synchronization of ti:sapphire and cr:forsterite mode-locked lasers with 100-attosecond precision by...

Synchronization of Ti:sapphire andCr:forsterite mode-locked lasers with

100-attosecond precision byoptical-phase stabilization

Dai Yoshitomi, Yohei Kobayashi, Masayuki Kakehata, HideyukiTakada, and Kenji Torizuka

National Institute of Advanced Industrial Science and Technology (AIST),1-1-1 Umezono, Tsukuba 305-8568, Japan

[email protected]

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

© 2006 Optical Society of America

OCIS codes: (320.7090) Ultrafast lasers; (320.7100) Ultrafast measurements.

References and links1. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann,

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Ti:sapphire and Cr:forsterite lasers,” Opt. Lett. 28, 746-748 (2003).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).11. A. Bartels, N. R. Newbury, I. Thomann, L. Hollberg, and S. Diddams, “Broadband phase-coherent optical fre-

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12. J. Kim, T. R. Schibli, L. Matos, H. Byunn, and F. X. Kartner, “Phase-coherent spectrum from ultrabroadbandTi:sapphire and Cr:forsterite lasering covering the visible to the infrared,” in Joint Conference on Ultrafast OpticsV 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 synchronizationof two passively mode-locked Ti:sapphire oscillators,” Phys. Rev. A 64, 021802(R) (2001).

#70304 - $15.00 USD Received 25 April 2006; revised 8 June 2006; accepted 9 June 2006

(C) 2006 OSA 26 June 2006 / Vol. 14, No. 13 / OPTICS EXPRESS 6359

mailto:[email protected]

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).

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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).

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21. J. Tian, Z. Wei, P. Wang, H. Han, J. Zhang, L. Zhao, Z. Wang, J. Zhang, T. Yang, and J. Pan, “Independentlytunable 1.3W femtosecond Ti:sapphire lasers passively synchronized with attosecond timing jitter and ultrahighrobustness,” Opt. Lett. 30, 2161-2163 (2005).

22. C. Furst, A. Leitenstorfer, and A. Laubereau, “Mechanism for self-synchronization of femtosecond pulses in atwo-color Ti:Sapphire laser,” IEEE Sel. Top. Quantum. Electron. 2, 473-479 (1996).

23. Z. Wei, Y. Kobayashi, and K. Torizuka, “Passive synchronization between femtosecond Ti:sapphire andCr:forsterite lasers,” Appl. Phys. B 74, S171-S176 (2002).

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

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

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

1. Introduction

Growing interest in ultrafast electronic processes of atoms, molecules, or condensed mattterhas been the driving force behind efforts to shorten the duration of ultrashort-pulse lasers. Re-cent demonstrations of attosecond pulse generation by high-order harmonics have opened anew frontier to the so-called attosecond science [1, 2]. Fourier synthesis of optically phase-locked multicolor pulses [3–6] is another attractive method for attosecond pulse generationbecause of its scalability of repetition rate or pulse energy. It would be possible to synthe-size arbitrary electric-field waveform including attosecond pulse shape, by superimposing sev-eral phase-locked ultrashort pulses with separate spectral components that span far beyond anoctave. In recent years, optical phase locking among multicolor pulses has been realized bya femtosecond optical parametric oscillator [7, 8] and two-color synchronized mode-lockedlasers [9–12]. Obviously, stable phase locking and reproducible waveform synthesis requiretight synchronization of pulses with a very low timing jitter. Until now, several groups havereported synchronization of two mode-locked lasers with active [13–17] and passive [18–21]schemes. In an active scheme, the laser cavity is actively controlled with electronic feedbackcircuits to minimize the relative timing jitter. Schibli et al. demonstrated active synchronizationof Ti:sapphire and Cr:forsterite mode-locked lasers with a timing jitter as low as 300 attosec-onds (as) [17].

In contrast, passive synchronization is all-optical, in that cross-phase modulation is utilizedfor synchronization. The two laser cavities are designed to cross on one of the laser crystals. Thecross-phase modulation causes the wavelength shifts, and the change in round-trip group delaysin combination with intracavity group-delay dispersion. The two pulses are self-synchronizedwith the negative dispersion in typical mode-locking conditions [22, 23]. Since the feedbackbandwidth is not limited by that of electronic circuits, a low timing jitter can be expected. Nev-



SHG SFG

WP

WP SHGCM

SFGDP

PMT

PMT

SFG

TiS

CrF

Balanced Cross-Correlator

APD

EOM

Pol.

PZT

Phase-LockedLoop

40MHz rf

beat ref

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

ertheless there are still two remaining causes of jitter on the observation point. First, the pathlengths to the observation point fluctuate with environmental disturbances. Second, the spectralshifts induced by the mechanism of passive synchronization in combination with extracavitydispersion causes jitter. In a previous work, we achieved a timing jitter of 126 as by applyingactive control to passively synchronized Ti:sapphire and Cr:forsterite mode-locked lasers [24].Recently, we also demonstrated long-term phase locking between the two-color lasers with aphase noise of 0.43 rad [25]. Since the relative optical-phase slip between two lasers is verysensitive to changes in the cavity-length difference, optical-phase stabilization plays a role instabilizing cavity-length fluctuation. Therefore one can expect that the optical phase stabiliza-tion helps suppress the abovementioned spectral shifts and subsequently reduces the timingjitter. However, the influence of optical phase locking on the timing jitter has never been ad-dressed to our knowledge.

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. Becauseof reduction by a factor of 1.7, an rms timing jitter of 123 as was achieved in a frequency rangefrom 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( fTiS) and Cr:forsterite ( fCrF) mode-locked pulse trains are expressed as fTiS = δTiS + m frep

and fCrF = δCrF + m′ frep, where frep 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 samespectral range (∼410nm), the two harmonic-frequency combs generate heterodyne beats. Thebeat frequencies are given by fbeat = |2 fTiS−3 fCrF|= |δ +n frep|, where δ = 2δTiS−3δCrF andn is an integer. The cavity-length variation leads to a change in pulse-to-pulse slip of relativecarrier-envelope phase and results in a change in beat frequency. Since the changes in repetitionfrequencies are negligible for a cavity-length change of several microns, the changes in carrier-envelope phase slips of Ti:sapphire (ΔφTiS) and Cr:forsterite (ΔφCrF) laser pulses are given by



ΔφTiS = 2π · 2ΔlTiS/λTiS and ΔφCrF = 2π · 2ΔlCrF/λCrF, respectively, where ΔlTiS and ΔlCrF

are the cavity-length changes of Ti:sapphire and Cr:forsterite lasers, and λ TiS and λCrF are theirwavelengths. Thus the changes in phase slips cause changes in carrier-envelope offset frequen-cies of Ti:sapphire (ΔδTiS) and Cr:forsterite (ΔδCrF) lasers given by ΔδTiS = 2ΔlTiS frep/λTiS

and ΔδCrF = 2ΔlCrF frep/λCrF. Hence, the beat-frequency shift (Δ fbeat) caused by a change inthe cavity-length difference (Δl) is given by [26],

Δ fbeat = 4Δl frep/λTiS = 6Δl frep/λCrF, (1)

where we used some relations written as Δl = ΔlTiS−ΔlCrF and λTiS : λCrF = 2 : 3 for derivationof Eq. (1). This equation suggests that the cavity-length fluctuation can be suppressed by thephase locking in a sensitive manner.

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

3. High-resolution jitter measurement

A cross-correlation trace is utilized in typical jitter measurements, in which the timing jitter canbe estimated from the fluctuation of the cross-correlation signal at the slope of half maximum.When the cross-correlation trace is written as Icc = I0gcc(τ), where I0 is the peak intensity,gcc(τ) is the normalized cross-correlation function, and τ is the relative delay between twopulses, 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 rep-resents the amplitude noise (ΔI0). If the delay is set to gcc(τ) = 1/2 and typical parameters inour experiment are assumed (full width of correlation ∼ 70 fs, ampliutude noise ∼ 0.1%), thesecond term is comparable to the first term in a sub-100-as regime, which limits the resolutionof this method.

To overcome this problem, the balanced cross-correlator proposed and demonstrated by Schi-bli et al [17] was used. The balanced cross-correlator consists of two cross-correlators withdifferent relative delays between two pulses, as illustrated in Fig. 1, and opposite slopes of cor-relation traces are used to monitor the fluctuation. A 3-mm-thick fused-silica delay plate wasinserted on one branch to shift its delay to the opposite slope. The balanced cross-correlation isdefined as the difference of two correlations, namely,

Ibcc(τ) = Icc(τ + τ0/2)− Icc(τ − τ0/2) (3)

= I0{gcc(τ + τ0/2)−gcc(τ − τ0/2)},where τ0 is the relative delay given by the delay plate. The fluctuation of the signal is

ΔIbcc(τ) = I0

{dgcc(τ)

dτ

∣∣∣∣τ+τ0/2

− dgcc(τ)dτ

∣∣∣∣τ−τ0/2

}Δτ (4)

+{gcc(τ + τ0/2)−gcc(τ − τ0/2)}ΔI0.



-1.0

-0.5

0.0

0.5

1.0

Del

ay (

fs)

100806040200

Time (s)

Locked 1 kHz BW

rms = 87 + 8 as

-1.0

-0.5

0.0

0.5

1.0

Del

ay (

fs)

100806040200

Time (s)

Unlocked1 kHz BW

rms = 194 + 30 as

-1.0

-0.5

0.0

0.5

1.0

Del

ay (

fs)

0.200.150.100.050.00

Time (s)

Locked400 kHz BW

rms = 96 + 4 as

-1.0

-0.5

0.0

0.5

1.0

Del

ay (

fs)

0.200.150.100.050.00

Time (s)

Unlocked400 kHz BW

rms = 108 + 9 as

-1.0

-0.5

0.0

0.5

1.0

Del

ay (

fs)

4x10-3

3210

Time (s)

Locked1 MHz BW

rms = 88 + 2 as

-1.0

-0.5

0.0

0.5

1.0

Del

ay (

fs)

4x10-3

3210

Time (s)

Unlocked1 MHz BW

rms = 101 + 8 as

(a) (b) (c)

_

_ _

_

_

_

Fig. 2. Measured timing jitter at bandwidths of (a) 1 kHz, (b) 400 kHz, and (c) 1 MHz. Thetop 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 representsthe amplitude noise (ΔI0). In this case, the amplitude noise can be excluded by choosing a delayto satisfy gcc(τ +τ0/2) = gcc(τ −τ0/2), which is τ = 0 for symmetric correlation functions. Inother words, since the amplitude noise affects the two correlations in the same way when thecondition is satisfied, the effects are cancelled by taking the difference of two correlations. Thetwo correlation signals were detected simultaneously with two photomultiplier tubes and meas-ured with a multichannel digital oscilloscope. The balanced signal was obtained by calculateddifference of two traces.

4. Results and discussion

Figure 2 presents the timing-jitter results measured with observation bandwidths of 1 kHz, 400kHz, and 1 MHz. As seen in Fig. 2(a), there is clear evidence of suppression of the drift andfluctuation by the phase locking at 1-kHz bandwidth. As a result, an rms jitter of 194 ± 30as was reduced to 87 ± 8 as. Likewise, an rms jitter decreased from 108 ± 9 as to 96 ± 4as 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 fastestbandwidths.

Figure 3 depicts the beat-frequency variation measured at the same time as the 1-kHz jittermeasurement shown in Fig. 2(a). There was a drift of about 5 MHz in beat frequency, which issimilar 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 commercialpump sources were power-stabilized and the active control by the electro-optic modulator wasnot done in the case without phase locking. To confirm this, the cavity length of the Ti:sapphirelaser was modulated by swinging the end mirror with the piezoelectric transducer at a frequencyof 500 Hz. Figure 4 illustrates the response of (a) beat frequency and (b) relative delay to themodulation. The slow fluctuation seen in the relative delay is a 50-Hz jitter, which originatesfrom the ac power-supply noise. In Fig. 4(a), the modulation amplitude of beat frequency was 5



44

42

40

38

36

Bea

t fr

equ

ency

(M

Hz)

100806040200

Time (s)

44

42

40

38

36

Bea

t fr

equ

ency

(M

Hz

)

100806040200

Time (s)

(a) (b)

Fig. 3. Beat frequency variation at a bandwidth of 1 kHz (a) with and (b) without phaselocking.

-1.0

-0.5

0.0

0.5

1.0

Del

ay (

fs)

40x10-3

3020100

Time (s)

44

42

40

38

36Bea

t F

req

uen

cy (

MH

z)

40x10-3

3020100

Time (s)

(a) (b)

Fig. 4. (a) Beat frequency and (b) relative delay response to the cavity-length modulation.

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 correspondsto an optical delay of only 30 as, which is not a primary cause of the delay change, because itis considered to be compensated by the passive-synchronization mechanism on a much shortertime scale.

The observed timing shift originating from the cavity-length change has two possible mech-anisms. First, the spectral shift inherent in the passive synchronization mechanism possiblycauses a timing shift in combination with the group-delay dispersion on the extracavity opti-cal paths. A shift of 0.3 nm in the Cr:forsterite spectrum was observed, whereas no shift wasseen in the Ti:sapphire spectrum. The estimated group-delay change resulting from this spectralshift is 200 as with the estimated extracavity dispersion of 500 fs2. Second, the relative timingdifference of two pulses inside the Ti:sapphire crystal varies depending on the cavity-lengthmismatch, because it is passively tuned to an optimal value to induce the spectral shift whichmakes the round-trip group delays of two pulses identical. As well as the cavity-length fluctua-tion, 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.

Figure 5 shows the power spectral density profiles calculated directly from the time-domaindata in Fig. 2 and the integrated rms values. The timing jitter is effectively suppressed in thelow-frequency region, especially lower than 1 Hz, whereas no remarkable suppression is seen inthe high-frequency region. The results suggest that the cavity-length control with the piezoelec-



10-9

10-7

10-5

10-3

10-1

101

Jitt

er P

SD

(fs

2 /Hz)

10-2 10

0 102 10

4 106

Frequency (Hz)

0.25

0.20

0.15

0.10

0.05

0.00

Integ

rated rm

s jitter (fs)

Lockedrms = 123 as(10mHz-1MHz)

10-9

10-7

10-5

10-3

10-1

101

Jitt

er P

SD

(fs

2 /Hz)

10-2 10

0 102 10

4 106

Frequency (Hz)

0.25

0.20

0.15

0.10

0.05

0.00

Integ

rated rm

s jitter (fs)

Unlockedrms = 213 as(10mHz-1MHz)

(a) (b)

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

tric transducer contributes to the jitter reduction. This fact agrees well with the abovementionedspeculation. Finally, the rms jitter integrated over a frequency range from 10 mHz to 1 MHzwas 213± 31 as without phase locking, which was reduced to 123± 8 as by phase locking. Thereduction factor was approximately 1.7. The obtained rms jitter is comparable to the previousresult with active jitter control in Ref. 24. The scheme presented in this paper requires a simplersetup than the previous one because it allows simultaneous locking of timing and phase withone active control.

5. Conclusion

Reduction of the timing jitter between passively synchronized Ti:sapphire and Cr:forsteritemode-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 resultof timing-jitter reduction by a factor of 1.7, an rms jitter of 123 as was achieved in a frequencyrange from 10 mHz to 1 MHz. It would be possible to generate two-color pulses with a fixedcarrier-envelope phase relation for every pulse by locking the beat frequency to dc. Fouriersynthesis is now feasible with the phase-locked two-color pulses synchronized with 100-asprecision.



synchronization of ti:sapphire and cr:forsterite mode-locked lasers with 100-attosecond precision by...

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