Abstract

The carrier-envelope phase (CEP) of femtosecond pulses from a mode-locked Ti:sapphire laser is stabilized using a novel method operating in the time domain. This is a direct and relatively simple method for stabilizing the CEP of femtosecond laser pulses, compared to the conventional method based on phase-locked loop. Using this method, we have directly locked the pulse-to-pulse CEP slip to zero with an in-loop phase jitter of 0.05 rad. Out-of-loop measurement has revealed a comparable phase jitter of 0.1 rad, verifying a good performance of this locking technique. The capability of electrical CEP modulation is also demonstrated.

© 2005 Optical Society of America

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Appl. Phys. B

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spilmann, T. W. Hänsch, and F. Krausz, �??Few-cycle optical waveform synthesis,�?? Appl. Phys. B 72, 373-376 (2001).
[CrossRef]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, �??Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,�?? Appl. Phys. B 69, 327-332 (1999).
[CrossRef]

Appl. Phys. Lett.

M. Nisoli, S. De Silvestri, and O. Svelto, �??Generation of high energy 10 fs pulses by a new pulse compression technique,�?? Appl. Phys. Lett. 68, 2793-2795 (1996).
[CrossRef]

J. Kor. Phys. Soc.

Kyung-Han Hong, Tae Jun Yu, Yong Soo Lee, Chang Hee Nam, and Robert S. Windeler, �??Measurement of the shot-to-shot carrier-envelope phase slip of femtosecond laser pulses,�?? J. Kor. Phys. Soc. 42, 101-105 (2003).

Nature

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, �??Absolute-phase phenomena in photoionization with few-cycle laser pulses,�?? Nature (London) 414, 182-184 (2001).
[CrossRef]

A. Baltuška, Th. Udem, M. Uiberacker,M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, �??Attosecond control of electronic processes by intense light fields,�?? Nature (London) 421, 611-615 (2003).
[CrossRef]

Opt. Commun.

D. Strickland and G. Mourou, �??Compression of Amplified Chirped Optical Pulses,�?? Opt. Commun. 56, 219- 221 (1985).
[CrossRef]

J. Reichert, R. Holzwarth, Th. Udem, and T. W. Hänsch, �??Measuring the frequency of light with mode-locked lasers,�?? Opt. Commun. 172, 59-68 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

K. T. Kim, C. M. Kim, M. G. Baik, G. Umesh, and C. H. Nam , �??Single sub-50-attosecond pulse generation from chirp-compensated harmonic radiation using material dispersion,�?? Phys. Rev. A 69, 051805(R) (2004).
[CrossRef]

Phys. Rev. Lett.

Armelle de Bohan, Philippe Antoine, Dejan B. Miloševi�?, and Bernard Piraux, �??Phase-Dependent Harmonic Emission with Ultrashort Laser Pulses,�?? Phys. Rev. Lett. 81, 1837 (1998).
[CrossRef]

G.G. Paulus, F. Lindner, H.Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, �??Measurement of the Phase of Few-Cycle Laser Pulses,�?? Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, �??Observation of Light-Phase-Sensitive Photoemission from a Metal,�?? Phys. Rev. Lett. 92, 073902 (2004).
[CrossRef] [PubMed]

Science

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] [PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the direct locking method for CEP stabilization(for the in-loop and the out-of-loop measurements). (Ti:S: Ti:sapphire crystal, AOM: acousto-optic modulator, PCF: photonic crystal fiber, DB: dichroic beam-splitter, SHG: second-harmonic generation crystal, HWP: half-wave plate, BPF: band-pass filter, PBS: polarizing beamsplitter, APD: avalanche photodiode)

Fig. 2.
Fig. 2.

CEP stabilization using the direct locking method. (a) Pure beat signal extracted from the interference signal. (b) Quenching of the beat signal with the activation of feedback loop at time zero. Histograms of the beat signal before (blue) and after (red) stabilization are also shown on the right side.

Fig. 3.
Fig. 3.

In-loop and out-of-loop measurement: (a) Stabilized beat signals from in-loop (upper) and out-of-loop (lower). (b)Power spectral densities and accumulated phases of the in-loop (black) and the out-of-loop (blue) after locking.

Fig. 4.
Fig. 4.

CEP modulation: (a) DC and (b) Saw tooth signals (red) were added at time t 1 and t 2, respectively, during the locking process. Stabilized CEP signals exactly tracked the added input signals.

Equations (4)

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Δ ϕ = 2 π f ceo f rep ,
I 1 = A I f 2 n + B I 2 f n + C I f 2 n I 2 f n sin ( 2 π f ceo t + ϕ 0 ) ,
I 2 = D I f 2 n + E I 2 f n ,
Δ ϕ RMS = [ 2 1 τ obs S ϕ ( ν ) d ν ] 1 2 ,

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