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Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 13 — Jun. 26, 2006
  • pp: 6359–6365
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Synchronization of Ti:sapphire and Cr:forsterite mode-locked lasers with 100-attosecond precision by optical-phase stabilization

Dai Yoshitomi, Yohei Kobayashi, Masayuki Kakehata, Hideyuki Takada, and Kenji Torizuka  »View Author Affiliations


Optics Express, Vol. 14, Issue 13, pp. 6359-6365 (2006)
http://dx.doi.org/10.1364/OE.14.006359


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Abstract

An optical-phase stabilization technique was utilized to reduce the timing jitter between passively synchronized Ti:sapphire and Cr:forsterite two-color mode-locked lasers. The suppression of cavity-length fluctuation by stabilizing pulse-to-pulse slips of relative carrier-envelope phase allowed timing-jitter reduction by a factor of 1.7, resulting in an rms value of 123 attoseconds (as) in a frequency range from 10 mHz to 1 MHz.

© 2006 Optical Society of America

1. Introduction

Growing interest in ultrafast electronic processes of atoms, molecules, or condensed mattter has been the driving force behind efforts to shorten the duration of ultrashort-pulse lasers. Recent demonstrations of attosecond pulse generation by high-order harmonics have opened a new frontier to the so-called attosecond science [1

1. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001). [CrossRef] [PubMed]

, 2

2. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432, 605–608 (2004). [CrossRef] [PubMed]

]. Fourier synthesis of optically phase-locked multicolor pulses [3

3. T. W. Hänsch, “A proposed sub-femtosecond pulse synthesizer using separate phase-locked laser oscillators,” Opt. Comm. 80, 71–75 (1990). [CrossRef]

6

6. 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] [PubMed]

] is another attractive method for attosecond pulse generation because of its scalability of repetition rate or pulse energy. It would be possible to synthesize arbitrary electric-field waveform including attosecond pulse shape, by superimposing several phase-locked ultrashort pulses with separate spectral components that span far beyond an octave. In recent years, optical phase locking among multicolor pulses has been realized by a femtosecond optical parametric oscillator [7

7. Y. Kobayashi, H. Takada, M. Kakehata, and K. Torizuka, “Phase-coherent multicolor femtosecond pulse generation,” Appl. Phys. Lett. 83, 839–841 (2003). [CrossRef]

, 8

8. Y. Kobayashi, H. Takada, M. Kakehata, and K. Torizuka, “Optical phase locking among femtosecond subharmonic pulses,” Opt. Lett. 28, 1377–1379 (2003). [CrossRef] [PubMed]

] and two-color synchronized mode-locked lasers [9

9. Y. Kobayashi, K. Torizuka, and Z. Wei, “Control of relative carrier-envelope phase slip in femtosecond Ti:sapphire and Cr:forsterite lasers,” Opt. Lett. 28, 746–748 (2003). [CrossRef] [PubMed]

12

12. J. Kim, T. R. Schibli, L. Matos, H. Byunn, and F. X. Kärtner, “Phase-coherent spectrum from ultrabroadband Ti:sapphire and Cr:forsterite lasering covering the visible to the infrared,” in Joint Conference on Ultrafast Optics V and Applications of High Field and Short Wavelength Sources XI (Springer, 2005), paper M3-5.

]. Obviously, stable phase locking and reproducible waveform synthesis require tight synchronization of pulses with a very low timing jitter. Until now, several groups have reported synchronization of two mode-locked lasers with active [13

13. L-S. Ma, R. K. Shelton, H. C. Kapteyn, M. M. Murnane, and J. Ye, “Sub-10-femtosecond active synchronization of two passively mode-locked Ti:sapphire oscillators,” Phys. Rev. A 64, 021802(R) (2001). [CrossRef]

17

17. T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett. 28, 947–949 (2003). [CrossRef] [PubMed]

] and passive [18

18. A. Leitenstorfer, C. Fürst, and A. Laubereau, “Widely tunable two-color mode-locked Ti:sapphire laser with pulse jitter of less than 2 fs,” Opt. Lett. 20, 916–918(1995). [CrossRef] [PubMed]

21

21. J. Tian, Z. Wei, P. Wang, H. Han, J. Zhang, L. Zhao, Z. Wang, J. Zhang, T. Yang, and J. Pan, “Independently tunable 1.3W femtosecond Ti:sapphire lasers passively synchronized with attosecond timing jitter and ultrahigh robustness,” Opt. Lett. 30, 2161–2163 (2005). [CrossRef] [PubMed]

] schemes. In an active scheme, the laser cavity is actively controlled with electronic feedback circuits to minimize the relative timing jitter. Schibli et al. demonstrated active synchronization of Ti:sapphire and Cr:forsterite mode-locked lasers with a timing jitter as low as 300 attoseconds (as) [17

17. T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett. 28, 947–949 (2003). [CrossRef] [PubMed]

].

Fig. 1. Experimental setup. EOM, electro-optic modulator; Pol., polarizer; PZT, piezoelectric transducer; PMT’s, photomultiplier tube; CM’s, chirped mirrors; WP’s, half-wave plates; SHG’s, second harmonic generators; SFG’s, sum-frequency generators; DP, delay plate; APD, avalanche photodiode.

In this paper, we demonstrate a timing-jitter reduction of the passively synchronized two-color mode-locked lasers by locking the relative optical phase slip to an rf reference. Because of reduction by a factor of 1.7, an rms timing jitter of 123 as was achieved in a frequency range from 10 mHz to 1 MHz.

2. Optical-phase stabilization

The passively synchronized Ti:sapphire and Cr:forsterite laser system is described in Ref. 24. Both lasers have a common repetition frequency of 100 MHz. The frequencies of Ti:sapphire (f TiS) and Cr:forsterite (f CrF) mode-locked pulse trains are expressed as f TiS=δ TiS+mf rep and f CrF=δ CrF+m f rep, where f rep is the repetition frequency, δTiS and δCrF are the carrier-envelope offset frequencies of Ti:sapphire and Cr:forsterite lasers, and m and m are integers. Since the second harmonic of Ti:sapphire and the third harmonic of Cr:forsterite are in the same spectral range (~410nm), the two harmonic-frequency combs generate heterodyne beats. The beat frequencies are given by f beat=|2 f TiS-3f CrF|=|δ+n f rep|, where δ=2δ TiS-3δCrF and n is an integer. The cavity-length variation leads to a change in pulse-to-pulse slip of relative carrier-envelope phase and results in a change in beat frequency. Since the changes in repetition frequencies are negligible for a cavity-length change of several microns, the changes in carrierenvelope phase slips of Ti:sapphire (ΔϕTiS) and Cr:forsterite (ΔϕCrF) laser pulses are given by ΔϕTiS=2π·2Δl TiSTiS and ΔϕCrF=2π·2Δl CrF/λ CrF, respectively, where Δl TiS and Δl CrF are the cavity-length changes of Ti:sapphire and Cr:forsterite lasers, and λ TiS and λCrF are their wavelengths. Thus the changes in phase slips cause changes in carrier-envelope offset frequencies of Ti:sapphire (Δδ TiS) and Cr:forsterite (Δδ CrF) lasers given by Δδ TiS=2Δl TiS f rep/λ TiS and Δδ CrF=2Δl CrF f rep/λ CrF. Hence, the beat-frequency shift (Δf beat) caused by a change in the cavity-length difference (Δl) is given by [26

26. Z. Wei, Y. Kobayashi, and K. Torizuka, “Relative carrier-envelope phase dynamics between passively synchronized Ti:sapphire and Cr:forsterite lasers,” Opt. Lett. 27, 2121–2123 (2002). [CrossRef]

],

Δfbeat=4ΔlfrepλTiS=6ΔlfrepλCrF,
(1)

where we used some relations written as Δll TiSl CrF and λ TiS : λ CrF=2 : 3 for derivation of Eq. (1). This equation suggests that the cavity-length fluctuation can be suppressed by the phase locking in a sensitive manner.

Figure 1 depicts the experimental setup. Ti:sapphire and Cr:forsterite laser pulses were split with half mirrors: some beams were then used for phase locking and the others for jitter measurement. Three BBO crystals were used to obtain the second harmonic of the Ti:sapphire laser and the third harmonic of the Cr:forsterite laser by the sum-frequency mixing of the fundamental and its second harmonic. Half-wave plates were positioned to get two harmonics with the same polarizations. The beat frequency was locked to a 40-MHz rf reference signal by active control of the cavity length of the Ti:sapphire laser with a piezoelectric transducer, and by control of the pump power of Ti:sapphire laser with an electro-optic modulator [25

25. Y. Kobayashi, D. Yoshitomi, M. Kakehata, H. Takada, and K. Torizuka, “Long-term optical phase locking between femtosecond Ti:sapphire and Cr:forsterite lasers,” Opt. Lett. 30, 2496–2498 (2005). [CrossRef] [PubMed]

].

3. High-resolution jitter measurement

A cross-correlation trace is utilized in typical jitter measurements, in which the timing jitter can be estimated from the fluctuation of the cross-correlation signal at the slope of half maximum. When the cross-correlation trace is written as I cc=I 0 g cc(τ), where I 0 is the peak intensity, g cc(τ) is the normalized cross-correlation function, and τ is the relative delay between two pulses, the fluctuation of the correlation signal is written as

ΔIcc=I0dgcc(τ)dτΔτ+gcc(τ)ΔI0.
(2)

The first term represents the fluctuation caused by the jitter (Δτ), while the second term represents the amplitude noise (ΔI 0). If the delay is set to g cc(τ)=1/2 and typical parameters in our experiment are assumed (full width of correlation ~70 fs, ampliutude noise ~0.1%), the second term is comparable to the first term in a sub-100-as regime, which limits the resolution of this method.

To overcome this problem, the balanced cross-correlator proposed and demonstrated by Schibli et al [17

17. T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett. 28, 947–949 (2003). [CrossRef] [PubMed]

] was used. The balanced cross-correlator consists of two cross-correlators with different relative delays between two pulses, as illustrated in Fig. 1, and opposite slopes of correlation traces are used to monitor the fluctuation. A 3-mm-thick fused-silica delay plate was inserted on one branch to shift its delay to the opposite slope. The balanced cross-correlation is defined as the difference of two correlations, namely,

Ibcc(τ)=Icc(τ+τ02)Icc(ττ02)
=I0{gcc(τ+τ02)gcc(ττ02)},
(3)

where τ0 is the relative delay given by the delay plate. The fluctuation of the signal is

ΔIbcc(τ)=I0{dgcc(τ)dττ+τ02dgcc(τ)dτττ02}Δτ
+{gcc(τ+τ0/2)gcc(ττ0/2)}ΔI0.
(4)
Fig. 2. Measured timing jitter at bandwidths of (a) 1 kHz, (b) 400 kHz, and (c) 1 MHz. The top and bottom figures are the results with and without phase locking, respectively.

Similarly, the first term represents contribution of the jitter (Δτ), and the second term represents the amplitude noise (ΔI 0). In this case, the amplitude noise can be excluded by choosing a delay to satisfy g cc(τ+τ0/2)=g cc(τ-τ0/2), which is τ=0 for symmetric correlation functions. In other words, since the amplitude noise affects the two correlations in the same way when the condition is satisfied, the effects are cancelled by taking the difference of two correlations. The two correlation signals were detected simultaneously with two photomultiplier tubes and measured with a multichannel digital oscilloscope. The balanced signal was obtained by calculated difference of two traces.

4. Results and discussion

Figure 2 presents the timing-jitter results measured with observation bandwidths of 1 kHz, 400 kHz, and 1 MHz. As seen in Fig. 2(a), there is clear evidence of suppression of the drift and fluctuation by the phase locking at 1-kHz bandwidth. As a result, an rms jitter of 194±30 as was reduced to 87±8 as. Likewise, an rms jitter decreased from 108±9 as to 96±4 as at 400-kHz bandwidth [Fig. 2(b)] and from 101±8 as to 88±2 as at 1-MHz bandwidth [Fig. 2(c)], although there was no significant evidence of jitter suppression at the two fastest bandwidths.

Figure 3 depicts the beat-frequency variation measured at the same time as the 1-kHz jitter measurement shown in Fig. 2(a). There was a drift of about 5 MHz in beat frequency, which is similar to the drift in relative delay displayed in the result without phase locking in Fig. 2(a). The beat-frequency drift can be attributed to the drift in cavity length, because the commercial pump sources were power-stabilized and the active control by the electro-optic modulator was not done in the case without phase locking. To confirm this, the cavity length of the Ti:sapphire laser was modulated by swinging the end mirror with the piezoelectric transducer at a frequency of 500 Hz. Figure 4 illustrates the response of (a) beat frequency and (b) relative delay to the modulation. The slow fluctuation seen in the relative delay is a 50-Hz jitter, which originates from the ac power-supply noise. In Fig. 4(a), the modulation amplitude of beat frequency was 5 MHz, which corresponds to a cavity-length change of 10 nm according to Eq. (1). In Fig. 4(b), the modulation amplitude of relative delay was 600 as. The intracavity-path change corresponds to an optical delay of only 30 as, which is not a primary cause of the delay change, because it is considered to be compensated by the passive-synchronization mechanism on a much shorter time scale.

Fig. 3. Beat frequency variation at a bandwidth of 1 kHz (a) with and (b) without phase locking.
Fig. 4. (a) Beat frequency and (b) relative delay response to the cavity-length modulation.

The observed timing shift originating from the cavity-length change has two possible mechanisms. First, the spectral shift inherent in the passive synchronization mechanism possibly causes a timing shift in combination with the group-delay dispersion on the extracavity optical paths. A shift of 0.3 nm in the Cr:forsterite spectrum was observed, whereas no shift was seen in the Ti:sapphire spectrum. The estimated group-delay change resulting from this spectral shift is 200 as with the estimated extracavity dispersion of 500 fs 2. Second, the relative timing difference of two pulses inside the Ti:sapphire crystal varies depending on the cavity-length mismatch, because it is passively tuned to an optimal value to induce the spectral shift which makes the round-trip group delays of two pulses identical. As well as the cavity-length fluctuation, the fluctuation of the pump power and/or the beam pointing would cause the timing jitter, which was not suppressed in the scheme presented in this paper.

Fig. 5. Power spectral density and integrated rms jitter (a) with and (b) without phase locking. Each color in power spectral density corrsponds to respective time-domain data with different bandwidths.

5. Conclusion

Reduction of the timing jitter between passively synchronized Ti:sapphire and Cr:forsterite mode-locked lasers was achieved by the optical-phase stabilization technique. The cavity-length fluctuation was suppressed by locking the beat frequency to an rf reference. As a result of timing-jitter reduction by a factor of 1.7, an rms jitter of 123 as was achieved in a frequency range from 10 mHz to 1 MHz. It would be possible to generate two-color pulses with a fixed carrier-envelope phase relation for every pulse by locking the beat frequency to dc. Fourier synthesis is now feasible with the phase-locked two-color pulses synchronized with 100-as precision.

References and links

1.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001). [CrossRef] [PubMed]

2.

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432, 605–608 (2004). [CrossRef] [PubMed]

3.

T. W. Hänsch, “A proposed sub-femtosecond pulse synthesizer using separate phase-locked laser oscillators,” Opt. Comm. 80, 71–75 (1990). [CrossRef]

4.

K. Shimoda, “Theory and application of optical subharmonic oscillator,” Jpn. J. Appl. Phys. 34, 3566–3569 (1995). [CrossRef]

5.

R. K. Shelton, L. Ma, H. C. Kapteyn, M. Murnane, J. L. Hall, and J. Ye, “Phase-coherent optical pulse synthesis from separate femtosecond lasers,” Science 293, 1286–1289 (2001). [CrossRef] [PubMed]

6.

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] [PubMed]

7.

Y. Kobayashi, H. Takada, M. Kakehata, and K. Torizuka, “Phase-coherent multicolor femtosecond pulse generation,” Appl. Phys. Lett. 83, 839–841 (2003). [CrossRef]

8.

Y. Kobayashi, H. Takada, M. Kakehata, and K. Torizuka, “Optical phase locking among femtosecond subharmonic pulses,” Opt. Lett. 28, 1377–1379 (2003). [CrossRef] [PubMed]

9.

Y. Kobayashi, K. Torizuka, and Z. Wei, “Control of relative carrier-envelope phase slip in femtosecond Ti:sapphire and Cr:forsterite lasers,” Opt. Lett. 28, 746–748 (2003). [CrossRef] [PubMed]

10.

K. W. Holman, D. J. Jones, J. Ye, and E. Ippen, “Orthogonal control of the frequency comb dynamics of a mode-locked laser diode,” Opt. Lett. 28, 2405–2407 (2003). [CrossRef] [PubMed]

11.

A. Bartels, N. R. Newbury, I. Thomann, L. Hollberg, and S. Diddams, “Broadband phase-coherent optical frequency synthesis with actively linked Ti:sapphire and Cr:forsterite femtosecond lasers,” Opt. Lett. 29, 403–405 (2004). [CrossRef] [PubMed]

12.

J. Kim, T. R. Schibli, L. Matos, H. Byunn, and F. X. Kärtner, “Phase-coherent spectrum from ultrabroadband Ti:sapphire and Cr:forsterite lasering covering the visible to the infrared,” in Joint Conference on Ultrafast Optics V and Applications of High Field and Short Wavelength Sources XI (Springer, 2005), paper M3-5.

13.

L-S. Ma, R. K. Shelton, H. C. Kapteyn, M. M. Murnane, and J. Ye, “Sub-10-femtosecond active synchronization of two passively mode-locked Ti:sapphire oscillators,” Phys. Rev. A 64, 021802(R) (2001). [CrossRef]

14.

R. K. Shelton, S. M. Foreman, L-S. Ma, J. L. Hall, H. C. Kapteyn, M. M. Murnane, M. Notcutt, and J. Ye, “Subfemtosecond timing jitter between two independent, actively synchronized, mode-locked lasers,” Opt. Lett. 27, 312–314 (2002). [CrossRef]

15.

T. Miura, H. Nagaoka, K. Takasago, K. Kobayashi, A. Endo, K. Torizuka, M. Washio, and F. Kannari, “Active synchronization of two mode-locked lasers with optical cross correlation,” Appl. Phys. B 75, 19–23 (2002). [CrossRef]

16.

A. Bartels, S. A. Diddams, T. M. Ramond, and L. Hollberg, “Mode-locked laser pulse trains with subfemtosecond timing jitter synchronized to an optical reference oscillator,” Opt. Lett. 28, 663–665 (2003). [CrossRef] [PubMed]

17.

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett. 28, 947–949 (2003). [CrossRef] [PubMed]

18.

A. Leitenstorfer, C. Fürst, and A. Laubereau, “Widely tunable two-color mode-locked Ti:sapphire laser with pulse jitter of less than 2 fs,” Opt. Lett. 20, 916–918(1995). [CrossRef] [PubMed]

19.

Z. Wei, Y. Kobayashi, Z. Zhang, and K. Torizuka, “Generation of two-color femtosecond pulses by self-synchronizing Ti:sapphire and Cr:forsterite lasers,” Opt. Lett. 26, 1806–1808 (2001). [CrossRef]

20.

M. Rusu, R. Herda, and O. G. Okhotnikov, “Passively synchronized erbium (1550-nm) and ytterbium (1040-nm) mode-locked fiber lasers sharing a cavity,” Opt. Lett. 29, 2246–2248 (2004). [CrossRef] [PubMed]

21.

J. Tian, Z. Wei, P. Wang, H. Han, J. Zhang, L. Zhao, Z. Wang, J. Zhang, T. Yang, and J. Pan, “Independently tunable 1.3W femtosecond Ti:sapphire lasers passively synchronized with attosecond timing jitter and ultrahigh robustness,” Opt. Lett. 30, 2161–2163 (2005). [CrossRef] [PubMed]

22.

C. Fürst, A. Leitenstorfer, and A. Laubereau, “Mechanism for self-synchronization of femtosecond pulses in a two-color Ti:Sapphire laser,” IEEE Sel. Top. Quantum. Electron. 2, 473–479 (1996). [CrossRef]

23.

Z. Wei, Y. Kobayashi, and K. Torizuka, “Passive synchronization between femtosecond Ti:sapphire and Cr:forsterite lasers,” Appl. Phys. B 74, S171–S176 (2002). [CrossRef]

24.

D. Yoshitomi, Y. Kobayashi, H. Takada, M. Kakehata, and K. Torizuka, “100-attosecond timing jitter between two-color mode-locked lasers by active-passive hybrid synchronization,” Opt. Lett. 30, 1408–1410 (2005). [CrossRef] [PubMed]

25.

Y. Kobayashi, D. Yoshitomi, M. Kakehata, H. Takada, and K. Torizuka, “Long-term optical phase locking between femtosecond Ti:sapphire and Cr:forsterite lasers,” Opt. Lett. 30, 2496–2498 (2005). [CrossRef] [PubMed]

26.

Z. Wei, Y. Kobayashi, and K. Torizuka, “Relative carrier-envelope phase dynamics between passively synchronized Ti:sapphire and Cr:forsterite lasers,” Opt. Lett. 27, 2121–2123 (2002). [CrossRef]

OCIS Codes
(320.7090) Ultrafast optics : Ultrafast lasers
(320.7100) Ultrafast optics : Ultrafast measurements

ToC Category:
Ultrafast Optics

History
Original Manuscript: April 25, 2006
Revised Manuscript: June 8, 2006
Manuscript Accepted: June 9, 2006
Published: June 26, 2006

Citation
Dai Yoshitomi, Yohei Kobayashi, Masayuki Kakehata, Hideyuki Takada, and Kenji Torizuka, "Synchronization of Ti:sapphire and Cr:forsterite mode-locked lasers with 100-attosecond precision by optical-phase stabilization," Opt. Express 14, 6359-6365 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-13-6359


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References

  1. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, "Attosecond metrology," Nature 414,509-513 (2001). [CrossRef] [PubMed]
  2. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, "Nonlinear optics in the extreme ultraviolet," Nature 432,605-608 (2004). [CrossRef] [PubMed]
  3. T. W. Hänsch, "A proposed sub-femtosecond pulse synthesizer using separate phase-locked laser oscillators," Opt. Commun. 80,71-75 (1990). [CrossRef]
  4. K. Shimoda, "Theory and application of optical subharmonic oscillator," Jpn. J. Appl. Phys. 34,3566-3569 (1995). [CrossRef]
  5. R. K. Shelton, L. Ma, H. C. Kapteyn, M. Murnane, J. L. Hall, and J. Ye, "Phase-coherent optical pulse synthesis from separate femtosecond lasers," Science 293,1286-1289 (2001). [CrossRef] [PubMed]
  6. 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] [PubMed]
  7. Y. Kobayashi, H. Takada, M. Kakehata, and K. Torizuka, "Phase-coherent multicolor femtosecond pulse generation," Appl. Phys. Lett. 83,839-841 (2003). [CrossRef]
  8. Y. Kobayashi, H. Takada, M. Kakehata, and K. Torizuka, "Optical phase locking among femtosecond subharmonic pulses," Opt. Lett. 28,1377-1379 (2003). [CrossRef] [PubMed]
  9. Y. Kobayashi, K. Torizuka, and Z. Wei, "Control of relative carrier-envelope phase slip in femtosecond Ti:sapphire and Cr:forsterite lasers," Opt. Lett. 28,746-748 (2003). [CrossRef] [PubMed]
  10. K. W. Holman, D. J. Jones, J. Ye, and E. Ippen, "Orthogonal control of the frequency comb dynamics of a mode-locked laser diode," Opt. Lett. 28,2405-2407 (2003). [CrossRef] [PubMed]
  11. A. Bartels, N. R. Newbury, I. Thomann, L. Hollberg, and S. Diddams, "Broadband phase-coherent optical frequency synthesis with actively linked Ti:sapphire and Cr:forsterite femtosecond lasers," Opt. Lett. 29,403-405 (2004). [CrossRef] [PubMed]
  12. J. Kim, T. R. Schibli, L. Matos, H. Byunn, and F. X. K¨artner, "Phase-coherent spectrum from ultrabroadband Ti:sapphire and Cr:forsterite lasering covering the visible to the infrared," in Joint Conference on Ultrafast Optics V and Applications of High Field and Short Wavelength Sources XI (Springer, 2005), paper M3-5.
  13. L-S. Ma, R. K. Shelton, H. C. Kapteyn, M. M. Murnane, and J. Ye, "Sub-10-femtosecond active synchronization of two passively mode-locked Ti:sapphire oscillators," Phys. Rev. A 64, 021802(R) (2001). [CrossRef]
  14. R. K. Shelton, S. M. Foreman, L-S. Ma, J. L. Hall, H. C. Kapteyn, M. M. Murnane, M. Notcutt, and J. Ye, "Subfemtosecond timing jitter between two independent, actively synchronized, mode-locked lasers," Opt. Lett. 27,312-314 (2002). [CrossRef]
  15. T. Miura, H. Nagaoka, K. Takasago, K. Kobayashi, A. Endo, K. Torizuka, M. Washio, and F. Kannari, "Active synchronization of two mode-locked lasers with optical cross correlation," Appl. Phys. B 75,19-23 (2002). [CrossRef]
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