Abstract

We numerically study the impact of feedback on supercontinuum generation within a microstructured fiber inside a ring resonator, synchronously pumped with femtosecond pulses. In certain parameter ranges we observe a steady-state oscillator-like operation mode of the system. Depending on pump power also period doubling up to chaos is shown by the system. Even with the inclusion of realistic pump noise as perturbation, the periodic behavior was still achievable in numerical modeling as well as in a first experimental verification.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J.K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 78, 25-27 (2000).
    [CrossRef]
  2. J.M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev.Mod. Phys. 78, 1135-1184 (2006).
    [CrossRef]
  3. M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, "Supercontinuum generation in a highly birefringent microstructured fiber," Appl. Phys. Lett. 82, 2197-2199 (2003).
    [CrossRef]
  4. Q1. X. Fu, L. Qian, S. Wen, and D. Fan, "Nonlinear chirped pulse propagation and supercontinuum generation in microstructured optical fibre," J. of Opt. A 6, 1012-1016 (2004).
    [CrossRef]
  5. Z. Zhu and T. Brown, "Effect of frequency chirping on supercontinuum generation in photonic crystal fibers," Opt. Express 12, 689-694 (2004).
    [CrossRef] [PubMed]
  6. S. Coen, A.H. L. Chau, R. Leonhardt, J.D. Harvey, J.C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Whitelight supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber," Opt. Lett. 26, 1356-1358 (2001).
    [CrossRef]
  7. A.V. Husakou and J. Herrmann, "Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers," Phys. Rev. Lett. 87, 203901 (2001).
    [CrossRef] [PubMed]
  8. B. Washburn, S. Ralph, and R. Windeler, "Ultrashort pulse propagation in air-silica microstructure fiber," Opt. Express 10, 575-580 (2002).
    [PubMed]
  9. H.N. Paulsen, K.M. Hilligsøe, J. Thøgersen, SR. Keiding, and J. J. Larsen, "Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source," Opt. Lett. 27, 1123-1125 (2003).
    [CrossRef]
  10. I. Hartl, X.D. Li, C. Chudoba, R.K. Ghanta, T.H. Ko, J.G. Fujimoto, J.K. Ranka, and R. S. Windeler, "Ultrahighresolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber," Opt. Lett. 26, 608-610 (2001).
    [CrossRef]
  11. A.D. Aguirre, N. Nishizawa, J.G. Fujimoto, W. Seitz, M. Lederer, and D. Kopf, "Continuum generation in a novel photonic crystal fiber for ultrahigh resolution optical coherence tomography at 800 nm and 1300 nm," Opt. Express 14, 1145-1160 (2006).
    [CrossRef] [PubMed]
  12. D. J. Jones, S.A. Diddams, J.K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
    [CrossRef] [PubMed]
  13. T. Udem, R. Holzwarth, and T.W. H¨ansch, "Optical frequency metrology," Nature 416, 233-237 (2002).
    [CrossRef] [PubMed]
  14. 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]
  15. T.M. Fortier, J. Ye, S. T. Cundiff, and R. S. Windeler, "Nonlinear phase noise generated in air-silica microstructure fiber and its effect on carrier-envelope phase," Opt. Lett. 27, 445-447 (2002).
    [CrossRef]
  16. F. Lu and W.H. Knox, "Generation of a broadband continuum with high spectral coherence in tapered singlemode optical fibers," Opt. Express 12, 347-353 (2004).
    [CrossRef] [PubMed]
  17. G. Genty, J.M. Dudley, and B. J. Eggleton, "Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime," Appl. Phys. B 94, 187-194 (2009).
    [CrossRef]
  18. 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]
  19. M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A.G. Vladimirov, and M. Taki, "Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities," Opt. Lett. 32, 662-664 (2007).
    [CrossRef] [PubMed]
  20. G. Steinmeyer, A. Buchholz, M. H¨ansel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
    [CrossRef] [PubMed]
  21. A. E. Siegman, Lasers, (University Science Books, 1986).
  22. P. Groß, K.-J. Boller, and M. E. Klein, "High-precision wavelength-flexible frequency division for metrology," Phys. Rev. A 71, 043824 (2005).
    [CrossRef]
  23. 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]
  24. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).
  25. Crystal Fibre, "NL-PM-750 data sheet," http://www.crystal-fibre.com/datasheets/NL-PM-750.pdf.
  26. M. J. Litzkow, M. Livny, and M.W. Mutka, "Condor - a hunter of idle workstations," in Proc. 8th Int. Conf. on Distributed Computing Systems (IEEE Computer Society Press, 1988), pp. 104-111.
  27. S.H. Strogatz and R. F. Fox, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering (Physics Today, 1995).
  28. A. Scott, Encyclopedia of Nonlinear Science (Routledge Taylor and Francis Group, 2005).

2009 (1)

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

2008 (1)

2007 (1)

2006 (2)

2005 (1)

P. Groß, K.-J. Boller, and M. E. Klein, "High-precision wavelength-flexible frequency division for metrology," Phys. Rev. A 71, 043824 (2005).
[CrossRef]

2004 (3)

2003 (2)

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, "Supercontinuum generation in a highly birefringent microstructured fiber," Appl. Phys. Lett. 82, 2197-2199 (2003).
[CrossRef]

H.N. Paulsen, K.M. Hilligsøe, J. Thøgersen, SR. Keiding, and J. J. Larsen, "Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source," Opt. Lett. 27, 1123-1125 (2003).
[CrossRef]

2002 (4)

2001 (3)

2000 (2)

D. J. Jones, S.A. Diddams, J.K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

J.K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 78, 25-27 (2000).
[CrossRef]

1995 (1)

G. Steinmeyer, A. Buchholz, M. H¨ansel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

1989 (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]

Aguirre, A.D.

Bang, O.

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]

Boller, K.-J.

P. Groß, K.-J. Boller, and M. E. Klein, "High-precision wavelength-flexible frequency division for metrology," Phys. Rev. A 71, 043824 (2005).
[CrossRef]

Brown, T.

Buchholz, A.

G. Steinmeyer, A. Buchholz, M. H¨ansel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

Chau, A.H. L.

Chudoba, C.

Coen, S.

Cundiff, S. T.

T.M. Fortier, J. Ye, S. T. Cundiff, and R. S. Windeler, "Nonlinear phase noise generated in air-silica microstructure fiber and its effect on carrier-envelope phase," Opt. Lett. 27, 445-447 (2002).
[CrossRef]

D. J. Jones, S.A. Diddams, J.K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Diddams, S.A.

D. J. Jones, S.A. Diddams, J.K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Dudley, J.M.

G. Genty, J.M. Dudley, and B. J. 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]

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. J.

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

Fan, D.

Q1. X. Fu, L. Qian, S. Wen, and D. Fan, "Nonlinear chirped pulse propagation and supercontinuum generation in microstructured optical fibre," J. of Opt. A 6, 1012-1016 (2004).
[CrossRef]

Fortier, T.M.

Frosz, M.H.

Fu, X.

Q1. X. Fu, L. Qian, S. Wen, and D. Fan, "Nonlinear chirped pulse propagation and supercontinuum generation in microstructured optical fibre," J. of Opt. A 6, 1012-1016 (2004).
[CrossRef]

Fujimoto, J.G.

Genty, G.

G. Genty, J.M. Dudley, and B. J. 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]

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, "Supercontinuum generation in a highly birefringent microstructured fiber," Appl. Phys. Lett. 82, 2197-2199 (2003).
[CrossRef]

Ghanta, R.K.

Groß, P.

P. Groß, K.-J. Boller, and M. E. Klein, "High-precision wavelength-flexible frequency division for metrology," Phys. Rev. A 71, 043824 (2005).
[CrossRef]

H¨ansch, T.W.

T. Udem, R. Holzwarth, and T.W. H¨ansch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

H¨ansel, M.

G. Steinmeyer, A. Buchholz, M. H¨ansel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

Hall, J. L.

D. J. Jones, S.A. Diddams, J.K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Hartl, I.

Harvey, J.D.

Herrmann, J.

A.V. Husakou and J. Herrmann, "Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers," Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

Heuer, M.

G. Steinmeyer, A. Buchholz, M. H¨ansel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

Hilligsøe, K.M.

Holzwarth, R.

T. Udem, R. Holzwarth, and T.W. H¨ansch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Husakou, A.V.

A.V. Husakou and J. Herrmann, "Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers," Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

Jones, D. J.

D. J. Jones, S.A. Diddams, J.K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Kaivola, M.

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, "Supercontinuum generation in a highly birefringent microstructured fiber," Appl. Phys. Lett. 82, 2197-2199 (2003).
[CrossRef]

Keiding, SR.

Klein, M. E.

P. Groß, K.-J. Boller, and M. E. Klein, "High-precision wavelength-flexible frequency division for metrology," Phys. Rev. A 71, 043824 (2005).
[CrossRef]

Knight, J.C.

Knox, W.H.

Ko, T.H.

Kopf, D.

Kozyreff, G.

Larsen, J. J.

Lederer, M.

Lehtonen, M.

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, "Supercontinuum generation in a highly birefringent microstructured fiber," Appl. Phys. Lett. 82, 2197-2199 (2003).
[CrossRef]

Leonhardt, R.

Li, X.D.

Louvergneaux, E.

Lu, F.

Ludvigsen, H.

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, "Supercontinuum generation in a highly birefringent microstructured fiber," Appl. Phys. Lett. 82, 2197-2199 (2003).
[CrossRef]

Mitschke, F.

G. Steinmeyer, A. Buchholz, M. H¨ansel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

Moselund, P.M.

Mussot, A.

Nishizawa, N.

Paulsen, H.N.

Qian, L.

Q1. X. Fu, L. Qian, S. Wen, and D. Fan, "Nonlinear chirped pulse propagation and supercontinuum generation in microstructured optical fibre," J. of Opt. A 6, 1012-1016 (2004).
[CrossRef]

Ralph, S.

Ranka, J.K.

I. Hartl, X.D. Li, C. Chudoba, R.K. Ghanta, T.H. Ko, J.G. Fujimoto, J.K. Ranka, and R. S. Windeler, "Ultrahighresolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber," Opt. Lett. 26, 608-610 (2001).
[CrossRef]

J.K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 78, 25-27 (2000).
[CrossRef]

D. J. Jones, S.A. Diddams, J.K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Russell, P. St. J.

Schwache, A.

G. Steinmeyer, A. Buchholz, M. H¨ansel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

Seitz, W.

Steinmeyer, G.

G. Steinmeyer, A. Buchholz, M. H¨ansel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

Stentz, A.

D. J. Jones, S.A. Diddams, J.K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Stentz, A. J.

J.K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 78, 25-27 (2000).
[CrossRef]

Taki, M.

Thøgersen, J.

Thomsen, C. L.

Tlidi, M.

Udem, T.

T. Udem, R. Holzwarth, and T.W. H¨ansch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Vladimirov, A.G.

Wadsworth, W. J.

Washburn, B.

Wen, S.

Q1. X. Fu, L. Qian, S. Wen, and D. Fan, "Nonlinear chirped pulse propagation and supercontinuum generation in microstructured optical fibre," J. of Opt. A 6, 1012-1016 (2004).
[CrossRef]

Windeler, R.

Windeler, R. S.

T.M. Fortier, J. Ye, S. T. Cundiff, and R. S. Windeler, "Nonlinear phase noise generated in air-silica microstructure fiber and its effect on carrier-envelope phase," Opt. Lett. 27, 445-447 (2002).
[CrossRef]

I. Hartl, X.D. Li, C. Chudoba, R.K. Ghanta, T.H. Ko, J.G. Fujimoto, J.K. Ranka, and R. S. Windeler, "Ultrahighresolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber," Opt. Lett. 26, 608-610 (2001).
[CrossRef]

J.K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 78, 25-27 (2000).
[CrossRef]

D. J. Jones, S.A. Diddams, J.K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

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]

Ye, J.

Zhu, Z.

Appl. Phys. B (1)

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

Appl. Phys. Lett. (1)

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, "Supercontinuum generation in a highly birefringent microstructured fiber," Appl. Phys. Lett. 82, 2197-2199 (2003).
[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. of Opt. A (1)

Q1. X. Fu, L. Qian, S. Wen, and D. Fan, "Nonlinear chirped pulse propagation and supercontinuum generation in microstructured optical fibre," J. of Opt. A 6, 1012-1016 (2004).
[CrossRef]

Nature (1)

T. Udem, R. Holzwarth, and T.W. H¨ansch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Lett. (7)

M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A.G. Vladimirov, and M. Taki, "Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities," Opt. Lett. 32, 662-664 (2007).
[CrossRef] [PubMed]

J.K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 78, 25-27 (2000).
[CrossRef]

I. Hartl, X.D. Li, C. Chudoba, R.K. Ghanta, T.H. Ko, J.G. Fujimoto, J.K. Ranka, and R. S. Windeler, "Ultrahighresolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber," Opt. Lett. 26, 608-610 (2001).
[CrossRef]

S. Coen, A.H. L. Chau, R. Leonhardt, J.D. Harvey, J.C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Whitelight supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber," Opt. Lett. 26, 1356-1358 (2001).
[CrossRef]

T.M. Fortier, J. Ye, S. T. Cundiff, and R. S. Windeler, "Nonlinear phase noise generated in air-silica microstructure fiber and its effect on carrier-envelope phase," Opt. Lett. 27, 445-447 (2002).
[CrossRef]

H.N. Paulsen, K.M. Hilligsøe, J. Thøgersen, SR. Keiding, and J. J. Larsen, "Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source," Opt. Lett. 27, 1123-1125 (2003).
[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]

Phys. Rev. A (2)

G. Steinmeyer, A. Buchholz, M. H¨ansel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

P. Groß, K.-J. Boller, and M. E. Klein, "High-precision wavelength-flexible frequency division for metrology," Phys. Rev. A 71, 043824 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

A.V. Husakou and J. Herrmann, "Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers," Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

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]

Science (1)

D. J. Jones, S.A. Diddams, J.K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Other (6)

A. E. Siegman, Lasers, (University Science Books, 1986).

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

Crystal Fibre, "NL-PM-750 data sheet," http://www.crystal-fibre.com/datasheets/NL-PM-750.pdf.

M. J. Litzkow, M. Livny, and M.W. Mutka, "Condor - a hunter of idle workstations," in Proc. 8th Int. Conf. on Distributed Computing Systems (IEEE Computer Society Press, 1988), pp. 104-111.

S.H. Strogatz and R. F. Fox, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering (Physics Today, 1995).

A. Scott, Encyclopedia of Nonlinear Science (Routledge Taylor and Francis Group, 2005).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1.
Fig. 1.

Relative spectral power as function of effective average fiber input power: (a) simulation and (b) experimental results. In both graphs, the relative spectral power is displayed on color-coded logarithmic density scale (see color bar on the right), with the wavelength given on the x-axis, and the effective average input power increasing from bottom to top (y-axis). The numbers 1–3 are indicating spectral features, which are explained in the text.

Fig. 2.
Fig. 2.

Schematic diagram of the SC feedback system. The path A (solid line) describes the scheme with simple feedback included, whereas the path B (dashed line) shows the scheme with an inclusion of a dynamical dispersion compensation (DDC). For details see text.

Fig. 3.
Fig. 3.

Bifurcation diagram with the spectral phase of a single spectral component as a function of average pump power: (a) for a pump power up to 12mW at a wavelength of 775 nm and (b) in more detail within the range from 8.8mW to 10.5mW at a wavelength of 775 nm (black dots) and 750 nm (gray dots).

Fig. 4.
Fig. 4.

Left: Spectral evolution of SC pumped with 6mWaverage power, the spectral power density is displayed on logarithmic density scale (see color bar). Right: Variability V 1 N of the whole spectrum as a function of the number of iterations, on linear (b) and on logarithmic scale (c). For definition of V 1 N see text.

Fig. 5.
Fig. 5.

Occupied phase space of the spectral component at 790 nm: on the right (a) for an average pump power in the range between 8.75mW and 9.35mW and on the left (b) a magnification for an average pump power from 8.75mW to 9.10mW. The color indicates the number of feedback iterations after which this coordinate was reached, representing the respective system state (see color-coding bar on the right side).

Fig. 6.
Fig. 6.

Inclusion of dynamic dispersion compensation: Spectral evolution of SC pumped with (a) 9.5mW and (c) 10.3mW average power, the spectral power density is displayed on logarithmic density scale (see color bar). Corresponding variability as a function of the number of iterations on logarithmic scale for (b) 9.5mW and (d) 10.3mW average power.

Fig. 7.
Fig. 7.

Exclusion of dynamic dispersion compensation: Spectral evolution of SC pumped with (a) 16mW and (c) 14mW average power. The spectral power density is displayed on logarithmic density scale (see color bar). Corresponding variability as a function of the number of iterations on logarithmic scale for (b) 16mW and (d) 14mW average power.

Fig. 8.
Fig. 8.

(a) Spectral evolution of SC pumped with 6mW average pump power without dispersion compensation. The spectral power density is displayed on logarithmic density scale (see color bar). (b) Cross section through phase space of the spectral component at 790 nm, color is indicating the number of feedback iterations to reach each individual coordinate which corresponds to a certain system state.

Fig. 9.
Fig. 9.

Inclusion of 0.5% rms technical noise and quantum noise: Spectral evolution of SC pumped with (a) 16mW and (c) 14mW average pump power, the spectral power density is displayed on logarithmic density scale (see color bar). Corresponding variability of the whole spectrum as a function of the number of iterations on logarithmic scale for (b) 16mW and (d) 14mW average power.

Fig. 10.
Fig. 10.

Fixed point environment in an amplitude and phase diagram for simulations with and without noise (a) at 16mW and (b) at 14mW for a spectral component at 775 nm, and (c) at 6mW for a spectral component at 790 nm. The dots and crosses denote the coordinate in phase space without noise and with technical as well as quantum noise, respectively, whereas the color bar is indicating the number of feedback iterations after which the respective coordinate was reached.

Fig. 11.
Fig. 11.

(a): Simulated radio frequency spectrum with the inclusion of noise at 14mW effective average pump power. (b): Measured radio frequency spectrum at 14mW effective average pump power.

Equations (5)

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

Ez=α2E+k2ik+1k!βkkEtk+(1+i1ω0t)(E(z,t)+R(t)E(z,tt)2dt).
E0(0)=Epump,
EN(L)=GNLSE(EN(0)),
EN+1(0)=ε·EN(L)+E0(0),
VNp = 1(λ2λ1) λ1λ2(EN(λ)EN+p(λ)2EN(λ)+EN+p(λ)2)dλ,

Metrics