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We have demonstrated a carrier-envelope phase (CEP) stabilized chirped-pulse amplification (CPA) system employing a grating-based pulse stretcher and compressor and a regenerative amplifier for the first time. In addition to stabilizing the carrier-envelope offset phase of a laser oscillator, a new pulse selection method referenced to the carrier-envelope offset beat signal was introduced. The pulse-selection method is more robust against the carrier-envelope offset phase fluctuations than a simple pulse-clock dividing method. We observed a stable fringe in a self-referencing spectrum interferometry of the amplified pulse, which implies that the CEP of amplified pulse is stabilized. We also measured the effect of the beam angle change on the CEP of amplified pulses. The result demonstrates that the CEP stabilized CPA is scalable to higher-pulse energies.
©2004 Optical Society of America
1. Introduction
The carrier-envelope phase (CEP) is the phase of the electric field at the peak of the pulse envelope. It is important in controlling high-order harmonic generation (HHG) with attosecond precision [1–5] because the highest instantaneous intensity and its timing depend on CEP for a few-cycle optical pulse. Figure 1 depicts the relation of the pulse envelope and the electric field for a few-cycle optical pulse. The electric field of transform limited optical pulse is expressed as E(t)=A(t) cos(ω 0 t - ϕ), where A(t) is the envelope of the electric field (symmetric and have maximum at t=0), ω 0 is the central angular frequency, and ϕ is the CEP.
Amplification of a CEP-stabilized pulse was first demonstrated in an optical parametric amplifier, however, the pulse energy is tens of micro joule [4]. A CEP-stabilized chirped-pulse-amplification (CPA) system composed of a material-based pulse stretcher, a prism-based pulse compressor, and a multi-pass amplifier was also demonstrated [2, 3]. The demonstrated system is compact and able to amplify pulses to the tens of milli-joule level. However, energy scaling to hundreds of milli-joules or more is difficult due to the short chirped-pulse duration, or due to the size of the prism pulse compressor. Because the CPA system incorporates a grating-based pulse stretcher and compressor is widely used to amplify pulses with energy up to the joule level, a CEP stabilized grating-based CPA system is favorable for performing experiments requiring higher pulse energies.
Several technical issues need to be studied to demonstrate CEP-stabilized CPA system. We previously reported measurement and analysis of the CEP fluctuation in a CPA system [6, 7]. We concluded that the random change of the CEP in the commonly used grating-based CPA system was due to the CEP fluctuation of the seed pulse. The estimated fluctuation that arose in the amplifier stage was not so large. However, it was not clear whether the beam pointing fluctuation coupled with the pulse stretcher/ compressor produced serious CEP fluctuations or not. For the commonly used double-pass pulse stretcher and compressor, the CEP fluctuation due to the beam-pointing fluctuation directing to the devices seems to be cancelled in the second pass. Because CEP-stabilized amplification with the material-based pulse stretcher was demonstrated, it is clear that the effect of the amplifier components except the grating-based stretcher and compressor on the CEP fluctuation is not so severe as to destroy the CEP coherence.
Another important parameter is the effect of the amplitude-to-phase noise conversion in the “hollow-clad fiber” used in the self-referencing interferometer to measure and control the carrier-envelope offset (CEO) beat of the oscillator [6]. The fibers are called “photonic crystal fiber (PCF)” or “microstructure fiber (MSF)” depending on the fiber’s supplier. If this effect is large enough to degrade the coherence of the CEO, fluctuation of the CEP of the seed pulse becomes large even when the in-loop CEO error is small enough.
In this paper, we demonstrate a CEP-stabilized CPA system that is scalable to pulse energies of hundreds of milli-joules or more. This result indicates that the CPA system composed of a grating-based pulse stretcher, pulse compressor, a regenerative amplifier, and a multi-pass amplifier can generate the CEP-controlled pulses that allow us to prepare a well-defined set of initial conditions for high-intensity laser-matter interaction experiments.
2. Experiment
2-1. CEP stabilized chirped-pulse amplification system
Figure 2 illustrates the CEP-stabilized CPA system. The system is composed of a CEO stabilized oscillator, a pulse-selection system, a grating-based pulse stretcher, a regenerative amplifier, a multi-pass amplifier, and a grating-based pulse compressor [7, 8]. A Ti:sapphire oscillator generates f osc=80MHz pulse trains with an average power of 400 mW and a spectrum width of 30 to 35 nm FWHM centered around 785 nm. The pulse stretcher, which is designed based on the report by Lemoff and Barty [9], is composed of two gratings (1200g/mm), two cylindrical mirrors (r=1000 mm), a roof mirror, and a retroreflector. The pulse experiences two round trips after reflected by the retroreflector, and the second-order dispersion is calculated as ϕ 2=3.6×106 fs2 at 800 nm. The pulse width of the stretched pulse exceeds 220 ps, which is adequate for amplification to the hundreds of milli-joule level. The CEP-stabilized seed pulses are selected by a Pockels cell with a trigger signal generated by the pulse-selection system described below. After being amplified by a regenerative amplifier and a four-pass amplifier, the pulse is compressed with a grating-based pulse compressor composed of two gratings (1200g/mm) and a folding mirror. A portion of the compressed-pulse energy was used to measure the relative CEP of the amplified pulse by the self-referencing spectral interferometry (SI) method. The measurement system is composed of a hollow-core fiber filled with Kr gas, a second harmonic generation crystal, a polarizer, and a spectrometer [6, 7]. Characteristics of each amplification system component are descried below.
2-2 CEO stabilized oscillator
First, we will describe the pulse-selection method. We controlled the CEO beat (f ceo) to about 1/8 of the pulse repetition rate of the oscillator (f rep=80MHz) using phase-lock-loop electronics so that almost every eighth pulse possesses nearly the same CEP. The CEO beat was monitored by an f-to-2f interferometer that is composed of a 60-mm long “hollow-clad fiber” and an SHG crystal as illustrated in Fig. 3 [10]. The phase comparator generates an error signal that is proportional to the phase difference between the CEO beat signal and the reference signal. The error signal was used to control a PZT that changes the angle of the end mirror of the prism-pair dispersion compensated oscillator.
Fig. 3. Self-referencing f-to-2f interferometer.DM: dichroic mirror, PBS: polarizing beam splitter, Pol: polarizer, G: grating, APD: Avalanche photodiode
We used an oscilloscope, a spectrum analyzer, a frequency counter, and a vector signal analyzer to investigate the quality of the in-loop CEO coherence. We measured the phase noise of the CEO beat signal with an oscilloscope triggered by the reference signal. Figure 4(a) displays 10-sec exposed traces of the reference signal at 10MHz and the phase-locked-loop (PLL) controlled CEO beat signal. The PLL feedback keeps the signal phase-locked, however, the CEO signal has phase jitter relative to the reference signal. The power spectrum density (PSD) of the phase noise S ϕ and the accumulated phase noise ϕ error are measured as in Fig. 4(b) by the demodulation technique [11]. The relation is expressed as
where ν high and ν low are the frequency range considered. The accumulated phase noise is about 1.2rad (integrated from ν=1MHz to 0.1Hz), reaching 1rad at frequency around 1kHz.
Fig. 4. Stability of the PLL-controlled CEO signal. (a) Stability of the controlled CEO beat signal (V CEO) relative to the reference signal (V ref) measured with an ocilloscope. (b) Power spectrum density of the phase noise (S ϕ) measured with a vector signal analyzer and the phase error calculated from integration of S ϕ.
2-3 Pulse-selection system and amplifier stage
Next, we will describe the pulse-selection method displayed in Fig. 2. Before explaining in detail, we will explain the relation between the self-referencing beat signal and the relative CEP of the pulse, together with the single-shot measurement of the relative CEP with the self-referencing SI method. The self-referencing SI signal is expressed as
where I F(ω) and I SH(ω) are the spectrum of the fundamental and the second harmonic of the measured pulse, τ is the time delay between the two component, ϕ is CEP and ϕ const is the unknown phase shift due to dispersion [6, 7].
Fig. 5. (a) Calculation of the self-referencing SI signal for different CEP value. (b) Trace of the intensity at 400 nm component, which shows sinusoidal intensity modulation corresponding to the CEO beat signal.
Figures 5 illustrate the relation between the self-referencing SI and the self-referencing CEO beat measurement. We assumed 10-nm FWHM Gaussian spectrum for both fundamental and the second harmonic component, relative delay of 100 fs, and ϕ const=0 for simplicity. Figure 5(a) displays the change of the self-referencing SI signal with the relative CEP. As the relative phase shifts, the fringe changes its phase, which is the basic idea of single-shot measurement of the relative CEP of an amplified pulse. Here, “relative” means that the measured phase has information on the CEP, however, it is not the CEP at a certain measurement point. This phase shift originates from the dispersion in the SHG crystal, CEP shift in the air, and the phase shift in the SHG process [7]. Figure 5(b) shows the dependence of the signal intensity at a certain wavelength component (400 nm in the figure) on the CEP. When measuring CEO by the self-referencing f-to-2f method, the relative delay between the two components is adjusted to make the signal stronger. This adjustment corresponds to making the delay between the two components small, and the visibility of the interference large at an observing wavelength window. This delay produces an arbitrary phase shift in the self-reference beat signal. Therefore, the phase of the measured signal shifts from the real value. However, if the arbitrary phase shift is fixed at a certain value during measurement, the measured phase of the beat signal corresponds to the relative CEP of the measuring pulses. The amplitude of the CEO beat signal has information of the relative CEP, therefore, we can select pulses that possess the same CEP by selecting pulses with referring to the CEO beat signal even if the CEO fluctuation is large [12].
Fig. 6. CEP error of the selected pulse as a function of the delay between the divider and the ready pulse
To select CEP-stabilized pulses, we generated a 1kHz “ready pulse” by dividing the CEO beat signal. Because the “ready pulse” has timing jitter relative to the pulse timing of the oscillator the ready pulse can not be used for the pulse selection timing. We introduced a synchronization circuit that generates electrical pulses synchronized to the first pulse timing that appears after the ready pulse. For the condition that the delay between the divider and the ready pulse is zero, this method limits the timing jitter between the ready pulse and the pick up timing within 1/f rep. The CEP error is limited below 2π(f ceo/f rep)=0.79rad (for delay=0). In the amplifier system, however, the delay between the divider and the ready pulse should be set to 3.4 μsec that corresponds to the build up of the pumping pulse of the amplifier. The CEP error was measured as a function of the delay. As shown in Fig. 6, the CEP error increases with the delay, which is similar to the accumulated phase error of the CEO signal as shown in Fig. 4(b).
Figure 7(a) displays 10-sec exposure of the build-up of the regenerative amplifier, the CEO beat signal V ceo, and the histogram of the timing jitter of V ceo. The timing jitter (shown as the finite width at the zero-cross line) gives information on the CEP jitter of the seed pulses. In Fig. 7(b), the histogram of the CEP error that is calculated from the measured timing jitter of V CEO (100ns corresponds to 2π) is shown. The in-loop CEP error of the seed pulse is estimated to be 0.42rad rms for a delay of 3.4 μs, which is consistent with Fig. 6.
Fig. 7. (a) Measurement of the CEP jitter of regenerative amplifier seed pulses. The delay between the divider and the ready pulse was 3.4 μs. The upper distribution (blue) shows the histogram of the timing jitter of V ceo. (b) Histogram of the CEP error (red dots) and the fitted Gaussian distribution with σ=0.42rad (dotted line).
The regenerative amplifier generates about 1.4 mJ/pulse, and the four-pass amplifier generates about 3.5 mJ/pulse up to a 1kHz repetition rate. The compressed pulse energy was about 1mJ due to the low efficiency of the old gratings in the pulse compressor. The pulse-selection method selects pulses that have the same CEP, while the method gives 12-ns timing jitter between the pumping pulse of the amplifier. Measured energy stability was 0.8% rms, which was same as the results obtained with the amplified pulses by the commonly used pulse selection method based on the division of the pulse repetition timing f rep. The 12-ns timing jitter does not cause an excess energy fluctuation because the lifetime of the Ti:sapphire is longer that the jitter. Figure 8 shows the spectrum of the amplified pulse. The compressed pulse has 21-nm FWHM spectrum corresponding to a 50-fs transform limited pulse.
2.4 CEP stability of amplified laser pulse
The CEP of the amplified pulse was measured by the self-referencing spectral interferometry method [6, 7]. The spectrum was broadened in a 150-μm inner-diameter 72-cm long Kr-filled hollow-core fiber (Fig. 9(a)). The second harmonic component was generated by passing the output pulse through a 300-μm-thick BBO crystal, and both the fundamental component and the SHG component are directed to a spectrometer after passing a polarizer (Fig. 9(b)). The self-referencing SI was observed around 390 nm as shown in Fig. 9(c). Exposure time of a CCD was set at 21 msec, and 16 pulses are exposed in one measurement.
Fig. 9. (a) Spectrum of the output pulse from the hollow-core fiber filled with Kr gas. (b) Spectrum of the fundamental component and the second harmonic component after the second harmonic crystal. (c) Self-referencing spectrum for the CEP-stabilized pulses. f Amp=762Hz, and the exposure time of CCD was set 21msec (16 pulses for one exposure)
Fig. 10. Self-referencing SI of amplified pulse. 1-sec integrated spectrum (upper), and temporal evolution of the fringe (lower). f Amp = 762Hz, Exposure time of CCD is 21 msec (16 pulses for one exposure). (a) Measured with the CEP of the seed pulse was not stabilized, and (b) measured with the CEP of seed pulses was stabilized.
We measured consecutive spectra for seconds without dead time. Figure 10 displays the 1-sec, 95-trace accumulated spectrum (upper) and the evolution of the consecutive 95 spectra (lower). With the CEP-stabilized seeding, the SI exhibits a fringe that remains for seconds and clear fringe is observed even after accumulation for 1 second ass shown in Fig. 10(b). In contrast, when the seed pulse was not stabilized, such a stable fringe is not observed and the spectrum integrated for 1 second shows no fringe as shown in Fig. 10(a). Figure 11(a) is the same as Fig. 10(b), while the total measurement time was set to 10 seconds. A slow drift was observed in the self-referencing SI fringe. Figure 11(b) shows comparison of the spectra for different integration period. The visibility of the fringe degraded for the longer integration period.
Fig. 11. Self-referencing SI of amplified pulse. (a) 10-sec integrated spectrum (upper), and temporal evolution of the fringe (lower). f Amp=762Hz, Exposure time of CCD is 21 msec (16 pulses for one exposure). (b) Comparison of the integrated spectra for different integration periods.
To confirm that the self-referencing SI really measures the relative CEP, we intentionally shifted the CEP of the seeding pulse by changing one of the optical path lengths in the self-referencing f-to-2f interferometer used to control the CEO of the oscillator. Change the relative delay of 1.7 μm (peak-to-peak) at 1Hz in the f-to-2f interferometer (wavelength of 500 nm) should cause a 21.7-rad peak-to-peak CEP shift of the seed pulse. Figure 13 depicts a clear fringe shift in the self-referencing SI signal at 1-Hz with 16.9-rad peak-to-peak shift, which is 24% smaller than the calculation, and is within the accuracy of the PZT actuator. The result confirms that the self-referencing SI signal really represents the relative CEP of amplified pulses and also indicates that the delay shift in the f-to-2f interferometer can be used to control the relative CEP of the seed pulse.
Fig. 12. (a) Temporal evolution of self-referencing SI fringe measured with changing the CEP of the seeding pulse by changing the delay of the f-to-2f interferometer by 1.7 μm at 1Hz. The fringe shows phase shift of 16.9rad. (b) Observed CEP shift as a function of the calculated CEP shift from the delay in the f-to-2f interferometer. The slope is 0.76.
2.5 Effect of the beam pointing to the pulse stretcher on CEP of amplified pulses
The effect of beam pointing (angle and position) on the CEP shift was investigated by changing the angle of a mirror with a PZT actuator at 2Hz. The distance between the tilting mirror and the first grating of the pulse stretcher was about 91 cm. The peak-to-peak beam-angle change of 84μrad (δθ beam=2 δθ mirror) resulted in a measured self-referencing SI fringe (relative CEP) shift of δϕ=7.0rad. We measured the fringe shift for different amplitudes of beam tilting; the slope of Fig. 13(b) gives a sensitivity of the fringe to the beam pointing of δϕ/δθ beam=8.3×104 rad/rad. The measured sensitivity includes several factors such as the sensitivity of the stretcher to the beam pointing and to the beam position shift. Compared with the calculated sensitivity of the grating-based pulse stretcher and compressor in one-pass configuration (order of 106 rad/rad) [6], the measured result is small and indicates that the CEP shift is cancelled to some extent in the round-trip configuration, as expected. We would like to mention that a similar sensitivity δϕ/δθ beam was observed when the retroreflector in the double-round-trip pulse-stretcher was replaced by a roof mirror. In this analysis, we assumed that the fringe shift was dominated by the CEP shift, however, the fringe depends both on the delay (τ) and the CEP (ϕ) as Eq. (2). To distinguish the CEP shift from the delay shift, SI signal spreading over a wider spectral range with a better signal-to-noise is required. A detailed analysis will be reported elsewhere.
Fig. 13. (a) Temporal evolution of self-referencing SI fringe measured with changing the beam direction to the pulse stretcher. Peak to peak angle change was 84 μrad and measured fringe (CEP) shift was 7.0rad. (b) Measured fringe shift as a function of the peak to peak angle change. The slope is 8.3×104 rad/rad
3. Discussion
The short-term jitter of the CEP will be due to the inaccuracy in the CEO control and it will be improved by using lower noise electronics and conditions. The long-term instability seems to be mainly due to a drift of the optical path length in the self-referencing f-to-2f interferometer or the beam-pointing fluctuation directing to the stretcher. The long-term CEO error can be compensated by providing feedback to the relative delay in the f-to-2f interferometer with monitoring the self-referencing SI of the amplified pulse as demonstrated by others[2,3].
One of the causes that gives CEP error to the seed pulse is the out-of-loop error caused by the amplitude-to-phase noise conversion in the self-referencing method using the hollow-clad fiber [13,14]. Because the dependence of the amplitude-to-phase noise conversion coefficient C AP on the experimental condition are not clear yet [13–16], we measured C AP for various experimental conditions. The zero dispersion wavelength of the hollow-clad fiber is 690 nm, and the core size is 1.7 μm. We found that shorter fibers and higher coupled power makes C AP small. We also found that C AP depends on the polarization direction, chirp of the coupled pulse, and the self-referencing wavelength. Qualitatively, to make C AP small, shorter fiber, shorter input pulse width, higher coupled power, and shorter self-referencing wavelength are preferable [17]. A typical value of C AP is 6.0 rad/mW for a 60-mm-long fiber with coupled average power (measured at the output of the fiber) of 31 mW, which is a typical parameters for the CEO stabilization.
We measured the amplitude noise of the oscillator for (a) free-running, (b) CEO controlled by moving the end mirror with a PZT, and (c) CEO controlled by PZT and an EO modulator to control the pumping power. The measured power spectral density (PSD) of amplitude noise above 10kHz is near the noise floor of the measurement system, therefore, we estimated the amplitude noise ∆P/P by integrating the PSD from 10kHz to 0.1Hz. The CEP error is calculated from the amplitude noise as
where, P is the coupled average power (31 mW), ∆P/P is the amplitude noise of the oscillator, and C AP=6.0 rad/mW. Using these parameters, the additional CEP error due to the amplitude noise is 0.13rad for the free-running case, 0.15rad for the PZT-controlled case, and 0.39rad for the EO and PZT controlled case. We employed PZT control to stabilize the oscillator because the additional out-of-loop CEP error is smaller compared with the PZT and EO control system. A similar increase of the CEP error has been reported for the CEO stabilized oscillator [14]. Because the amplitude noise depends on the operating condition and the method of the feedback control and the cavity configuration, the amplitude noise must be measured to evaluate the effect of the out-of-loop phase error.
4. Conclusions
We demonstrated the first carrier-envelope-phase stabilized chirped-pulse amplification system using a grating-based pulse stretcher and compressor together with a regenerative amplifer. Stabilization of the carrier-envelope offset of a laser oscillator and a new pulse-selection method that is robust against the carrier-envelope offset fluctuations have been employed. We observed that the fringe of the self-referencing SI stays for seconds when the CEP of the seed pulse is stabilized. The results indicate that the relative CEP is controlled in the CPA system utilizing a grating-based pulse stretcher and compressor. Our results suggest that control of the shape of the electric field (both the pulse shape and the carrier-envelope phase) of a high-intensity, high-energy (joule level) laser pulse is possible. Precise experiments on the laser-matter interaction by controlling the phase of the laser pulse can be conducted.
Acknowledgements
A part of this study was financially supported by the Budget for Nuclear Research of the Ministry of Education, Culture, Sports, Science and Technology, based on screening and counseling by the Atomic Energy Commission, Japan. The authors acknowledge University of Bath, U. K. for supplying the hollow-clad fibers (photonic crystal fiber).
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