Amplitude noise and coherence degradation of femtosecond supercontinuum generation in all-normal-dispersion fibers

Etienne Genier; Patrick Bowen; Thibaut Sylvestre; John M. Dudley; Peter Moselund; Ole Bang

doi:10.1364/JOSAB.36.00A161

Journal of the Optical Society of America B
Vol. 36,
Issue 2,
pp. A161-A167
(2019)
•https://doi.org/10.1364/JOSAB.36.00A161

Amplitude noise and coherence degradation of femtosecond supercontinuum generation in all-normal-dispersion fibers

Etienne Genier, Patrick Bowen, Thibaut Sylvestre, John M. Dudley, Peter Moselund, and Ole Bang

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Etienne Genier, Patrick Bowen, Thibaut Sylvestre, John M. Dudley, Peter Moselund, and Ole Bang, "Amplitude noise and coherence degradation of femtosecond supercontinuum generation in all-normal-dispersion fibers," J. Opt. Soc. Am. B 36, A161-A167 (2019)

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Abstract

Supercontinuum (SC) generation via femtosecond (fs) pumping in all-normal-dispersion (ANDi) fiber is predicted to offer completely coherent broadening mechanisms, potentially allowing for substantially reduced noise levels in comparison to those obtained when operating in the anomalous dispersion regime. However, previous studies of SC noise typically treat only the quantum noise, typically in the form of one-photon-per-mode noise, and do not consider other technical noise contributions, such as the stability of the pump laser, which become important when the broadening mechanism itself is coherent. In this work, we discuss the influence of the amplitude and pulse length noise of the pump laser, both added separately and combined. We show that for a typical mode-locked laser, in which the peak power and pulse duration are anticorrelated, their combined impact on the SC noise is generally smaller than in isolation. This means that the supercontinuum noise is smaller than the noise of the mode-locked pump laser itself, a fact that was recently observed in experiments but not explained. Our detailed numerical analysis shows that the coherence of ANDi SC generation is considerably reduced on the spectral edges when realistic pump laser noise levels are taken into account.

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Year
Author
Publication

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. Hartung, A. Heidt, and H. Bartelt, “Design of all-normal dispersion microstructured optical fibers for pulse-preserving supercontinuum generation,” Opt. Express 19, 7742–7749 (2011).
[Crossref]
L. Liu, T. Cheng, K. Nagasaka, H. Tong, G. Qin, T. Suzuki, and Y. Ohishi, “Coherent mid-infrared supercontinuum generation in all-solid chalcogenide microstructured fibers with all-normal dispersion,” Opt. Lett. 41, 392–395 (2016).
[Crossref]
R. Alfano, The Supercontinuum Laser Source, 3rd ed. (Springer, 2016).
U. Møller and O. Bang, “Intensity noise in normal-pumped picoseconds supercontinuum generation, where higher-order Raman lines cross into the anomalous dispersion regime,” Electron. Lett. 49, 63–65 (2013).
[Crossref]
M. Maria, I. B. Gonzalo, T. Feuchter, M. Denninger, P. M. Moselund, L. Leick, O. Bang, and A. Podoleanu, “Q-switch-pumped supercontinuum for ultra-high resolution optical coherence tomography,” Opt. Lett. 42, 4744–4747 (2017).
[Crossref]
T. Udem, R. Holzwarth, and T. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref]
M. K. Dasa, C. Markos, M. Maria, C. R. Petersen, P. M. Moselund, and O. Bang, “High-pulse energy supercontinuum laser for high-resolution spectroscopic photoacoustic imaging of lipids in the 1650–1850 nm region,” Biomed. Opt. Express 9, 1762–1770 (2018).
[Crossref]
C. R. Petersen, N. Prtljaga, M. Farries, J. Ward, B. Napier, G. R. Lloyd, J. Nallala, N. Stone, and O. Bang, “Mid-infrared multispectral tissue imaging using a chalcogenide fiber supercontinuum source,” Opt. Lett. 43, 999–1002 (2018).
[Crossref]
N. M. Israelsen, M. Maria, M. Mogensen, S. Bojesen, M. Jensen, M. Haedersdal, A. Podoleanu, and O. Bang, “The value of ultrahigh resolution OCT in dermatology—delineating the dermo-epidermal junction, capillaries in the dermal papillae and vellus hairs,” Biomed. Opt. Express 9, 2240–2265 (2018).
[Crossref]
B. Povazay, K. Bizheva, A. Unterhuber, B. Hermann, H. Sattmann, A. F. Fercher, W. Drexler, A. Apolonski, W. J. Wadsworth, J. C. Knight, P. St.J. Russell, M. Vetterlein, and E. Scherzer, “Submicrometer axial resolution optical coherence tomography,” Opt. Lett. 27, 1800–1802 (2002).
[Crossref]
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]
C. Finot, B. Kibler, L. Provost, and S. Wabnitz, “Beneficial impact of wave-breaking for coherent continuum formation in normally dispersive nonlinear fibers,” J. Opt. Soc. Am. B 25, 1938–1948(2008).
[Crossref]
I. Gonzalo, R. Engelsholm, M. Sørensen, and O. Bang, “Polarization noise places severe constraints on coherence of all-normal dispersion femtosecond supercontinuum generation,” Sci. Rep. 8, 6579 (2018).
[Crossref]
F. Li, Q. Li, J. Yuan, and P. K. A. Wai, “Highly coherent supercontinuum generation with picosecond pulses by using self-similar compression,” Opt. Express 22, 27339–27354 (2014).
[Crossref]
M. H. Frosz, O. Bang, and A. Bjarklev, “Soliton collision and Raman gain regimes in continuous-wave pumped supercontinuum generation,” Opt. Express 14, 9391–9407 (2006).
[Crossref]
A. Mussot, E. Lantz, H. Maillotte, T. Sylvestre, C. Finot, and S. Pitois, “Spectral broadening of a partially coherent CW laser beam in single-mode optical fibers,” Opt. Express 12, 2838–2843 (2004).
[Crossref]
S. T. Sørensen, C. Larsen, U. Møller, P. M. Moselund, C. L. Thomsen, and O. Bang, “The role of phase coherence in seeded supercontinuum generation,” Opt. Express 20, 22886–22894 (2012).
[Crossref]
Z. Zhu and T. G. Brown, “Polarization properties of supercontinuum spectra generated in birefringent photonic crystal fibers,” J. Opt. Soc. Am. B 21, 249–257 (2004).
[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, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27, 1180–1182 (2002).
[Crossref]
M. H. Frosz, “Validation of input-noise model for simulations of supercontinuum generation and rogue waves,” Opt. Express 18, 14778–14787 (2010).
[Crossref]
K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, B. R. Washburn, K. Weber, and R. S. Windeler, “Fundamental amplitude noise limitations to supercontinuum spectra generated in a microstructured fiber,” Appl. Phys. B 77, 269–277 (2003).
[Crossref]
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]
J. F. Corney and P. D. Drummond, “Quantum noise in optical fibers. II. Raman jitter in soliton communications,” J. Opt. Soc. Am. B 18, 153–161 (2001).
[Crossref]
R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 2489–2494 (1972).
[Crossref]
U. Møller, S. T. Sørensen, C. Jakobsen, J. Johansen, P. M. Moselund, C. L. Thomsen, and O. Bang, “Power dependence of supercontinuum noise in uniform and tapered PCFs,” Opt. Express 20, 2851–2857 (2012).
[Crossref]
S. Rao, R. Engelsholm, I. Gonzalo, B. Zhou, P. Bowen, P. Moselund, M. Bache, and O. Bang, “Ultra-low noise supercontinuum generation with flat near-zero normal dispersion fiber,” arXiv:1812.03877 (2018).
I. 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]
D. Buccollero, H. Steffensen, H. Ebendorff-Heidepriem, T. M. Monro, and O. Bang, “Midinfrared optical rogue waves in soft glass photonic crystal fiber,” Opt. Express 19, 17973–17978 (2011).
[Crossref]

2018 (5)

M. K. Dasa, C. Markos, M. Maria, C. R. Petersen, P. M. Moselund, and O. Bang, “High-pulse energy supercontinuum laser for high-resolution spectroscopic photoacoustic imaging of lipids in the 1650–1850 nm region,” Biomed. Opt. Express 9, 1762–1770 (2018).
[Crossref]

C. R. Petersen, N. Prtljaga, M. Farries, J. Ward, B. Napier, G. R. Lloyd, J. Nallala, N. Stone, and O. Bang, “Mid-infrared multispectral tissue imaging using a chalcogenide fiber supercontinuum source,” Opt. Lett. 43, 999–1002 (2018).
[Crossref]

N. M. Israelsen, M. Maria, M. Mogensen, S. Bojesen, M. Jensen, M. Haedersdal, A. Podoleanu, and O. Bang, “The value of ultrahigh resolution OCT in dermatology—delineating the dermo-epidermal junction, capillaries in the dermal papillae and vellus hairs,” Biomed. Opt. Express 9, 2240–2265 (2018).
[Crossref]

I. Gonzalo, R. Engelsholm, M. 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. 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]

2013 (1)

U. Møller and O. Bang, “Intensity noise in normal-pumped picoseconds supercontinuum generation, where higher-order Raman lines cross into the anomalous dispersion regime,” Electron. Lett. 49, 63–65 (2013).
[Crossref]

2012 (2)

U. Møller, S. T. Sørensen, C. Jakobsen, J. Johansen, P. M. Moselund, C. L. Thomsen, and O. Bang, “Power dependence of supercontinuum noise in uniform and tapered PCFs,” Opt. Express 20, 2851–2857 (2012).
[Crossref]

S. T. Sørensen, C. Larsen, U. Møller, P. M. Moselund, C. L. Thomsen, and O. Bang, “The role of phase coherence in seeded supercontinuum generation,” Opt. Express 20, 22886–22894 (2012).
[Crossref]

2011 (3)

D. Buccollero, H. Steffensen, H. Ebendorff-Heidepriem, T. M. Monro, and O. Bang, “Midinfrared optical rogue waves in soft glass photonic crystal fiber,” Opt. Express 19, 17973–17978 (2011).
[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. Hartung, A. Heidt, and H. Bartelt, “Design of all-normal dispersion microstructured optical fibers for pulse-preserving supercontinuum generation,” Opt. Express 19, 7742–7749 (2011).
[Crossref]

2010 (1)

M. H. Frosz, “Validation of input-noise model for simulations of supercontinuum generation and rogue waves,” Opt. Express 18, 14778–14787 (2010).
[Crossref]

2008 (1)

C. Finot, B. Kibler, L. Provost, and S. Wabnitz, “Beneficial impact of wave-breaking for coherent continuum formation in normally dispersive nonlinear fibers,” J. Opt. Soc. Am. B 25, 1938–1948(2008).
[Crossref]

2006 (2)

M. H. Frosz, O. Bang, and A. Bjarklev, “Soliton collision and Raman gain regimes in continuous-wave pumped supercontinuum generation,” Opt. Express 14, 9391–9407 (2006).
[Crossref]

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

2004 (2)

Z. Zhu and T. G. Brown, “Polarization properties of supercontinuum spectra generated in birefringent photonic crystal fibers,” J. Opt. Soc. Am. B 21, 249–257 (2004).
[Crossref]

A. Mussot, E. Lantz, H. Maillotte, T. Sylvestre, C. Finot, and S. Pitois, “Spectral broadening of a partially coherent CW laser beam in single-mode optical fibers,” Opt. Express 12, 2838–2843 (2004).
[Crossref]

2003 (1)

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, B. R. Washburn, K. Weber, and R. S. Windeler, “Fundamental amplitude noise limitations to supercontinuum spectra generated in a microstructured fiber,” Appl. Phys. B 77, 269–277 (2003).
[Crossref]

2002 (3)

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]

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

B. Povazay, K. Bizheva, A. Unterhuber, B. Hermann, H. Sattmann, A. F. Fercher, W. Drexler, A. Apolonski, W. J. Wadsworth, J. C. Knight, P. St.J. Russell, M. Vetterlein, and E. Scherzer, “Submicrometer axial resolution optical coherence tomography,” Opt. Lett. 27, 1800–1802 (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]

J. F. Corney and P. D. Drummond, “Quantum noise in optical fibers. II. Raman jitter in soliton communications,” J. Opt. Soc. Am. B 18, 153–161 (2001).
[Crossref]

1972 (1)

R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 2489–2494 (1972).
[Crossref]

Alfano, R.

R. Alfano, The Supercontinuum Laser Source, 3rd ed. (Springer, 2016).

Apolonski, A.

Bache, M.

S. Rao, R. Engelsholm, I. Gonzalo, B. Zhou, P. Bowen, P. Moselund, M. Bache, and O. Bang, “Ultra-low noise supercontinuum generation with flat near-zero normal dispersion fiber,” arXiv:1812.03877 (2018).

Bang, O.

I. 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]

M. H. Frosz, O. Bang, and A. Bjarklev, “Soliton collision and Raman gain regimes in continuous-wave pumped supercontinuum generation,” Opt. Express 14, 9391–9407 (2006).
[Crossref]

Bartelt, H.

Bizheva, K.

Bjarklev, A.

M. H. Frosz, O. Bang, and A. Bjarklev, “Soliton collision and Raman gain regimes in continuous-wave pumped supercontinuum generation,” Opt. Express 14, 9391–9407 (2006).
[Crossref]

Bojesen, S.

Bosman, G. W.

Bowen, P.

Brown, T. G.

Z. Zhu and T. G. Brown, “Polarization properties of supercontinuum spectra generated in birefringent photonic crystal fibers,” J. Opt. Soc. Am. B 21, 249–257 (2004).
[Crossref]

Buccollero, D.

Cheng, T.

Coen, S.

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

Corney, J. F.

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]

J. F. Corney and P. D. Drummond, “Quantum noise in optical fibers. II. Raman jitter in soliton communications,” J. Opt. Soc. Am. B 18, 153–161 (2001).
[Crossref]

Corwin, K. L.

Dasa, M. K.

Denninger, M.

Diddams, S. A.

Drexler, W.

Drummond, P. D.

J. F. Corney and P. D. Drummond, “Quantum noise in optical fibers. II. Raman jitter in soliton communications,” J. Opt. Soc. Am. B 18, 153–161 (2001).
[Crossref]

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]

Dudley, J. M.

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

Ebendorff-Heidepriem, H.

Engelsholm, R.

Farries, M.

Feehan, J. S.

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]

Fercher, A. F.

Feuchter, T.

Feurer, T.

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]

Finot, C.

Frosz, M. H.

M. H. Frosz, “Validation of input-noise model for simulations of supercontinuum generation and rogue waves,” Opt. Express 18, 14778–14787 (2010).
[Crossref]

M. H. Frosz, O. Bang, and A. Bjarklev, “Soliton collision and Raman gain regimes in continuous-wave pumped supercontinuum generation,” Opt. Express 14, 9391–9407 (2006).
[Crossref]

Genty, G.

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

Gonzalo, I.

I. 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]

Gonzalo, I. B.

Haedersdal, M.

Hänsch, T.

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

Hartung, A.

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]

Hermann, B.

Holzwarth, R.

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

Israelsen, N. M.

Jakobsen, C.

Jensen, M.

Johansen, J.

Kibler, B.

Knight, J. C.

Krok, P.

Lantz, E.

Larsen, C.

Leick, L.

Li, F.

F. Li, Q. Li, J. Yuan, and P. K. A. Wai, “Highly coherent supercontinuum generation with picosecond pulses by using self-similar compression,” Opt. Express 22, 27339–27354 (2014).
[Crossref]

Li, Q.

F. Li, Q. Li, J. Yuan, and P. K. A. Wai, “Highly coherent supercontinuum generation with picosecond pulses by using self-similar compression,” Opt. Express 22, 27339–27354 (2014).
[Crossref]

Liu, L.

Lloyd, G. R.

Maillotte, H.

Maria, M.

Markos, C.

Mogensen, M.

Møller, U.

Monro, T. M.

Moselund, P.

Moselund, P. M.

Mussot, A.

Nagasaka, K.

Nallala, J.

Napier, B.

Newbury, N. R.

Ohishi, Y.

Petersen, C. R.

Pitois, S.

Podoleanu, A.

Povazay, B.

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]

Provost, L.

Prtljaga, N.

Qin, G.

Rao, S.

Rohwer, E. G.

Sattmann, H.

Scherzer, E.

Schwoerer, H.

Smith, R. G.

R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 2489–2494 (1972).
[Crossref]

Sørensen, M.

Sørensen, S. T.

St.J. Russell, P.

Steffensen, H.

Stone, N.

Suzuki, T.

Sylvestre, T.

Thomsen, C. L.

Tong, H.

Udem, T.

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

Unterhuber, A.

Vetterlein, M.

Wabnitz, S.

Wadsworth, W. J.

Wai, P. K. A.

F. Li, Q. Li, J. Yuan, and P. K. A. Wai, “Highly coherent supercontinuum generation with picosecond pulses by using self-similar compression,” Opt. Express 22, 27339–27354 (2014).
[Crossref]

Ward, J.

Washburn, B. R.

Weber, K.

Windeler, R. S.

Yuan, J.

F. Li, Q. Li, J. Yuan, and P. K. A. Wai, “Highly coherent supercontinuum generation with picosecond pulses by using self-similar compression,” Opt. Express 22, 27339–27354 (2014).
[Crossref]

Zhou, B.

Zhu, Z.

Z. Zhu and T. G. Brown, “Polarization properties of supercontinuum spectra generated in birefringent photonic crystal fibers,” J. Opt. Soc. Am. B 21, 249–257 (2004).
[Crossref]

Appl. Opt. (1)

R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 2489–2494 (1972).
[Crossref]

Appl. Phys. B (1)

Biomed. Opt. Express (2)

Electron. Lett. (1)

J. Opt. Soc. Am. B (6)

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]

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]

J. F. Corney and P. D. Drummond, “Quantum noise in optical fibers. II. Raman jitter in soliton communications,” J. Opt. Soc. Am. B 18, 153–161 (2001).
[Crossref]

Z. Zhu and T. G. Brown, “Polarization properties of supercontinuum spectra generated in birefringent photonic crystal fibers,” J. Opt. Soc. Am. B 21, 249–257 (2004).
[Crossref]

I. 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]

Nature (1)

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

Opt. Express (9)

M. H. Frosz, “Validation of input-noise model for simulations of supercontinuum generation and rogue waves,” Opt. Express 18, 14778–14787 (2010).
[Crossref]

F. Li, Q. Li, J. Yuan, and P. K. A. Wai, “Highly coherent supercontinuum generation with picosecond pulses by using self-similar compression,” Opt. Express 22, 27339–27354 (2014).
[Crossref]

M. H. Frosz, O. Bang, and A. Bjarklev, “Soliton collision and Raman gain regimes in continuous-wave pumped supercontinuum generation,” Opt. Express 14, 9391–9407 (2006).
[Crossref]

Opt. Lett. (5)

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]

Rev. Mod. Phys. (1)

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

Sci. Rep. (1)

Other (2)

R. Alfano, The Supercontinuum Laser Source, 3rd ed. (Springer, 2016).

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Fig. 1. (a) Measured (dashed blue) and modeled (solid black) dispersion profile, and fiber losses (solid red) of the NL-1050-NE-PM ANDi PCF. (b) Numerical SC spectra generated in 1 m of ANDi fiber with a 1054 nm pump with an average peak power and pulse duration of

P_{0} = 100 kW

and

T_{0} = 50 fs

, respectively. An amplitude noise of 0.5% was used, corresponding to a pulse duration noise of 0.4%.

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Fig. 2. (a) Average spectral coherence

⟨ | g_{12} | ⟩

of SC pulses generated with

P_{0} = 100 kW

peak power pump pulses as a function of pump pulse duration

T_{0}

and propagation distance for an amplitude noise value of 0.3% (pulse duration noise 0.24%). The dotted line indicates the limit

⟨ | g_{12} | ⟩ = 0.9

. (b) Limit

⟨ | g_{12} | ⟩ = 0.9

for a range of amplitude noise values from 0.1% to 1% (pulse duration noise 0.08%–0.8%).

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Fig. 3. (a) RIN profiles for different amplitude noise values and mean spectral profile out of 1 m of ANDi fiber pumped with 100 kW peak power, 50 fs long pulses at 1054 nm. (b) Evolution of the RIN along the fiber length for an amplitude noise value of 0.5% (pulse duration noise 0.4%). Note: The color map has a dynamic range limited to a RIN equal to 0.5%, meaning RIN data is only visible for wavelengths 800–1430 nm.

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Fig. 4. (a) RIN profile (blue line) and mean spectrum (red line) of an ensemble of 20 pulses after 10 cm of fiber with 100 kW peak power, 50 fs pulse duration at 1054 nm for an amplitude noise value of 0.5% (pulse duration noise of 0.4%). (b) RIN spectrum as a function of the input noise: OPM only (black line), amplitude noise plus OPM noise (red line), pulse duration noise plus OPM (pink line), and amplitude noise plus pulse duration noise and OPM (blue line).

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Equations (6)

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\frac{\partial A}{\partial z} = - \frac{α (ω)}{2} A + \sum_{k \geq 2} \frac{i^{k + 1}}{k!} β_{k} \frac{\partial^{k} A}{\partial T^{k}} + i γ (1 + i τ_{0} \frac{\partial}{\partial T}) (A \int_{- \infty}^{+ \infty} R (T^{'}) {| A (z, T - T^{'}) |}^{2} d T^{'}),

δ_{T_{0}} = - 0.8 * (δ_{AN} - 1),

A (0, t) = \sqrt{P_{0}} δ_{AN} sech (t / (T_{0} (1 - 0.8 (δ_{AN} - 1)))) + F^{- 1} {δ_{QN}},

| g_{12} (ω) | = | \frac{{⟨ {\tilde{A}}_{i}^{*} (ω) {\tilde{A}}_{j} (ω) ⟩}_{i \neq j}}{\sqrt{⟨ {| {\tilde{A}}_{i} (ω) |}^{2} ⟩ ⟨ {| {\tilde{A}}_{j} (ω) |}^{2} ⟩}} |, ⟨ | g_{12} | ⟩ = \frac{\int_{0}^{\infty} | g_{12} (ω) | ⟨ {| {\tilde{A}}_{i} (ω) |}^{2} ⟩ d ω}{\int_{0}^{\infty} ⟨ {| {\tilde{A}}_{i} (ω) |}^{2} ⟩ d ω},

RIN (ω) = \sqrt{⟨ {({| \tilde{A} (ω) |}^{2} - ⟨ {| \tilde{A} (ω) |}^{2} ⟩)}^{2} ⟩} / ⟨ {| \tilde{A} (ω) |}^{2} ⟩ .

{| \tilde{A} (ω) |}^{2} = P_{0} T_{0}^{2} {| \int_{0}^{+ \infty} sech (x) (e^{i (ω - ω_{0} + Δ ω) T_{0} x} + e^{- i (ω - ω_{0} - Δ ω) T_{0} x}) d x |}^{2},

Abstract

References

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