Abstract

The noise properties of a supercontinuum can be controlled by modulating the pump with a seed pulse. In this paper, we numerically investigate the influence of seeding with a partially phase coherent weak pulse or continuous wave. We demonstrate that the noise properties of the generated supercontinuum are highly sensitive to the degree of phase noise of the seed and that a nearly coherent seed pulse is needed to achieve a coherent pulse break-up and low noise supercontinuum. The specific maximum allowable linewidth of the seed laser is found to decrease with increasing pump power.

© 2012 Optical Society of America

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References

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  1. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
    [Crossref]
  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] [PubMed]
  3. D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101, 233902 (2008).
    [Crossref] [PubMed]
  4. P. M. Moselund, M. H. Frosz, C. L. Thomsen, and O. Bang, “Back-seeding of higher order gain processes in picosecond supercontinuum generation,” Opt. Express 16, 11954–11968 (2008).
    [Crossref] [PubMed]
  5. G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194 (2009).
    [Crossref]
  6. G. Genty and J. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45, 1331 –1335 (2009).
    [Crossref]
  7. N. Brauckmann, M. Kues, T. Walbaum, P. Groß, and C. Fallnich, “Experimental investigations on nonlinear dynamics in supercontinuum generation with feedback,” Opt. Express 18, 7190–7202 (2010).
    [Crossref] [PubMed]
  8. D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105, 233902 (2010).
    [Crossref]
  9. K. K. Y. Cheung, C. Zhang, Y. Zhou, K. K. Y. Wong, and K. K. Tsia, “Manipulating supercontinuum generation by minute continuous wave,” Opt. Lett. 36, 160–162 (2011).
    [Crossref] [PubMed]
  10. Q. Li, F. Li, K. K. Y. Wong, A. P. T. Lau, K. K. Tsia, and P. K. A. Wai, “Investigating the influence of a weak continuous-wave-trigger on picosecond supercontinuum generation,” Opt. Express 19, 13757–13769 (2011).
    [Crossref] [PubMed]
  11. S. T. Sørensen, C. Larsen, U. Møller, P. M. Moselund, C. L. Thomsen, and O. Bang, “Influence of pump power and modulation instability gain spectrum on seeded supercontinuum and rogue wave generation,” J. Opt. Soc. Am. B 29, 2875–2885 (2012).
  12. J. Laegsgaard, “Mode profile dispersion in the generalised nonlinear Schrödinger equation,” Opt. Express 15, 16110–16123 (2007).
    [Crossref] [PubMed]
  13. S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
    [Crossref] [PubMed]
  14. M. H. Frosz, “Validation of input-noise model for simulations of supercontinuum generation and rogue waves,” Opt. Express 18, 14778–14787 (2010).
    [Crossref] [PubMed]
  15. 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]
  16. 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]
  17. G. Genty, M. Surakka, J. Turunen, and A. T. Friberg, “Complete characterization of supercontinuum coherence,” J. Opt. Soc. Am. B 28, 2301–2309 (2011).
    [Crossref]
  18. P. M. Moselund, “Long-pulse supercontinuum light sources,” Ph.D. thesis (Technical University of Denmark, 2009).

2012 (3)

2011 (3)

2010 (3)

2009 (2)

G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194 (2009).
[Crossref]

G. Genty and J. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45, 1331 –1335 (2009).
[Crossref]

2008 (2)

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101, 233902 (2008).
[Crossref] [PubMed]

P. M. Moselund, M. H. Frosz, C. L. Thomsen, and O. Bang, “Back-seeding of higher order gain processes in picosecond supercontinuum generation,” Opt. Express 16, 11954–11968 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (1)

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

2002 (1)

1995 (1)

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
[Crossref] [PubMed]

Agrawal, G. P.

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
[Crossref] [PubMed]

Bang, O.

Brauckmann, N.

Cavalcanti, S. B.

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
[Crossref] [PubMed]

Cheung, K. K. Y.

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]

Dudley, J.

G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194 (2009).
[Crossref]

G. Genty and J. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45, 1331 –1335 (2009).
[Crossref]

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]

Eggleton, B.

G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194 (2009).
[Crossref]

Fallnich, C.

Friberg, A. T.

Frosz, M. H.

Genty, G.

G. Genty, M. Surakka, J. Turunen, and A. T. Friberg, “Complete characterization of supercontinuum coherence,” J. Opt. Soc. Am. B 28, 2301–2309 (2011).
[Crossref]

G. Genty and J. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45, 1331 –1335 (2009).
[Crossref]

G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194 (2009).
[Crossref]

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

Groß, P.

Jakobsen, C.

Jalali, B.

D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105, 233902 (2010).
[Crossref]

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101, 233902 (2008).
[Crossref] [PubMed]

Johansen, J.

Kues, M.

Laegsgaard, J.

Larsen, C.

Lau, A. P. T.

Li, F.

Li, Q.

Møller, U.

Moselund, P. M.

Ropers, C.

D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105, 233902 (2010).
[Crossref]

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101, 233902 (2008).
[Crossref] [PubMed]

Solli, D. R.

D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105, 233902 (2010).
[Crossref]

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101, 233902 (2008).
[Crossref] [PubMed]

Sørensen, S. T.

Surakka, M.

Thomsen, C. L.

Tsia, K. K.

Turunen, J.

Wai, P. K. A.

Walbaum, T.

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]

Wong, K. K. Y.

Yu, M.

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
[Crossref] [PubMed]

Zhang, C.

Zhou, Y.

Appl. Phys. B (1)

G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194 (2009).
[Crossref]

IEEE J. Quantum Electron. (1)

G. Genty and J. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45, 1331 –1335 (2009).
[Crossref]

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

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 (6)

Opt. Lett. (2)

Phys. Rev. A (1)

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101, 233902 (2008).
[Crossref] [PubMed]

D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105, 233902 (2010).
[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]

Other (1)

P. M. Moselund, “Long-pulse supercontinuum light sources,” Ph.D. thesis (Technical University of Denmark, 2009).

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Figures (7)

Fig. 1
Fig. 1 (a) Dispersion and effective area for the used PCF with pitch Λ = 3.6 μm and hole-to-pitch ratio d/Λ = 0.52. (b) MI gain as a function of wavelength for the 1064 nm pump with a peak power of 250 W. The dashed line marks the seed wavelength.

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Fig. 2
Fig. 2 Ensemble averaged input spectra (bottom) and cross-spectral density (CSD) function relative to the pump (top) for varying seed linewidth, ΔνFWHM.

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Fig. 3
Fig. 3 Single shot simulations of (a) unseeded and (b)–(f) seeded SC generation with varying seed linewidth, ΔνFWHM. The top rows show the ensemble calculated spectral coherence function and SNR at the fiber output (10 m).

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Fig. 4
Fig. 4 Ensemble calculated spectra, coherence and SNR at a propagation distance of 1 m for (a) unseeded and (b)–(f) seeded SC generation with varying seed linewidth, ΔνFWHM. The grey spectra show single shot input.

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Fig. 5
Fig. 5 Comparison of ensemble calculated spectra, coherence and SNR at a propagation distance of 1 m for (a) coherent seeding with normal (black) and raised (blue) background noise levels, and (b) seed linewidths of 0 MHz (black) and 1 GHz (blue) with a normal noise background. The grey spectra show single shot input.

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Fig. 6
Fig. 6 Overall coherence as a function of seed linewidth, ΔνFWHM, for pulsed and CW seeds at the fiber output (10 m). For the pulsed seed is shown results of pump peak powers of 125, 250 and 500 W, respectively. The pulsed seeds had 5% of the peak power of the pump and the CW seed had 1%. The horizontal dashed lines mark the overall coherence for a fully coherent seed and the black stars mark the seed linewidth at which the coherence is decreased by 25%.

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Fig. 7
Fig. 7 (a) Overall coherence as a function of seed linewidth, ΔνFWHM, for varying numerical frequency resolution. (b) Overall coherence as a function of numerical frequency resolution for the four seed linewidths marked by dotted boxes in (a). In all cases the pump peak power was 125 W.

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Equations (4)

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A ( t ) = P p exp [ − t 2 2 T 0 2 ] + P s exp [ − t 2 2 T 0 2 ] e i Ω mod t exp [ i δ ϕ ( t ) ] + A OPPM
| g 12 ( 1 ) ( ω ) | = | 〈 A ˜ i * ( ω ) A ˜ j ( ω ) 〉 i ≠ j 〈 | A ˜ i ( ω ) | 2 〉 〈 | A ˜ j ( ω ) | 2 〉 | ,
SNR ( ω ) = μ ( ω ) σ ( ω ) .
| CSD ( ω i , ω j ) | = | 〈 A ˜ * ( ω i ) A ˜ ( ω j ) 〉 〈 | A ˜ ( ω i ) | 2 〉 〈 | A ˜ ( ω j ) | 2 〉 | ,

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