1. Introduction

Recent progress in femtosecond laser technology has made it possible to routinely generate few-cycle optical pulses [1]. This has led to a rapid growth of interest in the investigation of ultrafast physical phenomena. A number of ultrafast physical processes are sensitive to the electric field of the laser pulse rather than to its intensity profile [2]. Such processes include high-harmonic generation [3], above-threshold ionization [4], and coherent control of atomic and molecular systems [5]. Experimental investigation of such phenomena, using few-cycle laser pulses, requires the generation of identical high-power few-cycle laser pulses, i.e. ultrashort laser pulses having the same intensity profile and the same carrier-envelope phase (CEP).

The CEP stabilization technique of femtosecond mode-locked laser oscillator, based on a self-referencing nonlinear interferometer [6] and a phase-locked loop (PLL) circuit [7], has brought a revolutionary impact on attosecond science [2] as well as frequency metrology [8]. The CEP stabilized high-power femtosecond laser source is essential to the attosecond science based on high-harmonic generation. Kakehata et al. [9] demonstrated a single-shot f-2f spectral interferometer (SI) for the measurement of the relative CEP value in a conventional chirped-pulse amplification (CPA) laser. Phase stabilization of amplified femtosecond laser pulses was reported by Baltuska et al. [10] for the first time. They used the PLL-based technique for the oscillator CEP stabilization and selectively amplified the same-CEP pulses in a CPA chain, composed of a glass slab stretcher and a prism-based compressor. A slow feedback loop based on the f-2f SI was added for long-term stability. On the other hand, the CEP stabilization of the grating-based CPA systems which are more suitable for higher energies has also been demonstrated [11]. Recently, the CEP stabilization was achieved with the high-contrast relativistic-intensity laser pulses [12] and the long-term stability of ~10³ seconds was reported [13] in the grating-based systems. However, those systems were not combined with an additional feedback loop to suppress the slow phase drift. More recently, the slow feedback loop controlling a grating separation was realized [14–16]. Along with the CEP stabilization, an active CEP control of amplified pulses has also been demonstrated [11, 13, 14].

As an alternative approach to stabilize the CEP of a femtosecond laser oscillator, Lee et al. [17] proposed and demonstrated a novel scheme called the “direct locking technique.” This technique directly stabilized the CEP of femtosecond laser pulses in the time domain, in contrast to the conventional PLL method operating in the frequency domain. In addition to the simplicity of the locking system, the direct locking technique allowed to lock the CEP slip to zero for all laser pulses. Out-of-loop measurements also showed the phase jitter of this technique was low and comparable to that of the conventional PLL-based technique. Although the PLL-based CEP locking systems are commercially available and well developed by many groups, the direct locking technique provides several advantages such as a simple synchronization scheme in an amplifier chain and the capability of versatile electronic CEP modulation.

In this paper, we report on the CEP stabilization and control of a kHz CPA Ti:sapphire laser, which employs two multipass amplifiers, a grating-based stretcher and a compressor, using the direct locking technique and a slow feedback loop. An f-2f SI is set up for both monitoring the CEP change of compressed pulses and generating a slow feedback signal for further enhancement of long-term stability. Electronic CEP modulation of amplified pulses is also demonstrated. Our results will indicate that the direct locking technique can be well suited to not only stabilize the CEP, but also, alter or modulate the CEP of amplified laser pulses in a controlled manner by adding an electrical signal without changing any optical or mechanical parts.

2. Experimental setup of CEP-stabilized CPA laser

Our CEP-stabilized CPA Ti:sapphire laser system consists of three parts, as illustrated in Fig. 1: a CEP-controlled femtosecond oscillator, 2-stage chirped-pulse amplifiers [18], and an f-2f SI for monitoring the relative CEP value of amplified pulses. The prism-dispersion-controlled oscillator, pumped by a single-mode cw green laser (Verdi, Coherent, Inc.), produces the mode-locked pulses at f_osc = 27 MHz, having a pulse duration of 13 fs and an energy of 13 nJ per pulse [19]. The CEP variation of oscillator pulses is measured using a self-referencing f-2f interferometer. However, in contrast to the conventional PLL-based technique, the beat signal of the f-2f interferometer directly provides a feedback signal to an acouto-optic modulator (AOM), adjusting finely the pumping power to the oscillator [20]. This direct locking technique has the distinct advantage of locking the shot-to-shot CEP-slip to zero and is also simple to implement. The CEP-stabilized laser pulses are amplified in a grating-based CPA chain having two multipass amplifiers. The CEP stability is monitored at an f-2f SI and enhanced using a slow feedback loop.

The layout for CEP stabilization of the laser oscillator is depicted in Fig. 2(a). The carrier-offset frequency, f_ceo , of the signal from the photo detector APD₃ is measured using an RF spectrum analyzer and, by adjusting the insertion of the prism in the oscillator, f_ceo is brought within the operating bandwidth of the CEP direct locking electronics. By using the outputs of the avalanche photo detectors APD₁ and APD₂, the DC term and noise in the f-to-2f beat signal are subtracted out electronically for the extraction of a pure beat signal, and then, the locking electronics is turned on. Once the direct locking electronics is switched on, the beat signal amplitude is quenched to a nearly DC level, as observed on an oscilloscope, thereby indicating the onset of CEP locking. Since f_ceo is locked to zero in the direct locking technique, it enables one to lock the shot-to-shot CEP slip Δϕ_CEP to zero with a relatively simple setup [17].

 

Fig. 1. Schematics of a CEP-stabilized femtosecond Ti:Sapphire laser operating at 1kHz

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Fig. 2. (a) Direct locking technique to stabilize CEP of oscillator. (b) experimental setup for spectral interferometry. (c) spectra of seed pulse (dotted) and generated white-light continuum (solid) through a sapphire plate. (d) spectral interference fringe pattern generated by the superposition of the SH signal the red component at 1040 nm and the blue component at 520 nm of white light. (AOM: acousto-optic modulator, APD: avalanche photodiode, BPF: band-pass filter, CP: cubic polarizer, DB: dichroic beamsplitter, HWP: half-wave plate, PBS: polarizing beam-splitter, PCF: photonic crystal fiber, SHG: second-harmonic generation crystal,)

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The CEP-stabilized pulses from the oscillator are amplified by the conventional CPA chain. The laser pulses are first stretched in an Offner-triplet stretcher using a 1400 grooves/mm diffraction grating. The temporal width of the stretched pulses is about 200 ps, which is scalable for a higher-energy configuration. The stretched pulses then enter an 8-pass amplifier, wherein, after the first four passes, they are selected at 1 kHz using a Pockels cell.

The 1-kHz pulses are re-injected into the amplifier to complete the remaining 4 passes. These amplified pulses with the energy of 1.2 mJ are, next, passed through a second Pockels cell in order to suppress amplified spontaneous emission and also eliminate pre-pulses. The pulses are then passed through a 4-pass power amplifier to boost up their energy up to 6.5 mJ. Finally, the pulses are temporally compressed in a pulse compressor consisting of a grating pair whose groove numbers are 1480 grooves/mm. The laser pulses are compressed with the duration of 25 fs and the energy of 4.2 mJ. The compressed pulse is delivered to the filamentation setup for high-energy few-cycle pulse generation [21].

A small part of the amplified laser pulse with the energy of ~1 μJ is split off using a beam splitter and passed into an f-2f SI for measuring and controlling the CEP variation of the amplified laser pulses. The SI setup, employed in the experiments, is illustrated in Fig. 2(b). The horizontally polarized laser pulses are first focused on a 1-mm thick sapphire plate, resulting in a spectrally broadened continuum of more than one octave (Fig. 2(c)). The input energy should be finely controlled to avoid any multi-filamentation phenomena due to an excessive energy. These spectrally broadened pulses in horizontally polarized state are next focused on a 1-mm-thick type I BBO crystal with a proper phase-matching angle to produce the second-harmonic (SH) radiation centered at 520 nm (2f) in the vertically polarized state from the 1040 nm (f) part of the continuum. The SH 520 nm and the fundamental 520 nm of the continuum are spectrally mixed with the time delay determined by the group delay of two waves. For this, they now pass through a cube polarizer with its transmission axis oriented at around 45° with the horizontal and generate the spectral interference centered at 520 nm. The polarization angle is adjusted so that we obtain the highest fringe contrast. A color filter removes the strong 800 nm component. The spectrally interfered beams are transmitted into a fiber-coupled spectrometer (SM240, CVI, Inc.), interfaced to a computer for data analysis. Since the spectrometer is capable of recording data up to 50 Hz, it is externally triggered at 50 Hz by using a 1 kHz-to-50 Hz down-converter to synchronize it with the 1 kHz laser amplifiers. Hence, the spectrometer captures the SI signal of every 20^th amplified pulse and one such signal is shown in Fig. 2(d).

The relative CEP is recovered from the SI signal after a fast Fourier transform (FFT) and filtering [22–24]. The signal from the spectrometer is first passed through a low-pass filter, to get rid of high frequency noise, and then subjected to FFT. This procedure yields the relative CEP of every 20^th amplified pulse and, hence, the difference between successive values evaluated would be a measure of the CEP slip. The calculated relative CEP values are also utilized as the feedback signal of the slow feedback loop. The real-time interface of the CEP calculation and the feedback signal generation is developed using a LabVIEW (National Instruments, Inc.) code.

3. CEP stabilization of amplified laser pulses

We first measured the SI signal of consecutive amplified pulses without any CEP stabilization process. The accumulated SI signal in Fig. 3(a) and its time evolution in Fig. 3(b) show that the fringe pattern changes irregularly from shot to shot, as expected. In contrast, when the oscillator was CEP-stabilized using the direct locking technique, a stable f-2f SI signal was obtained as shown in Fig. 4(a). The fringe pattern was preserved even when the interferograms are accumulated up to several seconds. The measurement extending the time scale up to 30 seconds showed a slow drift in the CEP value as is evident from Fig. 4(a). The period of these slow variations was seen to be about 7–8 seconds (or ~0.1 Hz) and the phase fluctuations as shown in Fig. 4(b), the relative phase drift of about 1.2 rad was estimated. The magnitude of the relative phase drift depended on the operating conditions of the laser. The slow variation was caused by the random processes occurring inevitably during the amplification of laser pulses, such as fluctuations in laser pointing, pump energy, air turbulence, mechanical vibrations, and temperature change [11, 12].

 

Fig. 3. (a) SI signal with 15 ms integration time when CEP of the oscillator is not stabilized, and (b) time evolution of the interferogram.

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The slow drift in the relative CEP of the amplified laser pulses could be readily tracked in the real-time by the analysis of the f-2f SI fringe pattern (Fig. 4(a)). In order to generate a slow feed back signal to compensate for the slow phase drift [22], we first generated an error signal proportional to the difference of the phases between the consecutive SI signals from the realtime analysis of the fringe pattern. This error signal was then fed to the direct locking electronics in addition to the oscillator-loop error signal. Since the shot-to-shot CEP change was negligible compared to the slow drift, we were able to accumulate the SI signals for 10–20 milliseconds or 10-20 laser pulses. The implementation of the signal integration allowed the smooth operation of the feedback loop by preventing an accidental overshoot of the CEP control of the oscillator pulses.

 

Fig 4. (a) Interferogram of SI signal and (b) relative phase shift of amplified pulses when the CEP of the oscillator was stabilized.

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The effect of the slow feedback was clearly evident in Fig. 5(a), which depicts the time evolution of the interferogram after the slow feedback was turned on. The straight interference pattern was observed, in contrast to the oscillator-loop-only case in Fig. 4(a). The statistical analysis with the CEP distribution of the interferograms showed that the standard deviation of phase fluctuations was about 180 mrad, as shown in Fig. 5(b). The stability was more than 5 times enhanced in terms of the standard deviation by adding the slow feedback loop. Thus, by adopting the direct locking technique and providing the slow feedback to the oscillator loop, we could stabilize the CEP of the amplified laser pulses to a good extent. Currently we demonstrated the CEP stabilization with the slow feedback loop during 180 seconds. However, the slow feedback has no limitation in the long-term stability; it should be extendable over several tens of minutes because our oscillator loop based on the direct locking technique could easily preserve the CEP locking for more than 2 hours [26]. The utilization of a tapered fiber coupler to the microstructure fiber in the f-2f interferometer helped the enhanced long-term operation of the oscillator CEP locking loop. Currently, the environmental noise factors of our CPA system, such as abrupt air fluctuation, thermal drift, mechanical vibration, and pump energy stability, are more problematic with the long-term stable operation.

 

Fig. 5. (a) Interferogram of SI signal with the slow feedback and (b) relative phase shift and probability distribution.

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Baltuska et al. [25] obtained a phase jitter of about 75 mrad by applying a slow feedback to a single amplifier Ti:sapphire system with non-grating-based stretcher and compressor. However, our laser system, consisted of two multipass amplifiers together with a grating based stretcher and compressor system, is far more complex and, hence, the CEP stabilization process becomes more delicate, particularly for long-term CEP stability. On the other hand, Li et al. [14] recently obtained a phase jitter of 170 mrad during 200 seconds by controlling the grating separation of a stretcher in their CPA system with a single amplifier. They showed the phase jitter and the long-term operation very comparable to our results even though they reported technical improvements more recently [15, 16], Nevertheless, we produced the highest-energy (4.2 mJ) pulses from a slow-feedback-assisted CEP-stabilized system with the help of two amplifiers. This is an important demonstration showing that the CEP locking technique can be extended to multi-stage CPA systems scalable to even higher energy. Therefore, the direct locking technique combined with an electronic slow feedback loop can be an alternative and reliable method of the CEP stabilization of high-power femtosecond laser pulses amplified in a CPA system.

4. Electronic CEP modulation

One of the distinctive features with our direct locking method is the capability of direct electronic CEP modulation as demonstrated in Ref. [17]. To maximize this advantage in our amplifier system, we also directly modulated the CEP of amplified pulses with an electronic method, which can be easily achieved by adding a shaped electric signal to the slow feedback loop.

To demonstrate the modulation capability, we intentionally altered the CEP of the oscillator pulses periodically by applying a 1-Hz square-wave signal with the amplitude of 150 mV through the slow feedback loop to the AOM using the direct locking electronics. The corresponding square-wave modulation was observed in the SI signal at 1 Hz, as clearly seen in Fig. 6(a). The amplitude of the CEP variation was estimated to be about 1 rad from this modulated fringe pattern. The amplitude modulation with the driving signal of higher than 150 mV (or 1 rad in phase) could not be applied because it made the mode-locking unstable. However, the CEP modulation can be higher than p in principle as long as the mode-locking is safely maintained. The intracavity prism of the laser oscillator can also be utilized for further modulation if necessary. Similarly, when we applied a saw-tooth modulation instead of the square wave, at the same frequency and amplitude, the shape of the fringe pattern followed the applied waveform quite well as is evident from Fig. 6(b). The modulation results confirmed that the shift in CEP was directly proportional to the applied feedback voltage level.

 

Fig. 6. CEP control achieved by applying an electrical modulating signal to the slow feedback (a) square wave signal and (b) saw tooth signal.

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The mechanical schemes using stretcher grating alignment [11, 14, 16] can be used for the slow feedback or CEP modulation. Even though they have wider tuning range of CEP than our electronic feedback method, the signal shape applicable to these schemes is limited to relatively simple wave forms and a misalignment can be induced when the feedback loop fails due to unexpected noise. On the other hand, an electronic method makes it possible to modulate the CEP with an arbitrary shaped signal. A similar electronic CEP modulation in the time domain with a conventional CEP-stabilized CPA system was recently demonstrated by supplying a slow sinusoidal signal and using lock-in analysis techniques [13]. However, our method based on the direct locking technique still provides more intuitive and versatile way of the time-domain CEP modulation because the locking and feedback processes are already realized in the time domain.

5. Conclusions

We have demonstrated the stabilization and electronic control of the CEP of high-power femtosecond laser pulses, generated in a grating-based CPA kHz Ti:sapphire laser, using the direct locking technique and the slow feedback loop. An f-2f SI was set up for monitoring the CEP evolution of the amplified laser pulses and providing the slow feedback signal. We measured the CEP stability of 1.2 rad only with the direct locking loop and 180 mrad with an additional slow feedback loop. The long-term operation of up to 180 seconds was demonstrated. The electronic CEP modulations with arbitrarily shaped signals that can be easily and intuitively realized in the direct locking loop was also successfully demonstrated with the amplified pulses, confirming the reliability of our technique. Our result also demonstrates the CEP stabilization, driven by a slow feedback loop for a good long-term stability, is achieved with the highest pulse energy of 4.2 mJ.

In conclusion, we extended the usefulness of the direct CEP locking technique to our femtosecond CPA laser system, so that the CPA laser can provide high-power CEP-controlled femtosecond laser pulses with a low phase jitter. Further improvement of long-term stability and the high-energy pulse compression technique using filamentation phenomenon will allow an efficient way of generating high-power CEP-controlled few-cycle optical pulses for attosecond science.