Abstract

We theoretically and numerically study the influence of the Raman gain profile on the noise dynamics of the supercontinuum (SC) generation in a standard all-normal dispersion silica fiber using the scalar generalized nonlinear Schrödinger equation. In particular, we investigate the effect of the different secondary resonance gain peaks on the evolution of the SC coherence by comparing the coherence obtained when using the measured Raman gain of silica with that obtained using different analytical approximations. We demonstrate that the strongest secondary peak at 14.8 THz has a significant influence in that it leads to an early development of a decoherence band on the long wavelength side of the SC. In contrast, the decoherence is strongly dominated by the short wavelength side below the pump for all analytical models not taking this 14.8 THz gain peak into account. We demonstrate that this is due to the 14.8 THz peak being spectrally much narrower than the other gain peaks.

© 2018 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2018 (1)

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]

2017 (1)

2016 (1)

M. Klimczak, G. Soboń, R. Kasztelanic, K. M. Abramski, and R. Buczyński, “Direct comparison of shot-to-shot noise performance of all normal dispersion and anomalous dispersion supercontinuum pumped with sub-picosecond pulse fiber-based laser,” Sci. Rep. 6, 19284 (2016).
[Crossref]

2012 (1)

S. T. Sørensen, O. Bang, B. Wetzel, and J. M. Dudley, “Describing supercontinuum noise and rogue wave statistics using higher-order moments,” Opt. Commun. 285, 2451–2455 (2012).
[Crossref]

2011 (1)

2010 (2)

2008 (1)

2007 (2)

2006 (2)

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

Q. Lin and G. P. Agrawal, “Raman response function for silica fibers,” Opt. Lett. 31, 3086–3088 (2006).
[Crossref]

2005 (2)

K. Rottwitt and J. H. Povlsen, “Analyzing the fundamental properties of Raman amplification in optical fibers,” J. Lightwave Technol. 23, 3597–3605 (2005).
[Crossref]

J. Zhou, K. Tajima, K. Nakajima, K. Kurokawa, C. Fukai, T. Matsui, and I. Sankawa, “Progress on low loss photonic crystal fibers,” Opt. Fiber Technol. 11, 101–110 (2005).
[Crossref]

2003 (1)

2002 (2)

1995 (1)

1994 (1)

1989 (2)

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]

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[Crossref]

1977 (1)

R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1–68 (1977).
[Crossref]

1973 (1)

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–278 (1973).
[Crossref]

1964 (1)

N. Bloembergen and Y. R. Shen, “Coupling between vibrations and light waves in Raman laser media,” Phys. Rev. Lett. 12, 504–507 (1964).
[Crossref]

Abramski, K. M.

M. Klimczak, G. Soboń, R. Kasztelanic, K. M. Abramski, and R. Buczyński, “Direct comparison of shot-to-shot noise performance of all normal dispersion and anomalous dispersion supercontinuum pumped with sub-picosecond pulse fiber-based laser,” Sci. Rep. 6, 19284 (2016).
[Crossref]

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics (Academic, 2013).

Agrawal, G. P.

Bang, O.

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]

S. T. Sørensen, O. Bang, B. Wetzel, and J. M. Dudley, “Describing supercontinuum noise and rogue wave statistics using higher-order moments,” Opt. Commun. 285, 2451–2455 (2012).
[Crossref]

Bartelt, H.

Bloembergen, N.

N. Bloembergen and Y. R. Shen, “Coupling between vibrations and light waves in Raman laser media,” Phys. Rev. Lett. 12, 504–507 (1964).
[Crossref]

Blow, K. J.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[Crossref]

Bosman, G. W.

Buczynski, R.

M. Klimczak, G. Soboń, R. Kasztelanic, K. M. Abramski, and R. Buczyński, “Direct comparison of shot-to-shot noise performance of all normal dispersion and anomalous dispersion supercontinuum pumped with sub-picosecond pulse fiber-based laser,” Sci. Rep. 6, 19284 (2016).
[Crossref]

Cantrell, C. D.

Coen, S.

Dougherty, D. J.

Dudley, J. M.

S. T. Sørensen, O. Bang, B. Wetzel, and J. M. Dudley, “Describing supercontinuum noise and rogue wave statistics using higher-order moments,” Opt. Commun. 285, 2451–2455 (2012).
[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]

Emplit, P.

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]

Feehan, J. S.

Feurer, T.

Finot, C.

Frosz, M. H.

Fukai, C.

J. Zhou, K. Tajima, K. Nakajima, K. Kurokawa, C. Fukai, T. Matsui, and I. Sankawa, “Progress on low loss photonic crystal fibers,” Opt. Fiber Technol. 11, 101–110 (2005).
[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]

Golovchenko, E. A.

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]

Gordon, J. P.

Hartung, A.

Haus, H. A.

Heidt, A. M.

Hellwarth, R. W.

R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1–68 (1977).
[Crossref]

Hollenbeck, D.

Hult, J.

Ippen, E. P.

Kärtner, F. X.

Kasztelanic, R.

M. Klimczak, G. Soboń, R. Kasztelanic, K. M. Abramski, and R. Buczyński, “Direct comparison of shot-to-shot noise performance of all normal dispersion and anomalous dispersion supercontinuum pumped with sub-picosecond pulse fiber-based laser,” Sci. Rep. 6, 19284 (2016).
[Crossref]

Kibler, B.

Klimczak, M.

M. Klimczak, G. Soboń, R. Kasztelanic, K. M. Abramski, and R. Buczyński, “Direct comparison of shot-to-shot noise performance of all normal dispersion and anomalous dispersion supercontinuum pumped with sub-picosecond pulse fiber-based laser,” Sci. Rep. 6, 19284 (2016).
[Crossref]

Krok, P.

Kurokawa, K.

J. Zhou, K. Tajima, K. Nakajima, K. Kurokawa, C. Fukai, T. Matsui, and I. Sankawa, “Progress on low loss photonic crystal fibers,” Opt. Fiber Technol. 11, 101–110 (2005).
[Crossref]

Lin, Q.

Matsui, T.

J. Zhou, K. Tajima, K. Nakajima, K. Kurokawa, C. Fukai, T. Matsui, and I. Sankawa, “Progress on low loss photonic crystal fibers,” Opt. Fiber Technol. 11, 101–110 (2005).
[Crossref]

Nakajima, K.

J. Zhou, K. Tajima, K. Nakajima, K. Kurokawa, C. Fukai, T. Matsui, and I. Sankawa, “Progress on low loss photonic crystal fibers,” Opt. Fiber Technol. 11, 101–110 (2005).
[Crossref]

Nishizawa, N.

Pilipetskii, A. N.

Povlsen, J. H.

Price, J. H. V.

Provost, L.

Rohwer, E. G.

Rottwitt, K.

Sankawa, I.

J. Zhou, K. Tajima, K. Nakajima, K. Kurokawa, C. Fukai, T. Matsui, and I. Sankawa, “Progress on low loss photonic crystal fibers,” Opt. Fiber Technol. 11, 101–110 (2005).
[Crossref]

Schwoerer, H.

Shen, Y. R.

N. Bloembergen and Y. R. Shen, “Coupling between vibrations and light waves in Raman laser media,” Phys. Rev. Lett. 12, 504–507 (1964).
[Crossref]

Sobon, G.

M. Klimczak, G. Soboń, R. Kasztelanic, K. M. Abramski, and R. Buczyński, “Direct comparison of shot-to-shot noise performance of all normal dispersion and anomalous dispersion supercontinuum pumped with sub-picosecond pulse fiber-based laser,” Sci. Rep. 6, 19284 (2016).
[Crossref]

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]

Sørensen, S. T.

S. T. Sørensen, O. Bang, B. Wetzel, and J. M. Dudley, “Describing supercontinuum noise and rogue wave statistics using higher-order moments,” Opt. Commun. 285, 2451–2455 (2012).
[Crossref]

Stolen, R. H.

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]

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–278 (1973).
[Crossref]

Tajima, K.

J. Zhou, K. Tajima, K. Nakajima, K. Kurokawa, C. Fukai, T. Matsui, and I. Sankawa, “Progress on low loss photonic crystal fibers,” Opt. Fiber Technol. 11, 101–110 (2005).
[Crossref]

Takayanagi, J.

Tomlinson, W. J.

Vanholsbeeck, F.

Wabnitz, S. J.

Wetzel, B.

S. T. Sørensen, O. Bang, B. Wetzel, and J. M. Dudley, “Describing supercontinuum noise and rogue wave statistics using higher-order moments,” Opt. Commun. 285, 2451–2455 (2012).
[Crossref]

Wood, D.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[Crossref]

Zhou, J.

J. Zhou, K. Tajima, K. Nakajima, K. Kurokawa, C. Fukai, T. Matsui, and I. Sankawa, “Progress on low loss photonic crystal fibers,” Opt. Fiber Technol. 11, 101–110 (2005).
[Crossref]

Appl. Phys. Lett. (1)

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–278 (1973).
[Crossref]

IEEE J. Quantum Electron. (1)

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (7)

Opt. Commun. (1)

S. T. Sørensen, O. Bang, B. Wetzel, and J. M. Dudley, “Describing supercontinuum noise and rogue wave statistics using higher-order moments,” Opt. Commun. 285, 2451–2455 (2012).
[Crossref]

Opt. Express (2)

Opt. Fiber Technol. (1)

J. Zhou, K. Tajima, K. Nakajima, K. Kurokawa, C. Fukai, T. Matsui, and I. Sankawa, “Progress on low loss photonic crystal fibers,” Opt. Fiber Technol. 11, 101–110 (2005).
[Crossref]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

N. Bloembergen and Y. R. Shen, “Coupling between vibrations and light waves in Raman laser media,” Phys. Rev. Lett. 12, 504–507 (1964).
[Crossref]

Prog. Quantum Electron. (1)

R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1–68 (1977).
[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. (2)

M. Klimczak, G. Soboń, R. Kasztelanic, K. M. Abramski, and R. Buczyński, “Direct comparison of shot-to-shot noise performance of all normal dispersion and anomalous dispersion supercontinuum pumped with sub-picosecond pulse fiber-based laser,” Sci. Rep. 6, 19284 (2016).
[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]

Other (1)

G. Agrawal, Nonlinear Fiber Optics (Academic, 2013).

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Figures (9)

Fig. 1.
Fig. 1. (a) Calculated dispersion (black) and total loss (blue), including material and confinement loss, of the ANDi fiber ( Λ = 1.44    μm , d / Λ = 0.39 ). (b) Raman gain measured at λ p R = 526    nm [12,13] (full blue), Lorentzian model (dotted red), and Q. Lin model (dashed green) used in the simulations. The inset in (b) shows the peak at around 14.8 THz in the measured Raman gain, which is missing in the analytical models.
Fig. 2.
Fig. 2. Normalized MPR gain profile for the measured Raman gain and the parameters used in the simulation (solid). The corresponding pure Raman gain, obtained for K , is shown as a dashed line. The inset shows a maximum around 14.8 THz for the MPR gain.
Fig. 3.
Fig. 3. Normalized MPR gain profile for the three Raman gain profiles in Fig 1(b): measured Raman gain (blue), Lorentzian (red), and Q. Lin (green) models. The inset shows the frequency dependence of | K | .
Fig. 4.
Fig. 4. Mean SC evolution and spectral coherence (for an ensemble of 20 simulations) over 2 m for 600 fs pump at 1 μm and 100 kW input peak power using the three different Raman gain profiles in Fig. 1(b). (a),(b) Q. Lin model; (c),(d) Lorentzian model; and (e),(f) measured Raman gain.
Fig. 5.
Fig. 5. Single-shot SC spectrograms for 600 fs pump at 1 μm and 100 kW input peak power using the three different Raman gain profiles in Fig. 1(b). (a)–(c) Q. Lin model, (d)–(f) Lorentzian model, and (g)–(i) measured Raman gain. Each column corresponds to a fixed propagation distance (0.5, 1, and 2 m).
Fig. 6.
Fig. 6. Mean SC spectrum (red), spectral fluctuations (gray), and spectral coherence (blue) at 2 m for 600 fs pump at 1 μm and 100 kW input peak power using (a) the full model for the measured Raman and (b) the model without the peak at 14.8 THz. (c) Full model for the measured Raman given in [25].
Fig. 7.
Fig. 7. Normalized Raman response in the time domain, corresponding to the full (including the 14.8 THz peak) multi-resonance Raman model (blue) and when the 14.8 THz peak is removed (red). The inset shows the longer decay time of the Raman response when the narrow resonance peak at 14.8 THz is included.
Fig. 8.
Fig. 8. (a) Pure Raman gain and (b) corresponding normalized Raman response time with numerically enhanced and wide (light blue) and narrow (dark blue) 24 THz peak. The inset in (b) shows longer decay time for the narrower 24 THz peak (dark blue). Mean SC spectrum (red), spectral fluctuations (gray), and spectral coherence (blue) at 2 m using the Raman gain with (c) the narrow and (d) the wide 24 THz peak.
Fig. 9.
Fig. 9. Mean SC evolution and spectral coherence (for an ensemble of 20 simulations) over 1 m for 1.6 ps pump at 1 μm and 100 kW input peak power using the three different Raman gain profiles in Fig. 1(b). (a),(b) Q. Lin model; (c),(d) Lorentzian model; and (e),(f) measured Raman gain.

Equations (6)

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

A ˜ ( Ω , z ) z = i [ β ( ω ) [ β ( ω 0 ) + β 1 ( ω 0 ) Ω ] ] A ˜ ( Ω , z ) α ( ω ) 2 A ˜ ( Ω , z ) + i γ ( 1 + Ω ω 0 ) · F { ( 1 f R ) A ( t , z ) | A ( t , z ) | 2 + f R A ( t , z ) · F 1 { h ˜ R ( Ω ) · F { | A ( t , z ) | 2 } } } ,
| g 12 ( 1 ) ( λ ) | = | A ˜ i * ( λ ) A ˜ j ( λ ) i j | A ˜ i ( λ ) | 2 | A ˜ j ( λ ) | 2 | ,
R ( τ ) = ( 1 f R ) δ ( τ ) + f R h R ( τ ) = ( 1 f R ) δ ( τ ) + f R [ R a ( τ ) + R b ( τ ) ] ,
h R ( τ ) = τ 1 ( τ 1 2 + τ 2 2 ) exp ( τ / τ 2 ) sin ( τ / τ 1 ) ,
h R ( τ ) = f a h a ( τ ) + [ f c h a ( τ ) + f b h b ( τ ) ] , h a ( τ ) = τ 1 ( τ 1 2 + τ 2 2 ) exp ( τ / τ 2 ) sin ( τ / τ 1 ) , h b ( τ ) = [ ( 2 τ b τ ) / τ b 2 ] exp ( τ / τ b ) ,
g * ( Ω ) = 2 γ P 0 Re { K ( 2 q K ) } ,

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