Abstract

Femtosecond pulses circulating in a synchronously driven fiber ring cavity have complex amplitude and phase profiles that can change completely from one round-trip to the next. We use a recently developed technique, combining dispersive Fourier transformation) with spectral interferometry, to reconstruct the spectral amplitude and phase at each round-trip and, thereby, follow in detail the pulse reorganization that occurs. We focus on two different regimes: a period-two regime in which the pulse alternates between two distinct states and a highly complex regime. We characterize the spectral amplitude and phase of the pulses in both regimes at a repetition rate of 75.6 MHz and find good agreement with modeling of the system based on numerical solutions of the generalized nonlinear Schrödinger equation with feedback.

© 2016 Optical Society of America

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References

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  1. K. Ikeda, Opt. Commun. 30, 257 (1979).
    [Crossref]
  2. N. Brauckmann, M. Kues, P. Groß, and C. Fallnich, Opt. Express 19, 14763 (2011).
    [Crossref]
  3. M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A. G. Vladimirov, and M. Taki, Opt. Lett. 32, 662 (2007).
    [Crossref]
  4. N. Brauckmann, M. Kues, P. Groß, and C. Fallnich, Opt. Express 18, 20667 (2010).
    [Crossref]
  5. S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, Opt. Lett. 38, 37 (2013).
    [Crossref]
  6. M. J. Schmidberger, W. Chang, P. St.J. Russell, and N. Y. Joly, Opt. Lett. 37, 3576 (2012).
    [Crossref]
  7. M. J. Schmidberger, D. Novoa, F. Biancalana, P. St.J. Russell, and N. Y. Joly, Opt. Express 22, 3045 (2014).
    [Crossref]
  8. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
    [Crossref]
  9. R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, Phys. Rev. E 80, 026207 (2009).
    [Crossref]
  10. Y. Tong, L. Chan, and H. Tsang, Electron. Lett. 33, 983 (1997).
    [Crossref]
  11. K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, Phys. Rev. A 80, 043821 (2009).
    [Crossref]
  12. M. Takeda, H. Ina, and S. Kobayash, J. Opt. Soc. Am. 72, 156 (1982).
    [Crossref]
  13. L. Lepetit, G. Chériaux, and M. Joffre, J. Opt. Soc. Am. B 12, 2467 (1995).
    [Crossref]
  14. M. H. Asghari, Y. Park, and J. Azaña, Opt. Express 18, 16526 (2010).
    [Crossref]
  15. I. A. Walmsley and C. Dorrer, Adv. Opt. Photon. 1, 308 (2009).
    [Crossref]
  16. W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. D. Silvestri, and U. Keller, Opt. Lett. 28, 281 (2003).
    [Crossref]
  17. B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
    [Crossref]
  18. E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
    [Crossref]
  19. G. Herink, B. Jalali, C. Ropers, and D. R. Solli, Nat. Photonics 10, 321 (2016).
    [Crossref]
  20. D. R. Solli, S. Gupta, and B. Jalali, Appl. Phys. Lett. 95, 231108 (2009).
    [Crossref]
  21. A. M. Heidt, A. Hartung, G. W. Bosman, P. Krok, E. G. Rohwer, H. Schwoerer, and H. Bartelt, Opt. Express 19, 3775 (2011).
    [Crossref]
  22. K. Saitoh and M. Koshiba, Opt. Express 13, 267 (2005).
    [Crossref]
  23. J. M. Dudley, G. Genty, and A. S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
    [Crossref]
  24. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2006).
  25. C. Froehly, A. Lacourt, and J. C. Viénot, Nouv. Rev. Opt. 4, 183 (1973).
    [Crossref]
  26. J. Piasecki, B. Colombeau, M. Vampouille, C. Froehly, and J. A. Arnaud, Appl. Opt. 19, 3749 (1980).
    [Crossref]
  27. C. Dorrer, J. Opt. Soc. Am. B 16, 1160 (1999).
    [Crossref]
  28. Since the response time of PD1 (~500 ps) is much longer than the pulse duration (~100 fs), the measured signal, i.e., the convolution of both functions, is equal to the PD1 response function scaled by a factor proportional to the pulse energy.
  29. S. H. Strogatz, Nonlinear Dynamics and Chaos (Perseus Books, 1994).

2016 (1)

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, Nat. Photonics 10, 321 (2016).
[Crossref]

2015 (1)

E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
[Crossref]

2014 (1)

2013 (1)

2012 (2)

M. J. Schmidberger, W. Chang, P. St.J. Russell, and N. Y. Joly, Opt. Lett. 37, 3576 (2012).
[Crossref]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[Crossref]

2011 (2)

2010 (2)

2009 (4)

I. A. Walmsley and C. Dorrer, Adv. Opt. Photon. 1, 308 (2009).
[Crossref]

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, Phys. Rev. E 80, 026207 (2009).
[Crossref]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, Phys. Rev. A 80, 043821 (2009).
[Crossref]

D. R. Solli, S. Gupta, and B. Jalali, Appl. Phys. Lett. 95, 231108 (2009).
[Crossref]

2007 (1)

2006 (1)

J. M. Dudley, G. Genty, and A. S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[Crossref]

2005 (2)

K. Saitoh and M. Koshiba, Opt. Express 13, 267 (2005).
[Crossref]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[Crossref]

2003 (1)

1999 (1)

1997 (1)

Y. Tong, L. Chan, and H. Tsang, Electron. Lett. 33, 983 (1997).
[Crossref]

1995 (1)

1982 (1)

1980 (1)

1979 (1)

K. Ikeda, Opt. Commun. 30, 257 (1979).
[Crossref]

1973 (1)

C. Froehly, A. Lacourt, and J. C. Viénot, Nouv. Rev. Opt. 4, 183 (1973).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2006).

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[Crossref]

Argyris, A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[Crossref]

Arnaud, J. A.

Asghari, M. H.

Azaña, J.

Bartelt, H.

Biancalana, F.

Biegert, J.

Bielawski, S.

E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
[Crossref]

Bosman, G. W.

Brauckmann, N.

Brubach, J.-B.

E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
[Crossref]

Cassinari, L.

E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
[Crossref]

Chan, L.

Y. Tong, L. Chan, and H. Tsang, Electron. Lett. 33, 983 (1997).
[Crossref]

Chang, W.

Chériaux, G.

Coen, A. S.

J. M. Dudley, G. Genty, and A. S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[Crossref]

Coen, S.

Colet, P.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[Crossref]

Colombeau, B.

Couprie, M. E.

E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
[Crossref]

Dias, F.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[Crossref]

Dorrer, C.

Dudley, J.

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, Phys. Rev. E 80, 026207 (2009).
[Crossref]

Dudley, J. M.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[Crossref]

J. M. Dudley, G. Genty, and A. S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[Crossref]

Erkintalo, M.

Evain, C.

E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
[Crossref]

Fallnich, C.

Fischer, I.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[Crossref]

Froehly, C.

Garcia-Ojalvo, J.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[Crossref]

Genty, G.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[Crossref]

J. M. Dudley, G. Genty, and A. S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[Crossref]

Goda, K.

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, Phys. Rev. A 80, 043821 (2009).
[Crossref]

Groß, P.

Gupta, S.

D. R. Solli, S. Gupta, and B. Jalali, Appl. Phys. Lett. 95, 231108 (2009).
[Crossref]

Hartung, A.

Heidt, A. M.

Herink, G.

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, Nat. Photonics 10, 321 (2016).
[Crossref]

Ikeda, K.

K. Ikeda, Opt. Commun. 30, 257 (1979).
[Crossref]

Ina, H.

Jacquot, M.

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, Phys. Rev. E 80, 026207 (2009).
[Crossref]

Jalali, B.

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, Nat. Photonics 10, 321 (2016).
[Crossref]

D. R. Solli, S. Gupta, and B. Jalali, Appl. Phys. Lett. 95, 231108 (2009).
[Crossref]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, Phys. Rev. A 80, 043821 (2009).
[Crossref]

Joffre, M.

Joly, N. Y.

Keller, U.

Kobayash, S.

Kornelis, W.

Koshiba, M.

Kozyreff, G.

Krok, P.

Kudlinski, A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[Crossref]

Kues, M.

Labat, M.

E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
[Crossref]

Lacourt, A.

C. Froehly, A. Lacourt, and J. C. Viénot, Nouv. Rev. Opt. 4, 183 (1973).
[Crossref]

Lacourt, P. A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[Crossref]

Larger, L.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[Crossref]

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, Phys. Rev. E 80, 026207 (2009).
[Crossref]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[Crossref]

Lavrov, R.

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, Phys. Rev. E 80, 026207 (2009).
[Crossref]

Lepetit, L.

Louvergneaux, E.

Manceron, L.

E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
[Crossref]

Merolla, J. M.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[Crossref]

Mirasso, C. R.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[Crossref]

Mussot, A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[Crossref]

M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A. G. Vladimirov, and M. Taki, Opt. Lett. 32, 662 (2007).
[Crossref]

Nisoli, M.

Novoa, D.

Park, Y.

Parquier, M. L.

E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
[Crossref]

Peil, M.

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, Phys. Rev. E 80, 026207 (2009).
[Crossref]

Pesquera, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[Crossref]

Piasecki, J.

Randle, H. G.

Ricaud, J.-P.

E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
[Crossref]

Rohwer, E. G.

Ropers, C.

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, Nat. Photonics 10, 321 (2016).
[Crossref]

Roussel, E.

E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
[Crossref]

Roy, P.

E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
[Crossref]

Saitoh, K.

Sansone, G.

Schmidberger, M. J.

Schwoerer, H.

Shore, K. A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[Crossref]

Silvestri, S. D.

Solli, D. R.

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, Nat. Photonics 10, 321 (2016).
[Crossref]

D. R. Solli, S. Gupta, and B. Jalali, Appl. Phys. Lett. 95, 231108 (2009).
[Crossref]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, Phys. Rev. A 80, 043821 (2009).
[Crossref]

St.J. Russell, P.

Stefani, A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[Crossref]

Strogatz, S. H.

S. H. Strogatz, Nonlinear Dynamics and Chaos (Perseus Books, 1994).

Sylvestre, T.

S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, Opt. Lett. 38, 37 (2013).
[Crossref]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[Crossref]

Syvridis, D.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[Crossref]

Szwaj, C.

E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
[Crossref]

Takeda, M.

Taki, M.

Tisch, J. W. G.

Tlidi, M.

Tong, Y.

Y. Tong, L. Chan, and H. Tsang, Electron. Lett. 33, 983 (1997).
[Crossref]

Tordeux, M.-A.

E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
[Crossref]

Tsang, H.

Y. Tong, L. Chan, and H. Tsang, Electron. Lett. 33, 983 (1997).
[Crossref]

Tsia, K. K.

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, Phys. Rev. A 80, 043821 (2009).
[Crossref]

Udaltsov, V.

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, Phys. Rev. E 80, 026207 (2009).
[Crossref]

Vampouille, M.

Viénot, J. C.

C. Froehly, A. Lacourt, and J. C. Viénot, Nouv. Rev. Opt. 4, 183 (1973).
[Crossref]

Vladimirov, A. G.

Vozzi, C.

Walmsley, I. A.

Wetzel, B.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. R. Solli, S. Gupta, and B. Jalali, Appl. Phys. Lett. 95, 231108 (2009).
[Crossref]

Electron. Lett. (1)

Y. Tong, L. Chan, and H. Tsang, Electron. Lett. 33, 983 (1997).
[Crossref]

J. Opt. Soc. Am. (1)

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

Nat. Photonics (1)

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, Nat. Photonics 10, 321 (2016).
[Crossref]

Nature (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[Crossref]

Nouv. Rev. Opt. (1)

C. Froehly, A. Lacourt, and J. C. Viénot, Nouv. Rev. Opt. 4, 183 (1973).
[Crossref]

Opt. Commun. (1)

K. Ikeda, Opt. Commun. 30, 257 (1979).
[Crossref]

Opt. Express (6)

Opt. Lett. (4)

Phys. Rev. A (1)

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, Phys. Rev. A 80, 043821 (2009).
[Crossref]

Phys. Rev. E (1)

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, Phys. Rev. E 80, 026207 (2009).
[Crossref]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and A. S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[Crossref]

Sci. Rep. (2)

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[Crossref]

E. Roussel, C. Evain, M. L. Parquier, C. Szwaj, S. Bielawski, L. Manceron, J.-B. Brubach, M.-A. Tordeux, J.-P. Ricaud, L. Cassinari, M. Labat, M. E. Couprie, and P. Roy, Sci. Rep. 5, 10330 (2015).
[Crossref]

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2006).

Since the response time of PD1 (~500 ps) is much longer than the pulse duration (~100 fs), the measured signal, i.e., the convolution of both functions, is equal to the PD1 response function scaled by a factor proportional to the pulse energy.

S. H. Strogatz, Nonlinear Dynamics and Chaos (Perseus Books, 1994).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Dispersion of the spectral BF and the ring-PCF (RPCF). The inset shows a scanning electron micrograph of the BF structure. (b) Measured power dependence of the spectrum at the output of the BF. The line at 980    nm is residual CW pump light from the Yb-doped laser. It does not contribute to the ring cavity dynamics.

Fig. 2.
Fig. 2.

Experimental setup. The polarization state is adjusted with half-wave plates. The Mach–Zehnder interferometer is terminated by a polarization beam splitter at the entrance and a 50:50 beam splitter at the output. Photodiode 1 (PD1, 2 GHz) registers the shot-to-shot energies of the pulses exiting the ring cavity and triggers the DFT measurement. In the reference arm, the all-normal-dispersion PCF (BF) is 5    cm long, and the pulses from the BF are attenuated with a variable ND filter. A delay τ adjusts the overlap between the pulses traveling in the arms of the MZI. The output of the DFT is monitored with a 12 GHz photodiode PD2 connected to a 6 GHz oscilloscope. The ring cavity consists of a PCF (RPCF) embedded inside an optical feedback loop terminated by two beam splitters with fixed reflectivity (IC 90% and OC 99%). A delay δ t ring adjusts the temporal overlap between the circulating pulse and the pump.

Fig. 3.
Fig. 3.

(a) DFT traces recorded by PD2, corresponding to the spectra of two successive pulses. The time axis is normalized to the laser repetition rate T rep . Yellow, the RPCF signal; blue, the BF signal; green, the interference of the two signals. The inset compares the wavelength-calibrated DFT measurement of the interference (green) with the same signal recorded by the OSA (red); the green curve is a superposition of 10 single-shot measurements. (b) Red, spectrum of RPCF signal measured with the OSA; yellow, averaged spectrum measured with DFT after deconvolution; green, average over 1500 single-shot phase measurements of RPCF in a single-pass configuration with DFT+FTSI before the calibration described in the text; the curve is shifted upward for clarity. Blue, 15 single-shot phase measurements after calibration, corresponding to every tenth pulse from the measurement. A standard deviation of 0.04 π is estimated from 1500 consecutive pulses. The inset in (b) shows the averaged intensity profile of the pulse in the time domain.

Fig. 4.
Fig. 4.

(a) Solid blue, three consecutive pulses from the ring cavity, recorded by PD1. The peak height is proportional to the pulse energy and is found to alternate between two distinct states (V1 and V2). Solid orange, corresponding spectra recorded by PD2 at the output of the DFT (scaled up by a factor of 10); the spectrum alternates in line with the pulse energy. (b) First-return diagram of the pulse energy calculated by integrating the spectra, which plots the energy of pulse n versus that of pulse n + 1 . The yellow region shows the noise level in the steady state, and the orange region shows the period-two state. (c) A DFT-MZI measurement of the two states by interference with the reference pulses.

Fig. 5.
Fig. 5.

(a) Dashed green and blue, power spectra of both states averaged over 750 measurements each after the deconvolution process. Solid green and blue, single-shot phase measurements for both states. The 10 lines for each state correspond to 10 measurements evenly distributed over the total of 750 measured phases per state. The standard deviation is about 0.09 π for the whole set of phases. (b) Simulation of a period-two state for similar conditions as those in the experiment. Two distinct power spectra can be distinguished, and the characteristic phase jump can be observed. The insets in (a) and (b) show the averaged time-domain pulse in the experiment and the simulation, respectively.

Fig. 6.
Fig. 6.

(a) Seven consecutive spectra and spectral phases (gray) from a highly complex state. The pulse spectrum n has the same color as the corresponding entry ( E n , E n + 1 ) in (b). (b) First-return diagram of pulse energy in this state. In the main band, the seven colors repeat at every seventh round-trip, whereas each unique combination of color and marker (squares or x ’s) repeats every fourteenth round-trip. The yellow region (top right) shows for comparison the first-return diagram for the system in a steady state and illustrates the noise level. (c) Spectra and spectral phases for two different states in the complex regime; colors correspond to those in (b). (d) Spectra and spectral phases for two different states that are separated by exactly seven pulses.

Equations (1)

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S MZI ( ω ) = S 0 ( ω ) + S ( ω ) + 2 S 0 ( ω ) S ( ω ) cos [ φ 0 ( ω ) φ ( ω ) ω τ ] .

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