Abstract

We investigate numerically the formation of extreme events or rogue waves in soft glass tellurite fibers and demonstrate that optical loss drastically diminishes shot-to-shot fluctuations characteristic of picosecond pumped supercontinuum (SC). When loss is neglected these fluctuations include extreme events such as formation of highly energetic pulses located at the red end of the spectrum and we obtain right-skewed heavy-tailed distributions characteristic of extreme events statistics. On the other hand, when loss is included bandwidth fluctuations follow Gaussian-like statistical distributions. Our results thus implicitly show that rogue waves will not occur in any SC spectrum that is limited by loss, such as commercial silica fiber based SC sources.

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. O. Bang and M. Peyrard, “Generation of high-energy localized vibrational modes in nonlinear Klein–Gordon lattices,” Phys. Rev. E 53, 4143–4152 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2010 (5)

M. Erkintalo, G. Genty, and J. M. Dudley, “On the statistical interpretation of optical rogue waves,” Eur. Phys. J. Spec. Top. 185, 135–144 (2010).
[CrossRef]

D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, “Thulium pumped high power supercontinuum in loss-determined optimum lengths of tellurite photonic crystal fiber,” Appl. Phys. Lett. 97, 061106 (2010).
[CrossRef]

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

N. Akhmediev and E. Pelinovsky, “Editorial—Introductory remarks on ‘Discussion & debate: rogue waves—towards a unifying concept?’,” Eur. Phys. J. Spec. Top. 185, 1–4 (2010).
[CrossRef]

O. Vanvincq, B. Barviau, A. Mussot, G. Bouwmans, Y. Quiquempois, and A. Kudlinski, “Significant reduction of power fluctuations at the long-wavelength edge of a supercontinuum generated in solid-core photonic bandgap fibers,” Opt. Express 18, 24352–24360 (2010).
[CrossRef] [PubMed]

2009 (4)

2008 (1)

2007 (2)

2006 (3)

1996 (2)

O. Bang and P. D. Miller, “Exploiting discreteness for switching in waveguide arrays,” Opt. Lett. 21, 1105–1107 (1996).
[CrossRef] [PubMed]

O. Bang and M. Peyrard, “Generation of high-energy localized vibrational modes in nonlinear Klein–Gordon lattices,” Phys. Rev. E 53, 4143–4152 (1996).
[CrossRef]

1995 (1)

O. Bang and M. Peyrard, “High-order breather solutions to a discrete nonlinear Klein–Gordon model,” Physica D 81, 9–22 (1995).
[CrossRef]

1994 (1)

A. V. Buryak and N. Akhmediev, “Internal friction between solitons in near integrable systems,” Phys. Rev. E 50, 3126–3133 (1994).
[CrossRef]

1993 (1)

T. Dauxois and M. Peyrard, “Energy localization in nonlinear lattices,” Phys. Rev. Lett. 70, 3935–3938 (1993).
[CrossRef] [PubMed]

1989 (1)

1970 (1)

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24, 584–587 (1970).
[CrossRef]

Afshar V., S.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

Akhmediev, N.

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

N. Akhmediev and E. Pelinovsky, “Editorial—Introductory remarks on ‘Discussion & debate: rogue waves—towards a unifying concept?’,” Eur. Phys. J. Spec. Top. 185, 1–4 (2010).
[CrossRef]

A. V. Buryak and N. Akhmediev, “Internal friction between solitons in near integrable systems,” Phys. Rev. E 50, 3126–3133 (1994).
[CrossRef]

Alfano, R. R.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24, 584–587 (1970).
[CrossRef]

Bang, O.

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, “Thulium pumped high power supercontinuum in loss-determined optimum lengths of tellurite photonic crystal fiber,” Appl. Phys. Lett. 97, 061106 (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] [PubMed]

O. Bang and M. Peyrard, “Generation of high-energy localized vibrational modes in nonlinear Klein–Gordon lattices,” Phys. Rev. E 53, 4143–4152 (1996).
[CrossRef]

O. Bang and P. D. Miller, “Exploiting discreteness for switching in waveguide arrays,” Opt. Lett. 21, 1105–1107 (1996).
[CrossRef] [PubMed]

O. Bang and M. Peyrard, “High-order breather solutions to a discrete nonlinear Klein–Gordon model,” Physica D 81, 9–22 (1995).
[CrossRef]

Bar-Joseph, I.

Barviau, B.

Bjarklev, A.

Bouwmans, G.

Brawley, G.

Buccoliero, D.

D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, “Thulium pumped high power supercontinuum in loss-determined optimum lengths of tellurite photonic crystal fiber,” Appl. Phys. Lett. 97, 061106 (2010).
[CrossRef]

Buryak, A. V.

A. V. Buryak and N. Akhmediev, “Internal friction between solitons in near integrable systems,” Phys. Rev. E 50, 3126–3133 (1994).
[CrossRef]

Chemla, D.

Coen, S.

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

Dauxois, T.

T. Dauxois and M. Peyrard, “Energy localization in nonlinear lattices,” Phys. Rev. Lett. 70, 3935–3938 (1993).
[CrossRef] [PubMed]

de Sterke, C. M.

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

Dias, F.

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

Douay, M.

Dudley, J. M.

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

M. Erkintalo, G. Genty, and J. M. Dudley, “On the statistical interpretation of optical rogue waves,” Eur. Phys. J. Spec. Top. 185, 135–144 (2010).
[CrossRef]

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

J. C. Travers, M. H. Frosz, and J. M. Dudley, in Supercontinuum Generation in Optical Fibers, J. M. Dudley and J. R. Taylor, eds. (Cambridge University Press, 2010).

Ebendorff-Heidepriem, H.

D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, “Thulium pumped high power supercontinuum in loss-determined optimum lengths of tellurite photonic crystal fiber,” Appl. Phys. Lett. 97, 061106 (2010).
[CrossRef]

H. Ebendorff-Heidepriem, T.-C. Foo, Y. Li, M. Oermann, and T. M. Monro, “New tellurite glasses for erbium fibre lasers,” in Australian Conference on Optical Fibre Technology (ACOFT’2008), Sydney, 2008.

Eggleton, B. J.

Erkintalo, M.

M. Erkintalo, G. Genty, and J. M. Dudley, “On the statistical interpretation of optical rogue waves,” Eur. Phys. J. Spec. Top. 185, 135–144 (2010).
[CrossRef]

Foo, T.-C.

H. Ebendorff-Heidepriem, T.-C. Foo, Y. Li, M. Oermann, and T. M. Monro, “New tellurite glasses for erbium fibre lasers,” in Australian Conference on Optical Fibre Technology (ACOFT’2008), Sydney, 2008.

Frosz, M. H.

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] [PubMed]

J. C. Travers, M. H. Frosz, and J. M. Dudley, in Supercontinuum Generation in Optical Fibers, J. M. Dudley and J. R. Taylor, eds. (Cambridge University Press, 2010).

Geng, J.

Genty, G.

M. Erkintalo, G. Genty, and J. M. Dudley, “On the statistical interpretation of optical rogue waves,” Eur. Phys. J. Spec. Top. 185, 135–144 (2010).
[CrossRef]

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

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

Gordon, J.

Hadžievski, Lj.

A. Maluckov, Lj. Hadžievski, N. Lazarides, and G. P. Tsironis, “Extreme events in discrete nonlinear lattices,” Phys. Rev. E 79, 025601 (2009).
[CrossRef]

Hult, J.

Islam, M.

Jalali, B.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1058 (2007).
[CrossRef] [PubMed]

Jiang, S.

Knight, J.

Kolobov, M.

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1058 (2007).
[CrossRef] [PubMed]

Kudlinski, A.

Lazarides, N.

A. Maluckov, Lj. Hadžievski, N. Lazarides, and G. P. Tsironis, “Extreme events in discrete nonlinear lattices,” Phys. Rev. E 79, 025601 (2009).
[CrossRef]

Li, Y.

H. Ebendorff-Heidepriem, T.-C. Foo, Y. Li, M. Oermann, and T. M. Monro, “New tellurite glasses for erbium fibre lasers,” in Australian Conference on Optical Fibre Technology (ACOFT’2008), Sydney, 2008.

Louvergneaux, E.

Luan, F.

Luo, T.

Maluckov, A.

A. Maluckov, Lj. Hadžievski, N. Lazarides, and G. P. Tsironis, “Extreme events in discrete nonlinear lattices,” Phys. Rev. E 79, 025601 (2009).
[CrossRef]

Miller, P. D.

Monro, T. M.

D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, “Thulium pumped high power supercontinuum in loss-determined optimum lengths of tellurite photonic crystal fiber,” Appl. Phys. Lett. 97, 061106 (2010).
[CrossRef]

W. Q. Zhang, S. Afshar V., and T. M. Monro, “A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation,” Opt. Express 17, 19311–19327 (2009).
[CrossRef]

H. Ebendorff-Heidepriem, T.-C. Foo, Y. Li, M. Oermann, and T. M. Monro, “New tellurite glasses for erbium fibre lasers,” in Australian Conference on Optical Fibre Technology (ACOFT’2008), Sydney, 2008.

Moss, D. J.

Mussot, A.

Oermann, M.

H. Ebendorff-Heidepriem, T.-C. Foo, Y. Li, M. Oermann, and T. M. Monro, “New tellurite glasses for erbium fibre lasers,” in Australian Conference on Optical Fibre Technology (ACOFT’2008), Sydney, 2008.

Pelinovsky, E.

N. Akhmediev and E. Pelinovsky, “Editorial—Introductory remarks on ‘Discussion & debate: rogue waves—towards a unifying concept?’,” Eur. Phys. J. Spec. Top. 185, 1–4 (2010).
[CrossRef]

Peyrard, M.

O. Bang and M. Peyrard, “Generation of high-energy localized vibrational modes in nonlinear Klein–Gordon lattices,” Phys. Rev. E 53, 4143–4152 (1996).
[CrossRef]

O. Bang and M. Peyrard, “High-order breather solutions to a discrete nonlinear Klein–Gordon model,” Physica D 81, 9–22 (1995).
[CrossRef]

T. Dauxois and M. Peyrard, “Energy localization in nonlinear lattices,” Phys. Rev. Lett. 70, 3935–3938 (1993).
[CrossRef] [PubMed]

Quiquempois, Y.

Ropers, C.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1058 (2007).
[CrossRef] [PubMed]

Shapiro, S. L.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24, 584–587 (1970).
[CrossRef]

Skryabin, D.

Solli, D. R.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1058 (2007).
[CrossRef] [PubMed]

Steffensen, H.

D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, “Thulium pumped high power supercontinuum in loss-determined optimum lengths of tellurite photonic crystal fiber,” Appl. Phys. Lett. 97, 061106 (2010).
[CrossRef]

Sucha, G.

Taki, M.

Travers, J. C.

J. C. Travers, M. H. Frosz, and J. M. Dudley, in Supercontinuum Generation in Optical Fibers, J. M. Dudley and J. R. Taylor, eds. (Cambridge University Press, 2010).

Tsironis, G. P.

A. Maluckov, Lj. Hadžievski, N. Lazarides, and G. P. Tsironis, “Extreme events in discrete nonlinear lattices,” Phys. Rev. E 79, 025601 (2009).
[CrossRef]

Tuniz, A.

Vanvincq, O.

Wang, Q.

Wegener, M.

Yulin, A.

Zhang, W. Q.

Appl. Phys. Lett. (1)

D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, “Thulium pumped high power supercontinuum in loss-determined optimum lengths of tellurite photonic crystal fiber,” Appl. Phys. Lett. 97, 061106 (2010).
[CrossRef]

Eur. Phys. J. Spec. Top. (2)

M. Erkintalo, G. Genty, and J. M. Dudley, “On the statistical interpretation of optical rogue waves,” Eur. Phys. J. Spec. Top. 185, 135–144 (2010).
[CrossRef]

N. Akhmediev and E. Pelinovsky, “Editorial—Introductory remarks on ‘Discussion & debate: rogue waves—towards a unifying concept?’,” Eur. Phys. J. Spec. Top. 185, 1–4 (2010).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

Nature (1)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1058 (2007).
[CrossRef] [PubMed]

Opt. Express (6)

Opt. Lett. (2)

Phys. Lett. A (1)

G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010).
[CrossRef]

Phys. Rev. E (3)

A. V. Buryak and N. Akhmediev, “Internal friction between solitons in near integrable systems,” Phys. Rev. E 50, 3126–3133 (1994).
[CrossRef]

O. Bang and M. Peyrard, “Generation of high-energy localized vibrational modes in nonlinear Klein–Gordon lattices,” Phys. Rev. E 53, 4143–4152 (1996).
[CrossRef]

A. Maluckov, Lj. Hadžievski, N. Lazarides, and G. P. Tsironis, “Extreme events in discrete nonlinear lattices,” Phys. Rev. E 79, 025601 (2009).
[CrossRef]

Phys. Rev. Lett. (2)

T. Dauxois and M. Peyrard, “Energy localization in nonlinear lattices,” Phys. Rev. Lett. 70, 3935–3938 (1993).
[CrossRef] [PubMed]

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24, 584–587 (1970).
[CrossRef]

Physica D (1)

O. Bang and M. Peyrard, “High-order breather solutions to a discrete nonlinear Klein–Gordon model,” Physica D 81, 9–22 (1995).
[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 (3)

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

H. Ebendorff-Heidepriem, T.-C. Foo, Y. Li, M. Oermann, and T. M. Monro, “New tellurite glasses for erbium fibre lasers,” in Australian Conference on Optical Fibre Technology (ACOFT’2008), Sydney, 2008.

J. C. Travers, M. H. Frosz, and J. M. Dudley, in Supercontinuum Generation in Optical Fibers, J. M. Dudley and J. R. Taylor, eds. (Cambridge University Press, 2010).

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Figures (3)

Fig. 1
Fig. 1

(a) Optical loss for tellurite fiber with Λ=3 μm and d/Λ=0.4. Shown are the combined contribution from both material and confinement loss, as well as confinement loss alone. (b) Raman gain spectrum R (Ω) of tellurite with maximum peak at Ω R ∼22.5 THz. and silica with peak at Ω R ∼13.2 THz. The dashed curve shows the approximate Raman gain spectrum of tellurite.

Fig. 2
Fig. 2

Output spectra for various peak powers with and without including optical loss. In each ensemble the black lined spectrum depicts the ensemble median and the inserts on the right show (top, bottom) a RW and the narrowest spectrum and (middle) a spectrum close to the median.

Fig. 3
Fig. 3

(left column) Series of short pulses corresponding to the filtered components of the spectra. (right column) Statistical distributions of peak powers in the series of pulses. Inserts depict the RWs and their absolute frequency.

Metrics