Abstract

Integer and fractional spectral self-imaging effects are induced on infinite-duration periodic frequency combs (probe signal) using cross-phase modulation (XPM) with a parabolic pulse train as pump signal. Free-spectral-range tuning (fractional effects) or wavelength-shifting (integer effects) of the frequency comb can be achieved by changing the parabolic pulse peak power or/and repetition rate without affecting the spectral envelope shape and bandwidth of the original comb. For design purposes, we derive the complete family of different pump signals that allow implementing a desired spectral self-imaging process. Numerical simulation results validate our theoretical analysis. We also investigate the detrimental influence of group-delay walk-off and deviations in the nominal temporal shape or power of the pump pulses on the generated output frequency combs.

© 2013 Optical Society of America

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    [CrossRef]

2013

E. R. Andresen, C. Finot, D. Oron, and H. Rigneault, “Spectral analog of the Gouy phase shift,” Phys. Rev. Lett.110(14), 143902 (2013).
[CrossRef]

A. Malacarne and J. Azaña, “Discretely tunable comb spacing of a frequency comb by multilevel phase modulation of a periodic pulse train,” Opt. Express21(4), 4139–4144 (2013).
[CrossRef] [PubMed]

2011

2010

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: Technology and applications,” Annu. Rev. Anal. Chem.3(1), 175–205 (2010).
[CrossRef] [PubMed]

2009

P. Del'Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009).
[CrossRef]

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, “Optical parabolic pulse generation and applications,” IEEE J. Sel. Top. Quantum Electron.45(11), 1482–1489 (2009).
[CrossRef]

D. Krcmarík, R. Slavík, Y. Park, and J. Azaña, “Nonlinear pulse compression of picosecond parabolic-like pulses synthesized with a long period fiber grating filter,” Opt. Express17(9), 7074–7087 (2009).
[CrossRef] [PubMed]

A. Alatawi, R. P. Gollapalli, and L. Duan, “Radio-frequency clock delivery via free-space frequency comb transmission,” Opt. Lett.34(21), 3346–3348 (2009).
[CrossRef] [PubMed]

2008

T. Hirooka, M. Nakazawa, and K. Okamoto, “Bright and dark 40 GHz parabolic pulse generation using a picosecond optical pulse train and an arrayed waveguide grating,” Opt. Lett.33(10), 1102–1104 (2008).
[CrossRef] [PubMed]

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett.20(13), 1097–1099 (2008).
[CrossRef]

T. Hirooka and M. Nakazawa, “All-optical 40-GHz time-domain Fourier transformation using XPM with a dark parabolic pulse,” IEEE Photon. Technol. Lett.20(22), 1869–1871 (2008).
[CrossRef]

M. Galili, L. K. Oxenløwe, H. C. H. Mulvad, A. T. Clausen, and P. Jeppesen, “Optical wavelength conversion by cross-phase modulation of data signals up to 640 Gb/s,” IEEE J. Sel. Top. Quantum Electron.14(3), 573–579 (2008).
[CrossRef]

2007

2006

2005

J. Azaña, “Spectral Talbot phenomena of frequency combs induced by cross-phase modulation in optical fibers,” Opt. Lett.30(3), 227–229 (2005).
[CrossRef] [PubMed]

Y. Ozeki, Y. Takushima, K. Aiso, and K. Kikuchi, “High repetition-rate similariton generation in normal dispersion erbium-doped fiber amplifiers and its application to multi-wavelength light sources,” IEICE Trans. Electron.88(5), 904–911 (2005).
[CrossRef]

2004

2003

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett.15(4), 581–583 (2003).
[CrossRef]

2002

2001

S. Fukushima, C. F. C. Silva, Y. Muramoto, and A. J. Seeds, “10 to 110 GHz tunable opto-electronic frequency synthesis using optical frequency comb generator and uni-travelling-carrier photodiode,” Electron. Lett.37(12), 780–781 (2001).
[CrossRef]

J. Azaña and M. A. Muriel, “Temporal self-imaging effects: theory and application for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron.7(4), 728–744 (2001).
[CrossRef]

Adler, F.

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: Technology and applications,” Annu. Rev. Anal. Chem.3(1), 175–205 (2010).
[CrossRef] [PubMed]

Aiso, K.

Y. Ozeki, Y. Takushima, K. Aiso, and K. Kikuchi, “High repetition-rate similariton generation in normal dispersion erbium-doped fiber amplifiers and its application to multi-wavelength light sources,” IEICE Trans. Electron.88(5), 904–911 (2005).
[CrossRef]

Alatawi, A.

Amaya, W.

Andresen, E. R.

E. R. Andresen, C. Finot, D. Oron, and H. Rigneault, “Spectral analog of the Gouy phase shift,” Phys. Rev. Lett.110(14), 143902 (2013).
[CrossRef]

Arcizet, O.

P. Del'Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009).
[CrossRef]

Azaña, J.

Beltrán, M.

Berger, N. K.

Bull, J. D.

Cancio, P.

Caraquitena, J.

Chan, S. C.

Chou, J.

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett.15(4), 581–583 (2003).
[CrossRef]

Clausen, A. T.

M. Galili, L. K. Oxenløwe, H. C. H. Mulvad, A. T. Clausen, and P. Jeppesen, “Optical wavelength conversion by cross-phase modulation of data signals up to 640 Gb/s,” IEEE J. Sel. Top. Quantum Electron.14(3), 573–579 (2008).
[CrossRef]

Clausnitzer, T.

Consolino, L.

Cossel, K. C.

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: Technology and applications,” Annu. Rev. Anal. Chem.3(1), 175–205 (2010).
[CrossRef] [PubMed]

De Natale, P.

Del'Haye, P.

P. Del'Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009).
[CrossRef]

Duan, L.

Dudley, J. M.

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, “Optical parabolic pulse generation and applications,” IEEE J. Sel. Top. Quantum Electron.45(11), 1482–1489 (2009).
[CrossRef]

Dupriez, P.

Ellis, A. D.

Erro, M. J.

Fatome, J.

S. Pitois, C. Finot, J. Fatome, B. Sinardet, and G. Millot, “Generation of 20-Ghz picosecond pulse trains in the normal and anomalous dispersion regimes of optical fibers,” Opt. Commun.260(1), 301–306 (2006).
[CrossRef]

Finot, C.

E. R. Andresen, C. Finot, D. Oron, and H. Rigneault, “Spectral analog of the Gouy phase shift,” Phys. Rev. Lett.110(14), 143902 (2013).
[CrossRef]

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, “Optical parabolic pulse generation and applications,” IEEE J. Sel. Top. Quantum Electron.45(11), 1482–1489 (2009).
[CrossRef]

S. Pitois, C. Finot, J. Fatome, B. Sinardet, and G. Millot, “Generation of 20-Ghz picosecond pulse trains in the normal and anomalous dispersion regimes of optical fibers,” Opt. Commun.260(1), 301–306 (2006).
[CrossRef]

P. Dupriez, C. Finot, A. Malinowski, J. K. Sahu, J. Nilsson, D. J. Richardson, K. G. Wilcox, H. D. Foreman, and A. C. Tropper, “High-power, high repetition rate picosecond and femtosecond sources based on Yb-doped fiber amplification of VECSELs,” Opt. Express14(21), 9611–9616 (2006).
[CrossRef] [PubMed]

F. Parmigiani, C. Finot, K. Mukasa, M. Ibsen, M. A. F. Roelens, P. Petropoulos, and D. J. Richardson, “Ultra-flat SPM-broadened spectra in a highly nonlinear fiber using parabolic pulses formed in a fiber Bragg grating,” Opt. Express14(17), 7617–7622 (2006).
[CrossRef] [PubMed]

Fischer, B.

Foreman, H. D.

Fuchs, H. J.

Fukushima, S.

S. Fukushima, C. F. C. Silva, Y. Muramoto, and A. J. Seeds, “10 to 110 GHz tunable opto-electronic frequency synthesis using optical frequency comb generator and uni-travelling-carrier photodiode,” Electron. Lett.37(12), 780–781 (2001).
[CrossRef]

Galili, M.

M. Galili, L. K. Oxenløwe, H. C. H. Mulvad, A. T. Clausen, and P. Jeppesen, “Optical wavelength conversion by cross-phase modulation of data signals up to 640 Gb/s,” IEEE J. Sel. Top. Quantum Electron.14(3), 573–579 (2008).
[CrossRef]

Garcia Gunning, F. C.

Garde, M. J.

Giusfredi, G.

Gollapalli, R. P.

Gorodetsky, M. L.

P. Del'Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009).
[CrossRef]

Gupta, S.

Han, Y.

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett.15(4), 581–583 (2003).
[CrossRef]

Hänsch, T. W.

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature416(6877), 233–237 (2002).
[CrossRef] [PubMed]

Healy, T.

Hirooka, T.

Holzwarth, R.

P. Del'Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009).
[CrossRef]

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature416(6877), 233–237 (2002).
[CrossRef] [PubMed]

Ibsen, M.

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett.20(13), 1097–1099 (2008).
[CrossRef]

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Pulse retiming based on XPM using parabolic pulses formed in a fiber bragg grating,” IEEE Photon. Technol. Lett.18(7), 829–831 (2006).
[CrossRef]

F. Parmigiani, C. Finot, K. Mukasa, M. Ibsen, M. A. F. Roelens, P. Petropoulos, and D. J. Richardson, “Ultra-flat SPM-broadened spectra in a highly nonlinear fiber using parabolic pulses formed in a fiber Bragg grating,” Opt. Express14(17), 7617–7622 (2006).
[CrossRef] [PubMed]

Inguscio, M.

Jalali, B.

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett.15(4), 581–583 (2003).
[CrossRef]

Jeppesen, P.

M. Galili, L. K. Oxenløwe, H. C. H. Mulvad, A. T. Clausen, and P. Jeppesen, “Optical wavelength conversion by cross-phase modulation of data signals up to 640 Gb/s,” IEEE J. Sel. Top. Quantum Electron.14(3), 573–579 (2008).
[CrossRef]

Kibler, B.

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, “Optical parabolic pulse generation and applications,” IEEE J. Sel. Top. Quantum Electron.45(11), 1482–1489 (2009).
[CrossRef]

Kikuchi, K.

Y. Ozeki, Y. Takushima, K. Aiso, and K. Kikuchi, “High repetition-rate similariton generation in normal dispersion erbium-doped fiber amplifiers and its application to multi-wavelength light sources,” IEICE Trans. Electron.88(5), 904–911 (2005).
[CrossRef]

Kippenberg, T. J.

P. Del'Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009).
[CrossRef]

Kley, E. B.

Krcmarík, D.

Levit, B.

Limpert, J. P.

Liu, J. M.

Llorente, R.

Malacarne, A.

Malinowski, A.

Martí, J.

Millot, G.

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, “Optical parabolic pulse generation and applications,” IEEE J. Sel. Top. Quantum Electron.45(11), 1482–1489 (2009).
[CrossRef]

S. Pitois, C. Finot, J. Fatome, B. Sinardet, and G. Millot, “Generation of 20-Ghz picosecond pulse trains in the normal and anomalous dispersion regimes of optical fibers,” Opt. Commun.260(1), 301–306 (2006).
[CrossRef]

Mukasa, K.

Mulvad, H. C. H.

M. Galili, L. K. Oxenløwe, H. C. H. Mulvad, A. T. Clausen, and P. Jeppesen, “Optical wavelength conversion by cross-phase modulation of data signals up to 640 Gb/s,” IEEE J. Sel. Top. Quantum Electron.14(3), 573–579 (2008).
[CrossRef]

Muramoto, Y.

S. Fukushima, C. F. C. Silva, Y. Muramoto, and A. J. Seeds, “10 to 110 GHz tunable opto-electronic frequency synthesis using optical frequency comb generator and uni-travelling-carrier photodiode,” Electron. Lett.37(12), 780–781 (2001).
[CrossRef]

Muriel, M. A.

Nakazawa, M.

Ng, T. T.

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett.20(13), 1097–1099 (2008).
[CrossRef]

Nilsson, J.

Okamoto, K.

Oron, D.

E. R. Andresen, C. Finot, D. Oron, and H. Rigneault, “Spectral analog of the Gouy phase shift,” Phys. Rev. Lett.110(14), 143902 (2013).
[CrossRef]

Oxenløwe, L. K.

M. Galili, L. K. Oxenløwe, H. C. H. Mulvad, A. T. Clausen, and P. Jeppesen, “Optical wavelength conversion by cross-phase modulation of data signals up to 640 Gb/s,” IEEE J. Sel. Top. Quantum Electron.14(3), 573–579 (2008).
[CrossRef]

Ozeki, Y.

Y. Ozeki, Y. Takushima, K. Aiso, and K. Kikuchi, “High repetition-rate similariton generation in normal dispersion erbium-doped fiber amplifiers and its application to multi-wavelength light sources,” IEICE Trans. Electron.88(5), 904–911 (2005).
[CrossRef]

Park, Y.

Parmigiani, F.

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett.20(13), 1097–1099 (2008).
[CrossRef]

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Pulse retiming based on XPM using parabolic pulses formed in a fiber bragg grating,” IEEE Photon. Technol. Lett.18(7), 829–831 (2006).
[CrossRef]

F. Parmigiani, C. Finot, K. Mukasa, M. Ibsen, M. A. F. Roelens, P. Petropoulos, and D. J. Richardson, “Ultra-flat SPM-broadened spectra in a highly nonlinear fiber using parabolic pulses formed in a fiber Bragg grating,” Opt. Express14(17), 7617–7622 (2006).
[CrossRef] [PubMed]

Petropoulos, P.

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett.20(13), 1097–1099 (2008).
[CrossRef]

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Pulse retiming based on XPM using parabolic pulses formed in a fiber bragg grating,” IEEE Photon. Technol. Lett.18(7), 829–831 (2006).
[CrossRef]

F. Parmigiani, C. Finot, K. Mukasa, M. Ibsen, M. A. F. Roelens, P. Petropoulos, and D. J. Richardson, “Ultra-flat SPM-broadened spectra in a highly nonlinear fiber using parabolic pulses formed in a fiber Bragg grating,” Opt. Express14(17), 7617–7622 (2006).
[CrossRef] [PubMed]

Pitois, S.

S. Pitois, C. Finot, J. Fatome, B. Sinardet, and G. Millot, “Generation of 20-Ghz picosecond pulse trains in the normal and anomalous dispersion regimes of optical fibers,” Opt. Commun.260(1), 301–306 (2006).
[CrossRef]

Richardson, D. J.

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, “Optical parabolic pulse generation and applications,” IEEE J. Sel. Top. Quantum Electron.45(11), 1482–1489 (2009).
[CrossRef]

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett.20(13), 1097–1099 (2008).
[CrossRef]

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Pulse retiming based on XPM using parabolic pulses formed in a fiber bragg grating,” IEEE Photon. Technol. Lett.18(7), 829–831 (2006).
[CrossRef]

F. Parmigiani, C. Finot, K. Mukasa, M. Ibsen, M. A. F. Roelens, P. Petropoulos, and D. J. Richardson, “Ultra-flat SPM-broadened spectra in a highly nonlinear fiber using parabolic pulses formed in a fiber Bragg grating,” Opt. Express14(17), 7617–7622 (2006).
[CrossRef] [PubMed]

P. Dupriez, C. Finot, A. Malinowski, J. K. Sahu, J. Nilsson, D. J. Richardson, K. G. Wilcox, H. D. Foreman, and A. C. Tropper, “High-power, high repetition rate picosecond and femtosecond sources based on Yb-doped fiber amplification of VECSELs,” Opt. Express14(21), 9611–9616 (2006).
[CrossRef] [PubMed]

Rigneault, H.

E. R. Andresen, C. Finot, D. Oron, and H. Rigneault, “Spectral analog of the Gouy phase shift,” Phys. Rev. Lett.110(14), 143902 (2013).
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Roelens, M. A. F.

Sahu, J. K.

Sales, S.

Schreiber, T.

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S. Fukushima, C. F. C. Silva, Y. Muramoto, and A. J. Seeds, “10 to 110 GHz tunable opto-electronic frequency synthesis using optical frequency comb generator and uni-travelling-carrier photodiode,” Electron. Lett.37(12), 780–781 (2001).
[CrossRef]

Silva, C. F. C.

S. Fukushima, C. F. C. Silva, Y. Muramoto, and A. J. Seeds, “10 to 110 GHz tunable opto-electronic frequency synthesis using optical frequency comb generator and uni-travelling-carrier photodiode,” Electron. Lett.37(12), 780–781 (2001).
[CrossRef]

Sinardet, B.

S. Pitois, C. Finot, J. Fatome, B. Sinardet, and G. Millot, “Generation of 20-Ghz picosecond pulse trains in the normal and anomalous dispersion regimes of optical fibers,” Opt. Commun.260(1), 301–306 (2006).
[CrossRef]

Slavík, R.

Tainta, S.

Takushima, Y.

Y. Ozeki, Y. Takushima, K. Aiso, and K. Kikuchi, “High repetition-rate similariton generation in normal dispersion erbium-doped fiber amplifiers and its application to multi-wavelength light sources,” IEICE Trans. Electron.88(5), 904–911 (2005).
[CrossRef]

Thorpe, M. J.

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: Technology and applications,” Annu. Rev. Anal. Chem.3(1), 175–205 (2010).
[CrossRef] [PubMed]

Tropper, A. C.

Tünnermann, A.

Udem, Th.

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature416(6877), 233–237 (2002).
[CrossRef] [PubMed]

Wilcox, K. G.

Xia, G. Q.

Ye, J.

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: Technology and applications,” Annu. Rev. Anal. Chem.3(1), 175–205 (2010).
[CrossRef] [PubMed]

Zellmer, H.

Zhang, Z.

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett.20(13), 1097–1099 (2008).
[CrossRef]

Zöllner, K.

Annu. Rev. Anal. Chem.

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: Technology and applications,” Annu. Rev. Anal. Chem.3(1), 175–205 (2010).
[CrossRef] [PubMed]

Appl. Opt.

Electron. Lett.

S. Fukushima, C. F. C. Silva, Y. Muramoto, and A. J. Seeds, “10 to 110 GHz tunable opto-electronic frequency synthesis using optical frequency comb generator and uni-travelling-carrier photodiode,” Electron. Lett.37(12), 780–781 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, “Optical parabolic pulse generation and applications,” IEEE J. Sel. Top. Quantum Electron.45(11), 1482–1489 (2009).
[CrossRef]

J. Azaña and M. A. Muriel, “Temporal self-imaging effects: theory and application for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron.7(4), 728–744 (2001).
[CrossRef]

M. Galili, L. K. Oxenløwe, H. C. H. Mulvad, A. T. Clausen, and P. Jeppesen, “Optical wavelength conversion by cross-phase modulation of data signals up to 640 Gb/s,” IEEE J. Sel. Top. Quantum Electron.14(3), 573–579 (2008).
[CrossRef]

IEEE Photon. Technol. Lett.

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett.20(13), 1097–1099 (2008).
[CrossRef]

T. Hirooka and M. Nakazawa, “All-optical 40-GHz time-domain Fourier transformation using XPM with a dark parabolic pulse,” IEEE Photon. Technol. Lett.20(22), 1869–1871 (2008).
[CrossRef]

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Pulse retiming based on XPM using parabolic pulses formed in a fiber bragg grating,” IEEE Photon. Technol. Lett.18(7), 829–831 (2006).
[CrossRef]

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett.15(4), 581–583 (2003).
[CrossRef]

IEICE Trans. Electron.

Y. Ozeki, Y. Takushima, K. Aiso, and K. Kikuchi, “High repetition-rate similariton generation in normal dispersion erbium-doped fiber amplifiers and its application to multi-wavelength light sources,” IEICE Trans. Electron.88(5), 904–911 (2005).
[CrossRef]

J. Lightwave Technol.

Nat. Photonics

P. Del'Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3(9), 529–533 (2009).
[CrossRef]

Nature

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature416(6877), 233–237 (2002).
[CrossRef] [PubMed]

Opt. Commun.

S. Pitois, C. Finot, J. Fatome, B. Sinardet, and G. Millot, “Generation of 20-Ghz picosecond pulse trains in the normal and anomalous dispersion regimes of optical fibers,” Opt. Commun.260(1), 301–306 (2006).
[CrossRef]

Opt. Express

J. P. Limpert, T. Schreiber, T. Clausnitzer, K. Zöllner, H. J. Fuchs, E. B. Kley, H. Zellmer, and A. Tünnermann, “High-power femtosecond Yb-doped fiber amplifier,” Opt. Express10(14), 628–638 (2002).
[CrossRef] [PubMed]

J. Azaña and S. Gupta, “Complete family of periodic Talbot filters for pulse repetition rate multiplication,” Opt. Express14(10), 4270–4279 (2006).
[CrossRef] [PubMed]

F. Parmigiani, C. Finot, K. Mukasa, M. Ibsen, M. A. F. Roelens, P. Petropoulos, and D. J. Richardson, “Ultra-flat SPM-broadened spectra in a highly nonlinear fiber using parabolic pulses formed in a fiber Bragg grating,” Opt. Express14(17), 7617–7622 (2006).
[CrossRef] [PubMed]

P. Dupriez, C. Finot, A. Malinowski, J. K. Sahu, J. Nilsson, D. J. Richardson, K. G. Wilcox, H. D. Foreman, and A. C. Tropper, “High-power, high repetition rate picosecond and femtosecond sources based on Yb-doped fiber amplification of VECSELs,” Opt. Express14(21), 9611–9616 (2006).
[CrossRef] [PubMed]

T. Healy, F. C. Garcia Gunning, A. D. Ellis, and J. D. Bull, “Multi-wavelength source using low drive-voltage amplitude modulators for optical communications,” Opt. Express15(6), 2981–2986 (2007).
[CrossRef] [PubMed]

D. Krcmarík, R. Slavík, Y. Park, and J. Azaña, “Nonlinear pulse compression of picosecond parabolic-like pulses synthesized with a long period fiber grating filter,” Opt. Express17(9), 7074–7087 (2009).
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L. Consolino, G. Giusfredi, P. De Natale, M. Inguscio, and P. Cancio, “Optical frequency comb assisted laser system for multiplex precision spectroscopy,” Opt. Express19(4), 3155–3162 (2011).
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A. Malacarne and J. Azaña, “Discretely tunable comb spacing of a frequency comb by multilevel phase modulation of a periodic pulse train,” Opt. Express21(4), 4139–4144 (2013).
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Opt. Lett.

Phys. Rev. Lett.

E. R. Andresen, C. Finot, D. Oron, and H. Rigneault, “Spectral analog of the Gouy phase shift,” Phys. Rev. Lett.110(14), 143902 (2013).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

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Figures (8)

Fig. 1
Fig. 1

Illustration of (a) the temporal self-imaging effect using quadratic phase filtering in frequency (1st-order dispersion) and (b) the spectral self-imaging using quadratic phase modulation in time domain (time-lens). F stands for Fourier transform.

Fig. 2
Fig. 2

Schematic of the principle of SSI through XPM by a periodic parabolic pulse train as a time-lens. HNLF, Highly Nonlinear Fiber; BPF, Band-Pass Filter. ‘t’ stands for time variable, ‘f’ stands for optical frequency variable.

Fig. 3
Fig. 3

Dispersion and group delay characteristics of HNLF.

Fig. 4
Fig. 4

Results from numerical simulations, illustrating fractional SSI on infinite-duration periodic pulse trains, where the FSR division factor is tuned by modifying the repetition period and peak power of the parabolic pump pulse train: (a)-(b) temporal traces of input probe and pump signals and periodic frequency comb (probe) spectra before and after XPM for m = 2 and m = 3, when p = 1. GE: Gaussian envelope of the input periodic frequency comb.

Fig. 5
Fig. 5

Results from numerical simulations, illustrating integer and fractional SSI on infinite-duration periodic pulse trains, where the FSR division factor is tuned by modifying only the peak power of the bright/ dark parabolic pump pulse trains; (a) and (f): Temporal traces of input probe and bright/dark pump signals, respectively; periodic frequency comb (probe) spectra (b, g) before and after XPM with (c-e) bright and (h-j) dark parabolic pump pulse trains for m = 1, m = 2 and m = 4, respectively, with fixed T p u = 4 T and different pump peak powers (values given in the text). The dotted green curves in plots (b)-(e) and plots (g)-(j) represent the spectral Gaussian envelope of the input periodic frequency comb.

Fig. 6
Fig. 6

(a) Spectral distribution of the probe signal’s spectrum as a function of the pump peak power (SSI carpet), and (b) defined criterion to determine the acceptable power deviation from the SSI condition.

Fig. 7
Fig. 7

Results from numerical simulations, illustrating SSI through XPM by a sinusoidally modulated pump signal. GE: Gaussian envelope of the input periodic frequency comb.

Fig. 8
Fig. 8

Influence of group-delay walk-off effect on observation of SSI phenomena with walk-off parameter δ = 5   p s / k m . The dotted green curves in the bottom plots (output spectra) represent the spectral Gaussian envelope of the input periodic frequency comb.

Equations (2)

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φ( t )= ϕ 2 t 2 =± s m π T 2 t 2
φ max = s m π ( T pu 2T ) 2

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