Abstract

In this work, we study the timing instability of a scalar twin-pulse soliton molecule generated by a passively mode-locked Er-fiber laser. Subfemtosecond precision relative timing jitter characterization between the two solitons composing the molecule is enabled by the balanced optical cross-correlation (BOC) method. Jitter spectral density reveals a short-term (on the microsecond to millisecond timescale) random fluctuation of the pulse separation even in the robust stationary soliton molecules. The root-mean-square (rms) timing jitter is on the order of femtoseconds depending on the pulse separation and the mode-locking regime. The lowest rms timing jitter is 0.83 fs, which is observed in the dispersion managed mode-locking regime. Moreover, the BOC method has proved to be capable of resolving the soliton interaction dynamics in various vibrating soliton molecules.

© 2018 Optical Society of America

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K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, Phys. Rev. Lett. 118, 243901 (2017).
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W. Hänsel, H. Hoogland, M. Giunta, S. Schmid, T. Steinmetz, and R. Doubek, Appl. Phys. B 123, 41 (2017).
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2012 (1)

P. Grelu and N. Akhmediev, Nat. Photonics 6, 84 (2012).
[Crossref]

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A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 79, 053841 (2009).
[Crossref]

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A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, Phys. Rev. A 78, 043806 (2008).
[Crossref]

2007 (1)

2006 (1)

2005 (2)

D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. Tam, Phys. Rev. E 72, 016616 (2005).
[Crossref]

M. Stratmann, T. Pagel, and F. Mitschke, Phys. Rev. Lett. 95, 143902 (2005).
[Crossref]

2003 (3)

2002 (1)

2001 (1)

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, Phys. Rev. A 64, 033814 (2001).
[Crossref]

2000 (1)

L. S. Ma, R. K. Shelton, H. C. Kapteyn, M. M. Murnane, and J. Ye, Phys. Rev. A 64, 021802 (2000).
[Crossref]

1999 (1)

1998 (2)

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, J. Opt. Soc. Am. B 15, 515 (1998).
[Crossref]

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, IEEE J. Quantum Electron. 34, 1749 (1998).
[Crossref]

1997 (1)

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Phys. Rev. Lett. 79, 4047 (1997).
[Crossref]

1995 (2)

Afanasjev, V. V.

Akhmediev, N.

Akhmediev, N. N.

Andral, U.

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, Phys. Rev. Lett. 118, 243901 (2017).
[Crossref]

Ankiewicz, A.

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, J. Opt. Soc. Am. B 15, 515 (1998).
[Crossref]

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Phys. Rev. Lett. 79, 4047 (1997).
[Crossref]

Béal, J.

Bekker, A.

Belhache, F.

Bergman, K.

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, IEEE J. Quantum Electron. 34, 1749 (1998).
[Crossref]

Chen, J.

Collings, B. C.

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, IEEE J. Quantum Electron. 34, 1749 (1998).
[Crossref]

Cox, J.

Doubek, R.

W. Hänsel, H. Hoogland, M. Giunta, S. Schmid, T. Steinmetz, and R. Doubek, Appl. Phys. B 123, 41 (2017).
[Crossref]

Drummond, P. D.

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, Phys. Rev. A 64, 033814 (2001).
[Crossref]

Egorov, O.

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 79, 053841 (2009).
[Crossref]

Fischer, B.

Fujimoto, J. G.

Gat, O.

Giunta, M.

W. Hänsel, H. Hoogland, M. Giunta, S. Schmid, T. Steinmetz, and R. Doubek, Appl. Phys. B 123, 41 (2017).
[Crossref]

Golovchenko, E. A.

Gopinath, J. T.

Grapinet, M.

Grelu, P.

Gutty, F.

Haboucha, A.

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, Phys. Rev. A 78, 043806 (2008).
[Crossref]

Hänsel, W.

W. Hänsel, H. Hoogland, M. Giunta, S. Schmid, T. Steinmetz, and R. Doubek, Appl. Phys. B 123, 41 (2017).
[Crossref]

Herink, G.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, Science 356, 50 (2017).
[Crossref]

Hoogland, H.

W. Hänsel, H. Hoogland, M. Giunta, S. Schmid, T. Steinmetz, and R. Doubek, Appl. Phys. B 123, 41 (2017).
[Crossref]

Iliew, R.

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 79, 053841 (2009).
[Crossref]

Ippen, E. P.

Jagadish, C.

Jalali, B.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, Science 356, 50 (2017).
[Crossref]

Kaertner, F. X.

Kapteyn, H. C.

L. S. Ma, R. K. Shelton, H. C. Kapteyn, M. M. Murnane, and J. Ye, Phys. Rev. A 64, 021802 (2000).
[Crossref]

Kärtner, F. X.

Kim, J.

Knox, W. H.

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, IEEE J. Quantum Electron. 34, 1749 (1998).
[Crossref]

Kolodziejski, L. A.

Komarov, A.

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, Phys. Rev. A 78, 043806 (2008).
[Crossref]

Krupa, K.

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, Phys. Rev. Lett. 118, 243901 (2017).
[Crossref]

Kurtz, F.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, Science 356, 50 (2017).
[Crossref]

Kutz, J. N.

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, IEEE J. Quantum Electron. 34, 1749 (1998).
[Crossref]

Kuzucu, O.

Leblond, H.

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, Phys. Rev. A 78, 043806 (2008).
[Crossref]

Lederer, F.

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 79, 053841 (2009).
[Crossref]

Lederer, M. J.

Luther-Davies, B.

Ma, L. S.

L. S. Ma, R. K. Shelton, H. C. Kapteyn, M. M. Murnane, and J. Ye, Phys. Rev. A 64, 021802 (2000).
[Crossref]

Malomed, B. A.

B. A. Malomed, Large Scale Structures in Nonlinear Physics, J. D. Fournier and P. L. Sulem, eds. (Springer-Verlag, 1991), pp. 288–294.

Man, W. S.

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, Phys. Rev. A 64, 033814 (2001).
[Crossref]

Menyuk, C. R.

Mitschke, F.

M. Stratmann, T. Pagel, and F. Mitschke, Phys. Rev. Lett. 95, 143902 (2005).
[Crossref]

Murnane, M. M.

L. S. Ma, R. K. Shelton, H. C. Kapteyn, M. M. Murnane, and J. Ye, Phys. Rev. A 64, 021802 (2000).
[Crossref]

Nithyanandan, K.

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, Phys. Rev. Lett. 118, 243901 (2017).
[Crossref]

Pagel, T.

M. Stratmann, T. Pagel, and F. Mitschke, Phys. Rev. Lett. 95, 143902 (2005).
[Crossref]

Petrich, G. S.

Pilipetskii, A. N.

Ropers, C.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, Science 356, 50 (2017).
[Crossref]

Salhi, M.

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, Phys. Rev. A 78, 043806 (2008).
[Crossref]

Sanchez, F.

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, Phys. Rev. A 78, 043806 (2008).
[Crossref]

Schibli, T. R.

Schmid, S.

W. Hänsel, H. Hoogland, M. Giunta, S. Schmid, T. Steinmetz, and R. Doubek, Appl. Phys. B 123, 41 (2017).
[Crossref]

Shelton, R. K.

L. S. Ma, R. K. Shelton, H. C. Kapteyn, M. M. Murnane, and J. Ye, Phys. Rev. A 64, 021802 (2000).
[Crossref]

Smulakovsky, V.

Solli, D. R.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, Science 356, 50 (2017).
[Crossref]

Song, Y. J.

Soto-Crespo, J. M.

Steinmetz, T.

W. Hänsel, H. Hoogland, M. Giunta, S. Schmid, T. Steinmetz, and R. Doubek, Appl. Phys. B 123, 41 (2017).
[Crossref]

Stratmann, M.

M. Stratmann, T. Pagel, and F. Mitschke, Phys. Rev. Lett. 95, 143902 (2005).
[Crossref]

Tam, H. Y.

D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. Tam, Phys. Rev. E 72, 016616 (2005).
[Crossref]

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, Phys. Rev. A 64, 033814 (2001).
[Crossref]

Tan, H. H.

Tandon, S. N.

Tang, D. Y.

D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. Tam, Phys. Rev. E 72, 016616 (2005).
[Crossref]

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, Phys. Rev. A 64, 033814 (2001).
[Crossref]

Tchofo-Dinda, P.

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, Phys. Rev. Lett. 118, 243901 (2017).
[Crossref]

Weill, R.

Ye, J.

L. S. Ma, R. K. Shelton, H. C. Kapteyn, M. M. Murnane, and J. Ye, Phys. Rev. A 64, 021802 (2000).
[Crossref]

Zavyalov, A.

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 79, 053841 (2009).
[Crossref]

Zhao, B.

D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. Tam, Phys. Rev. E 72, 016616 (2005).
[Crossref]

Zhao, L. M.

D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. Tam, Phys. Rev. E 72, 016616 (2005).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Phys. B (1)

W. Hänsel, H. Hoogland, M. Giunta, S. Schmid, T. Steinmetz, and R. Doubek, Appl. Phys. B 123, 41 (2017).
[Crossref]

IEEE J. Quantum Electron. (1)

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, IEEE J. Quantum Electron. 34, 1749 (1998).
[Crossref]

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

Nat. Photonics (1)

P. Grelu and N. Akhmediev, Nat. Photonics 6, 84 (2012).
[Crossref]

Opt. Express (1)

Opt. Lett. (7)

Optica (1)

Phys. Rev. A (4)

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, Phys. Rev. A 78, 043806 (2008).
[Crossref]

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 79, 053841 (2009).
[Crossref]

L. S. Ma, R. K. Shelton, H. C. Kapteyn, M. M. Murnane, and J. Ye, Phys. Rev. A 64, 021802 (2000).
[Crossref]

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, Phys. Rev. A 64, 033814 (2001).
[Crossref]

Phys. Rev. E (1)

D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. Tam, Phys. Rev. E 72, 016616 (2005).
[Crossref]

Phys. Rev. Lett. (3)

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, Phys. Rev. Lett. 118, 243901 (2017).
[Crossref]

M. Stratmann, T. Pagel, and F. Mitschke, Phys. Rev. Lett. 95, 143902 (2005).
[Crossref]

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Phys. Rev. Lett. 79, 4047 (1997).
[Crossref]

Science (1)

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, Science 356, 50 (2017).
[Crossref]

Other (1)

B. A. Malomed, Large Scale Structures in Nonlinear Physics, J. D. Fournier and P. L. Sulem, eds. (Springer-Verlag, 1991), pp. 288–294.

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Figures (6)

Fig. 1.
Fig. 1. Principle for measuring the relative timing jitter between the two bound pulses within a twin-pulse soliton molecule.
Fig. 2.
Fig. 2. Experimental setup. PBS, polarization beamsplitter; Col., collimator; BOC, balanced optical cross-correlator; ILP, in-line PBS; M, mirror; FR, Faraday rotator; WDM, wavelength division multiplexer; PPKTP, periodically poled KTiOPO4; λ/4, quarter wave plate.
Fig. 3.
Fig. 3. (a) Timing jitter PSDs and (b) the corresponding optical spectra of the soliton molecules at various binding separations. The bottom graph in (a) depicts the integrated timing jitter of PSD from 10 Hz to 2 MHz at different binding separations.
Fig. 4.
Fig. 4. (a) Timing jitter PSDs and (b) the corresponding optical spectra of the DM soliton molecules at various binding separations. The bottom graph in (a) shows the integrated timing jitter from 10 Hz to 2 MHz at different separations.
Fig. 5.
Fig. 5. (a) Optical spectra and (b) timing jitter PSDs of the weak vibrating soliton molecules at different binding separations in the soliton regime and the DM soliton regime.
Fig. 6.
Fig. 6. (a) Optical spectrum, (b) BOC output signal voltage oscillation, and (c) timing jitter PSD of a compound vibrating soliton molecule.

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