEEE Photon. Technol. Lett. 14, 77–79 (2002).
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Shen, L.

Shepherd, D. P.

C. R. Head, H. Y. Chan, J. S. Feehan, D. P. Shepherd, S. Alam, A. C. Tropper, J. H. V. Price, and K. G. Wilcox, “Supercontinuum generation with GHz repetition rate femtosecond-pulse fiber-amplified VECSELs,” IEEE Photon. Technol. Lett. 25, 464–467 (2013).
[Crossref]

Shi, J.

J. H. V. Price, X. Feng, A. M. Heidt, G. Brambilla, P. Horak, F. Poletti, G. Ponzo, P. Petropoulos, M. Petrovich, J. Shi, M. Ibsen, W. H. Loh, H. N. Rutt, and D. J. Richardson, “Supercontinuum generation in non-silica fibers,” Opt. Fiber Technol. 18, 327–344 (2012).
[Crossref]

Silberberg, Y.

Silfies, M.

Siwicki, B.

Smith, R. G.

Sørensen, M. P.

I. B. Gonzalo, R. D. Engelsholm, M. P. Sørensen, and O. Bang, “Polarization noise places severe constraints on coherence of all-normal dispersion femtosecond supercontinuum generation,” Sci. Rep. 8, 6579 (2018).
[Crossref]

Sparks, J. R.

Stepniewski, G.

D. Dobrakowski, A. Rampur, G. Stępniewski, A. Anuszkiewicz, J. Lisowska, D. Pysz, R. Kasztelanic, and M. Klimczak, “Development of highly nonlinear polarization-maintaining fibers with normal dispersion across entire transmission window,” J. Opt. 21, 015504 (2018).
[Crossref]

Stifter, D.

Stock, M. L.

Stolen, R. H.

Swann, W. C.

Sylvestre, T.

Tamura, K.

Tarnowski, K.

Terunuma, Y.

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55µm,” Electron. Lett. 15, 106–108 (1979).
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Timmers, H.

Tomlinson, W. J.

Trillo, S.

Tropper, A. C.

C. R. Head, H. Y. Chan, J. S. Feehan, D. P. Shepherd, S. Alam, A. C. Tropper, J. H. V. Price, and K. G. Wilcox, “Supercontinuum generation with GHz repetition rate femtosecond-pulse fiber-amplified VECSELs,” IEEE Photon. Technol. Lett. 25, 464–467 (2013).
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Tünnermann, A.

Udem, T.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
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R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (2000).
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Urbanczyk, W.

Wabnitz, S.

Wadsworth, W. J.

Wague, A.

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S. Coen, D. A. Wardle, and J. D. Harvey, “Observation of non-phase-matched parametric amplification in resonant nonlinear optics,” Phys. Rev. Lett. 89, 273901 (2002).
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Wilcox, K. G.

C. R. Head, H. Y. Chan, J. S. Feehan, D. P. Shepherd, S. Alam, A. C. Tropper, J. H. V. Price, and K. G. Wilcox, “Supercontinuum generation with GHz repetition rate femtosecond-pulse fiber-amplified VECSELs,” IEEE Photon. Technol. Lett. 25, 464–467 (2013).
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J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler, “All-optical switching based on cross-phase modulation in microstructure fiber,” IEEE Photon. Technol. Lett. 14, 77–79 (2002).
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Xing, S.

Ycas, G.

Appl. Opt. (2)

Electron. Lett. (1)

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55µm,” Electron. Lett. 15, 106–108 (1979).
[Crossref]

IEEE J. Quantum Electron. (1)

E. A. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, “Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
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IEEE J. Sel. Top. Quantum Electron (1)

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IEEE Photon. J. (1)

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IEEE Photon. Technol. Lett. (3)

J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler, “All-optical switching based on cross-phase modulation in microstructure fiber,” IEEE Photon. Technol. Lett. 14, 77–79 (2002).
[Crossref]

B.-E. Olsson and D. J. Blumenthal, “All-optical demultiplexing using fiber cross-phase modulation (XPM) and optical filtering,” IEEE Photon. Technol. Lett. 13, 875–877 (2001).
[Crossref]

C. R. Head, H. Y. Chan, J. S. Feehan, D. P. Shepherd, S. Alam, A. C. Tropper, J. H. V. Price, and K. G. Wilcox, “Supercontinuum generation with GHz repetition rate femtosecond-pulse fiber-amplified VECSELs,” IEEE Photon. Technol. Lett. 25, 464–467 (2013).
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J. Lightwave Technol. (2)

J. Opt. (1)

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I. B. Gonzalo and O. Bang, “Role of the Raman gain in the noise dynamics of all-normal dispersion silica fiber supercontinuum generation,” J. Opt. Soc. Am. B 35, 2102–2110 (2018).
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Nature (1)

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Figures (8)

Fig. 1.
Fig. 1. Left (input pulses): the propagation of transform-limited high-energy pump (top row) and low-energy probe (bottom row) pulses in ANDi PCF is simulated to investigate how the pump modifies the probe coherence. This is done by tuning the GVM between the pump and probe, accessed using the fiber birefringence and probe central wavelength. Right (output pulses): the colormaps under the time-and frequency-domain plots have been matched to indicate how the pump and probe spectra are distributed in the time domain. The asymmetric spectral broadening of the probe shows that XPM driven by the pump pulse dominates, and that SPM within the probe is negligible. Equation (1) is therefore satisfied.
Fig. 2.
Fig. 2. Left axis (orange solid): dispersion curve for the silica hexagonal-lattice ANDi PCF. $\Lambda=1.7\;\unicode{x00B5}{\rm m}$, and $d/\Lambda=0.3$. Right axis (blue dashed): loss profile used in the simulations.
Fig. 3.
Fig. 3. Orthogonally polarized pump and probe ensembles after co-propagating in silica ANDi PCF with $\Delta {\beta_1}=0\;{\rm ps}/{\rm m}$. Left column: time-domain. Right column: normalized spectral power density (SPD, left $y$ axis) and coherence data (red trace, right $y$ axis). Blue traces show the ensemble average, and fine gray lines show the individual shots. Top: pump (60 nJ, 7 ps). Bottom: probe (5 pJ, 7 ps). The arrows mark the two most energetic Stokes peaks.
Fig. 4.
Fig. 4. Spectrograms of orthogonally polarized pump (blue colormap) and probe (black contour) with the same initial central wavelength (1040 nm, 288 THz) after propagating through 90 cm of ANDi PCF with $\Delta {\beta_1}=7\;{\rm ps}/{\rm m}$. The spectrograms are normalized to the peak of the pump pulse ($-{70}$ to 0 dB).
Fig. 5.
Fig. 5. Decoherence of orthogonally polarized pump and probe pulses with the same central wavelength (1040 nm, 288 THz), shown by the blue colormap and black contour, respectively, as a function of group velocity mismatch. Both the magnitude and sign of $\Delta {\beta_1}$ change the degradation of the probe coherence. ${E_{{\rm pump}}}=60\;{\rm nJ}$, ${E_{{\rm probe}}}=5\;{\rm pJ}$, ${T_0}=7\;{\rm ps}$, and ${L_{{\rm fiber}}}=130\;{\rm cm}$. Columns from left to right: $\Delta {\beta_1}=7\;{\rm ps}/{\rm m}$, $-{7}\;{\rm ps/m}$, and 10 ps/m. Insets: pump coherence (blue dashed) and probe coherence (solid black) as a function of frequency (THz) over the region of highest spectral power density.
Fig. 6.
Fig. 6. Top left: Average pump coherence (left $y$ axis, purple solid line) and $L_{\rm R}^\star /{L_{{\rm WB}}}$ (right $y$ axis, green dashed line) as a function of ${N_{{\rm pump}}}$ for a 1 m length of PCF. Top right: average probe coherence as a function of ${N_{{\rm pump}}}$ and $\Delta {\beta_1}$ for a 1 m length of PCF. The red dashed line in the right-hand plot shows where $\langle |g_{12}^{(1)}|\rangle$ is minimized for a given ${N_{{\rm pump}}}$. The purple region shows where ${L_{{\rm c}\,{\rm probe}}}$ is shorter than ${L_{{\rm c}\,{\rm pump}}}$, and therefore where the decoherence for the probe occurs at a higher rate than the pump. Bottom: energy transferred from the pump and probe pulses to the phonon field as a function of propagation distance (${N_{{\rm pump}}}=900$ and $\Delta {\beta_1}=0\;{\rm ps}/{\rm m}$).
Fig. 7.
Fig. 7. Average probe coherence for 1 m of ANDi PCF with $\Delta {\beta_1}=0\;{\rm ps}/{\rm m}$ as a function of the ratio of the probe energy to the pump energy. The pulse durations were constant at 7 ps, and the pump energy was held constant at 60 nJ. The shaded region shows the confidence interval of the linear fit to one standard deviation.
Fig. 8.
Fig. 8. Cross-wavelength decoherence for co-polarized pump and probe (XPM factor of 2). ${T_0}=7\;{\rm ps}$ and ${L_{{\rm fiber}}}=130\;{\rm cm}$ for all simulations, and the pulses have zero initial relative delay. Top: ${\lambda_{{\rm c}\,{\rm pump}}}=1040\;{\rm nm}$ (288 THz), ${\lambda_{{\rm c}\,{\rm probe}}}=1100\;{\rm nm}$ (273 THz). Bottom: ${\lambda_{{\rm c}\,{\rm pump}}}=1040\;{\rm nm}$, ${\lambda_{{\rm c}\,{\rm probe}}}=1300\;{\rm nm}$ (231 THz). Insets: pump and probe coherence for the region of highest spectral power density (dashed blue and solid black lines, respectively).

Equations (11)

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L N p r o b e L f i b e r L N p u m p ,
L W B > L R .
g s = 2 γ R e ( K ( 2 q K ) ) .
| g 12 ( 1 ) ( λ , t a t b ) | = | A a ( λ , t a ) A b ( λ , t b ) | A a ( λ , t a ) | 2 | A b ( λ , t b ) | 2 | a b ,
| g 12 ( 1 ) | = 0 | g 12 ( 1 ) | | A ( λ ) | 2 d λ 0 | A ( λ ) | 2 d λ .
L c 1 f R Ω R T 0 .
N = L D L N .
α P ( z ) = E ( z ) E i n p u t α f i b e r ( z ) .
A ( z , T ) z = ( D ^ + N ^ ) A ( z , T ) .
D ^ ( Ω ) = α ( Ω ) 2 i [ Δ β 1 Ω β 2 ( Ω ) 2 Ω 2 ] ,
N ^ p u m p ( Ω ) = i γ ( Ω ) ( 1 + Ω ω 0 ) ( F [ ( 1 f R ) ( | A p u m p ( z , T ) | 2 + ϵ X P M | A p r o b e ( z , T ) | 2 ) + f R F 1 [ h ~ R ( Ω ) F [ | A p u m p ( z , T ) | 2 + | A p r o b e ( z , T ) | 2 ] ] + i Γ R ( z , T ) ] ) .

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