Abstract

We present a theoretical and experimental study of passively mode-locked optoelectronic oscillators that generate a single-cycle pulse train with an autonomous envelope-carrier phase locking. The theoretical study is performed by developing a numerical simulation. A good agreement is achieved between the theoretical and the experimental results. We theoretically study the effect of the periodic frequency dependence of the dispersion coefficient on the generation of a single-cycle pulse train with an autonomous envelope-carrier phase locking. The timing jitter is experimentally measured by performing a spectral analysis of the pulse train. The spectral analysis suggests a timing jitter of about 5 ps by using an integration bandwidth of 100 Hz to 1 MHz. The measured jitter is compared to the result of the numerical simulation and to an analytical expression.

© 2012 Optical Society of America

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  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]
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    [CrossRef]
  3. G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4, 33–36 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. T. R. Clark, T. F. Carruthers, P. J. Matthews, and I. N. Duling, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
    [CrossRef]
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2011 (1)

2010 (1)

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4, 33–36 (2010).
[CrossRef]

2009 (1)

2008 (1)

2005 (1)

M. Y. Shverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, “Generation of a single-cycle optical pulse,” Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef]

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]

X. S. Yao, L. Davis, and L. Maleki, “Coupled optoelectronic oscillators for generating both RF signal and optical pulses,” J. Lightwave Technol. 18, 73–78 (2000).
[CrossRef]

1999 (3)

1996 (2)

1993 (1)

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983–996 (1993).
[CrossRef]

1991 (1)

1986 (1)

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201–217 (1986).
[CrossRef]

1972 (1)

E. P. Ippen, C. V. Shank, and S. Dienes, “Passive mode locking of the cw dye laser,” Appl. Phys. Lett. 21, 348–350 (1972).
[CrossRef]

Angelow, G.

Binhammer, T.

Carruthers, T. F.

T. R. Clark, T. F. Carruthers, P. J. Matthews, and I. N. Duling, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[CrossRef]

Chen, Y.

Cho, S. H.

Clark, T. R.

T. R. Clark, T. F. Carruthers, P. J. Matthews, and I. N. Duling, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[CrossRef]

Cundiff, S. T.

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]

Davis, L.

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]

Dienes, S.

E. P. Ippen, C. V. Shank, and S. Dienes, “Passive mode locking of the cw dye laser,” Appl. Phys. Lett. 21, 348–350 (1972).
[CrossRef]

Duling, I. N.

T. R. Clark, T. F. Carruthers, P. J. Matthews, and I. N. Duling, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[CrossRef]

Eggert, S.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4, 33–36 (2010).
[CrossRef]

Fujimoto, J. G.

Gallmann, L.

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]

Hanke, T.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4, 33–36 (2010).
[CrossRef]

Harris, S. E.

M. Y. Shverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, “Generation of a single-cycle optical pulse,” Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef]

Harth, A.

Haus, H. A.

Horowitz, M.

Huber, R.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4, 33–36 (2010).
[CrossRef]

Ippen, E. P.

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]

Kärtner, F. X.

Keller, U.

Krauss, G.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4, 33–36 (2010).
[CrossRef]

Krtner, F. X.

Leitenstorfer, A.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4, 33–36 (2010).
[CrossRef]

Levy, E. C.

Lohss, S.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4, 33–36 (2010).
[CrossRef]

Maleki, L.

Matthews, P. J.

T. R. Clark, T. F. Carruthers, P. J. Matthews, and I. N. Duling, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[CrossRef]

Matuschek, N.

Mecozzi, A.

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983–996 (1993).
[CrossRef]

Menyuk, C. R.

Morgner, U.

Morier-Genoud, F.

Namiki, S.

Ranka, J. K.

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]

Rausch, S.

Scheuer, V.

Sell, A.

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4, 33–36 (2010).
[CrossRef]

Shank, C. V.

E. P. Ippen, C. V. Shank, and S. Dienes, “Passive mode locking of the cw dye laser,” Appl. Phys. Lett. 21, 348–350 (1972).
[CrossRef]

Shverdin, M. Y.

M. Y. Shverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, “Generation of a single-cycle optical pulse,” Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef]

Steinmeyer, G.

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]

Sutter, D. H.

Tschudi, T.

von der Linde, D.

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201–217 (1986).
[CrossRef]

Walker, D. R.

M. Y. Shverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, “Generation of a single-cycle optical pulse,” Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef]

Windeler, R. S.

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]

Yao, X. S.

Yavuz, D. D.

M. Y. Shverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, “Generation of a single-cycle optical pulse,” Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef]

Yin, G. Y.

M. Y. Shverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, “Generation of a single-cycle optical pulse,” Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef]

Yu, X.

Appl. Phys. B (1)

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201–217 (1986).
[CrossRef]

Appl. Phys. Lett. (1)

E. P. Ippen, C. V. Shank, and S. Dienes, “Passive mode locking of the cw dye laser,” Appl. Phys. Lett. 21, 348–350 (1972).
[CrossRef]

Electron. Lett. (1)

T. R. Clark, T. F. Carruthers, P. J. Matthews, and I. N. Duling, “Phase noise measurements of ultrastable 10 GHz harmonically modelocked fibre laser,” Electron. Lett. 35, 720–721 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983–996 (1993).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (4)

Nat. Photonics (1)

G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, and A. Leitenstorfer, “Synthesis of a single cycle of light with compact erbium-doped fibre technology,” Nat. Photonics 4, 33–36 (2010).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

M. Y. Shverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, “Generation of a single-cycle optical pulse,” Phys. Rev. Lett. 94, 033904 (2005).
[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]

Other (1)

Infiniium DCA-J Agilent 86100C technical specification, http://cp.literature.agilent.com/litweb/pdf/5989-0278EN.pdf .

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Figures (7)

Fig. 1.
Fig. 1.

Schematic description of the experimental setup. Optical paths are represented by thick green curves and electrical paths are represented by thin black curves. Light from a continuous-wave (CW) laser is fed into a Mach–Zehnder modulator (MZM), which is used to convert an RF signal into a modulation of light intensity. The modulated light is coupled through an optical coupler to tap out 10% of the optical signal for measurements. The remaining 90% of the optical signal is sent through a long fiber, with a length of approximately 200 m, and is then detected by using a PD. The output electrical signal of the PD is amplified by a nonsaturated RF amplifier, G0, which is connected to a saturable amplifier, G, with a maximal gain of Gmax=14dB. The amplified signal is fed back into the RF port of the MZM through an RF coupler. The coupler that is connected to a splitter is used to tap out 18.7dB of the RF signal in order to measure it by both a real-time oscilloscope and an RF spectrum analyzer.

Fig. 2.
Fig. 2.

Measured frequency dependence of the power gain and the dispersion coefficient of the saturable amplifier. The measured power gain G(f) (red solid curve) is normalized to the maximal power gain, Gmax=14dB, and the dispersion coefficient is calculated from the measured phase response according to Eq. (2) (blue dashed-dotted-curve). The measured dispersion curve shows an oscillatory structure with a period and an amplitude of about 60 MHz and 0.2ns/MHz/km, respectively. The squared norm of the theoretical Lorenzian-bandpass filter spectral response that is described in Section 3, |F(f)|2, is also shown for comparison (black-dashed curve).

Fig. 3.
Fig. 3.

Measured gain dependence of the RF saturable amplifier as a function of the average RF input power, Pin (red circles), that is compared to the gain dependence function that was used in our numerical simulation, described in Section 2.A (black-dashed curve).

Fig. 4.
Fig. 4.

Phase-noise spectrum of our system after eliminating the saturation of the RF amplifier in order to generate a CW signal (blue solid curve). The generated signal has a frequency of 625 MHz and an oscillation power of POSC=12dBm. The theoretical phase noise calculated by using Eq. (5) is also given for comparison, using τ=1μs and δ=2·10131/Hz (gray-dashed curve).

Fig. 5.
Fig. 5.

Comparison between the measured single-cycle pulse waveform (red solid curve) and the waveform that was calculated by using the numerical simulation (black-dashed curve).

Fig. 6.
Fig. 6.

Theoretical dependence of the maximal amplitude, AD, of the oscillatory dispersion coefficient defined in Eq. (8), which gives a single-cycle pulse generation on the period of the dispersion oscillation (green circles). The theoretical results are obtained when all of the simulation parameters are the same as in Fig. 5, except for the dispersion coefficient. The dependence was fitted to be AD=2παconst/(LfD2), where αconst=0.12±0.01 (black-dashed curve).

Fig. 7.
Fig. 7.

Phase noise of the generated electrical pulse train measured around a carrier frequency of 625 MHz, which corresponds to n=593 harmonic order.

Equations (15)

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Pmod(t)=(αP0/2)(1ηsin{π[vin(t)/vπ,AC+vB/vπ,DC]}),
D=12πLd2φdf2,
G(t)=Gmax1+Pavg(t)/PS,
Pavgn=λavgPinnτ+(1λavg)Pavgn1,
Sϕ(f)=δ(2πfτ)2,
|F(f)|=|Θ(f)+Θ(f)|·|L(f)+L*(f)|,
L(f)=iΓ/2f0f+iΓ/2
Θ(f)=tanh[(ffmin)/frise,1]tanh[(ffmax)/frise,2]
φ(f)=2πfτD,fil+2πLAD(2π/fD)2cos[2π(ffc)/fD],
D=ADcos[2π(ffc)/fD].
AD<2παconstLfD2,
ξn=2fminfmaxLn(f)df,
ξn=A2+(2πn)2J2.
στ=2E0(GtotρNR/2)τ/2τ/2t2f2(t)dt,
E0=f2(t)dt.

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