Abstract

Fiber-stretcher based phase-lock loop (PLL) is a mature technique in fiber mode-locked lasers for repetition-rate stabilization. However, undesired side effects may be induced if not properly handled, which is easily overlooked owing to the lack of single-shot spectral analyzers. Thanks to the ultrafast spectral analyzing capability of optical time-stretch, an intriguing spectral dynamics is observed in a repetition-rate-stabilized nonlinear polarization rotation (NPR) mode-locked laser. Under the dynamic state, the optical spectra of pulses undergo dramatic evolution in every round trip while the pulse energy is relatively constant. Indicated by estimated cross-spectral densities, such spectral dynamics results in noticeable degradation in optical spectral coherence. The physical origin of the round-trip evolved spectral dynamics is attributed to the local birefringence induced by the fiber stretcher. Therefore, the results are helpful for a proper use of fiber-stretcher based PLL in fiber lasers, particularly when a good spectral coherence is desired. Furthermore, our study has also provided a potentially useful optical source for applications where fast spectral modulation is desired.

© 2017 Optical Society of America

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References

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2017 (1)

2016 (3)

2015 (1)

2014 (1)

C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fiber laser source,” Nat. Photonics 8(2), 153–159 (2014).
[Crossref] [PubMed]

2013 (4)

C. Xu and F. W. Wise, “Recent advances in fiber lasers for nonlinear microscopy,” Nat. Photonics 7(11), 875–882 (2013).
[Crossref] [PubMed]

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
[Crossref] [PubMed]

B. T. Bosworth and M. A. Foster, “High-speed ultrawideband photonically enabled compressed sensing of sparse radio frequency signals,” Opt. Lett. 38(22), 4892–4895 (2013).
[Crossref] [PubMed]

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

2012 (4)

X. Wei, S. Xu, H. Huang, M. Peng, and Z. Yang, “Compact all-fiber ring femtosecond laser with high fundamental repetition rate,” Opt. Express 20(22), 24607–24613 (2012).
[Crossref] [PubMed]

S. V. Sergeyev, C. Mou, A. Rozhin, and S. K. Turitsyn, “Vector solitons with locked and precessing states of polarization,” Opt. Express 20(24), 27434–27440 (2012).
[Crossref] [PubMed]

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012).
[Crossref] [PubMed]

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
[Crossref] [PubMed]

2011 (1)

T. Walbaum, M. Löser, P. Gross, and C. Fallnich, “Mechanisms in passive synchronization of erbium fiber lasers,” Appl. Phys. B 102(4), 743–750 (2011).
[Crossref]

2009 (1)

2008 (2)

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

2005 (1)

2004 (1)

2002 (2)

2000 (1)

1999 (1)

F. Coppinger, A. S. Bhushan, and B. Jalali, “Photonic time stretch and its application to analog-to-digital conversion,” IEEE Trans. Microw. Theory Tech. 47(7), 1309–1314 (1999).
[Crossref]

1997 (1)

1993 (1)

1991 (1)

1990 (1)

M. E. Fermann, M. Hofer, F. Haberl, and S. P. Craig-Ryan, “Femtosecond fibre laser,” Electron. Lett. 26(20), 1737–1738 (1990).
[Crossref]

Akhmediev, N. N.

Allison, T. K.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012).
[Crossref] [PubMed]

Arai, A.

Araujo-Hauck, C.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

Bergman, K.

Bhushan, A. S.

F. Coppinger, A. S. Bhushan, and B. Jalali, “Photonic time stretch and its application to analog-to-digital conversion,” IEEE Trans. Microw. Theory Tech. 47(7), 1309–1314 (1999).
[Crossref]

Bosworth, B. T.

Chin, S.

Cingöz, A.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012).
[Crossref] [PubMed]

Clark, C. G.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
[Crossref] [PubMed]

Collings, B.

Collings, B. C.

Coppinger, F.

F. Coppinger, A. S. Bhushan, and B. Jalali, “Photonic time stretch and its application to analog-to-digital conversion,” IEEE Trans. Microw. Theory Tech. 47(7), 1309–1314 (1999).
[Crossref]

Craig-Ryan, S. P.

M. E. Fermann, M. Hofer, F. Haberl, and S. P. Craig-Ryan, “Femtosecond fibre laser,” Electron. Lett. 26(20), 1737–1738 (1990).
[Crossref]

Cundiff, S.

Cundiff, S. T.

Curto, G. L.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
[Crossref] [PubMed]

D’Odorico, S.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

Diddams, S. A.

Duling, I. N.

Eaton, S.

Fallnich, C.

T. Walbaum, M. Löser, P. Gross, and C. Fallnich, “Mechanisms in passive synchronization of erbium fiber lasers,” Appl. Phys. B 102(4), 743–750 (2011).
[Crossref]

Fermann, M. E.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012).
[Crossref] [PubMed]

M. E. Fermann, M. Hofer, F. Haberl, and S. P. Craig-Ryan, “Femtosecond fibre laser,” Electron. Lett. 26(20), 1737–1738 (1990).
[Crossref]

Fortier, T.

Foster, M. A.

Freudiger, C. W.

C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fiber laser source,” Nat. Photonics 8(2), 153–159 (2014).
[Crossref] [PubMed]

Fu, S.

Gattass, R. R.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

Goda, K.

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

González Hernández, J. I.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
[Crossref] [PubMed]

Gross, P.

T. Walbaum, M. Löser, P. Gross, and C. Fallnich, “Mechanisms in passive synchronization of erbium fiber lasers,” Appl. Phys. B 102(4), 743–750 (2011).
[Crossref]

Haberl, F.

M. E. Fermann, M. Hofer, F. Haberl, and S. P. Craig-Ryan, “Femtosecond fibre laser,” Electron. Lett. 26(20), 1737–1738 (1990).
[Crossref]

Hänsch, T. W.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
[Crossref] [PubMed]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

Hartl, I.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012).
[Crossref] [PubMed]

Haus, H. A.

Herman, P.

Hofer, M.

M. E. Fermann, M. Hofer, F. Haberl, and S. P. Craig-Ryan, “Femtosecond fibre laser,” Electron. Lett. 26(20), 1737–1738 (1990).
[Crossref]

Holtom, G. R.

C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fiber laser source,” Nat. Photonics 8(2), 153–159 (2014).
[Crossref] [PubMed]

Holzwarth, R.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
[Crossref] [PubMed]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

Horton, N. G.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
[Crossref] [PubMed]

Huang, H.

Ippen, E. P.

Jalali, B.

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

F. Coppinger, A. S. Bhushan, and B. Jalali, “Photonic time stretch and its application to analog-to-digital conversion,” IEEE Trans. Microw. Theory Tech. 47(7), 1309–1314 (1999).
[Crossref]

Jones, D.

Jørgensen, C. G.

Kang, J.

Kentischer, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

Kieu, K. Q.

C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fiber laser source,” Nat. Photonics 8(2), 153–159 (2014).
[Crossref] [PubMed]

Knox, W.

Knox, W. H.

Kobat, D.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
[Crossref] [PubMed]

Li, B.

Li, L.

Liu, D.

Liu, M.

Löser, M.

T. Walbaum, M. Löser, P. Gross, and C. Fallnich, “Mechanisms in passive synchronization of erbium fiber lasers,” Appl. Phys. B 102(4), 743–750 (2011).
[Crossref]

Luo, A. P.

Luo, Z. C.

Manescau, A.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
[Crossref] [PubMed]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

Mazur, E.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

Mou, C.

Murphy, M. T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

Nelson, L. E.

Newbury, N. R.

Nicholson, J. W.

Pasquini, L.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
[Crossref] [PubMed]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
[Crossref] [PubMed]

Peng, M.

Peyghambarian, N.

C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fiber laser source,” Nat. Photonics 8(2), 153–159 (2014).
[Crossref] [PubMed]

Probst, R. A.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
[Crossref] [PubMed]

Rauschenberger, J.

Rebolo, R.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
[Crossref] [PubMed]

Ren, Z.

Y. Xu, X. Wei, Z. Ren, K. K. Y. Wong, and K. K. Tsia, “Ultrafast measurements of optical spectral coherence by single-shot time-stretch interferometry,” Sci. Rep. 6(1), 27937 (2016).
[Crossref] [PubMed]

Rozhin, A.

Ruehl, A.

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T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
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Y. Xu, X. Wei, Z. Ren, K. K. Y. Wong, and K. K. Tsia, “Ultrafast measurements of optical spectral coherence by single-shot time-stretch interferometry,” Sci. Rep. 6(1), 27937 (2016).
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Udem, T.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
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T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
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T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
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C. Xu and F. W. Wise, “Recent advances in fiber lasers for nonlinear microscopy,” Nat. Photonics 7(11), 875–882 (2013).
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N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
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Y. Xu, X. Wei, Z. Ren, K. K. Y. Wong, and K. K. Tsia, “Ultrafast measurements of optical spectral coherence by single-shot time-stretch interferometry,” Sci. Rep. 6(1), 27937 (2016).
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N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
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Xu, Y.

Y. Xu, X. Wei, Z. Ren, K. K. Y. Wong, and K. K. Tsia, “Ultrafast measurements of optical spectral coherence by single-shot time-stretch interferometry,” Sci. Rep. 6(1), 27937 (2016).
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Yang, W.

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Ye, J.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012).
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A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012).
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Zhao, L.

Zhao, L. M.

Appl. Phys. B (1)

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C. Xu and F. W. Wise, “Recent advances in fiber lasers for nonlinear microscopy,” Nat. Photonics 7(11), 875–882 (2013).
[Crossref] [PubMed]

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013).
[Crossref] [PubMed]

C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fiber laser source,” Nat. Photonics 8(2), 153–159 (2014).
[Crossref] [PubMed]

Nature (3)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012).
[Crossref] [PubMed]

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012).
[Crossref] [PubMed]

Opt. Express (7)

Opt. Lett. (7)

Sci. Rep. (1)

Y. Xu, X. Wei, Z. Ren, K. K. Y. Wong, and K. K. Tsia, “Ultrafast measurements of optical spectral coherence by single-shot time-stretch interferometry,” Sci. Rep. 6(1), 27937 (2016).
[Crossref] [PubMed]

Science (1)

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008).
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Other (1)

G. P. Agrawal, Fiber-Optic Communiation Systems, 3rd ed. (Wiley, 2002).

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Figures (4)

Fig. 1
Fig. 1

(a) Experimental setup of the repetition-rate stabilized mode-locked laser; inset: photo of home-made fiber stretcher. (b) RF spectrum of the laser output. (c) Zoom-in of the 12th harmonic RF tone without PLL stabilization. (d) Zoom-in of the 12th harmonic RF tone with PLL stabilization. PC, polarization controller; DCF, dispersion-compensating fiber; EDF, erbium-doped fiber; OIM, optical integrated module; PD, photodetector; BPF, band-pass filter; LPF, low pass filter; PID, proportional–integral–derivative controller.

Fig. 2
Fig. 2

Time- and spectral-domain characterization of the mode-locked laser under normal and dynamic states. (a) Time-domain waveform of the laser output. Inset: histogram of the intensity of pulse train over 2000 periods. (b) Time-stretch waveform of pulse trains showing a consistent optical spectrum in each round trip. (c) Comparing the average spectrum obtained by OSA with those captured by time-stretch spectroscopy over four periods indicated by the shadowed area in (b). (d)-(f): The same characterization for the case where the optical spectrum evolved at a period of two round-trips time. (g)-(i): The same characterization for the case where the optical spectrum evolved over multiple round trips.

Fig. 3
Fig. 3

(a) Time-stretch interferometry used to measure the optical spectral coherence. (b)-(d) 500 consecutive single-shot interferograms overlapped together for both normal/stable and spectrally-dynamic cases. The red curves show the averages. (e)-(g) The 2D spectral interferograms generated from 500 single-shot 1D interferograms. (h)-(j) The estimated cross-spectral densities calculated from (e)-(g).

Fig. 4
Fig. 4

Verification of polarization-rotating vector soliton state for spectral bifurcation (left column) and more complex cases (right column). (a), (b) Time domain pulse train after passing through a polarization beam splitter (PBS). (c), (d) RF spectrum. (e), (f) Polarization-resolved spectrum.

Equations (1)

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XX( λ 1 , λ 2 )= X( λ 1 )X( λ 2 ) | X( λ 1 ) || X( λ 2 ) |