1. Introduction

The progress in shortening the pulse duration of femtosecond oscillators, down to a few optical cycles [1-2], led to the necessity to control precisely the position of the carrier wave within the pulse envelope. The stabilization and control of this Carrier Envelope Phase (CEP) allowed a spectacular breakthrough in optical frequency metrology [3–5]. At the same time, amplified femtosecond laser systems with sub-10 fs duration [6–8] became available and started to be used in Strong Field Physics to study phenomena which often depend strongly on the CEP. Generation of single isolated attosecond pulses through high order harmonic generation [9–11] is probably one of the main examples. For such applications, CEP stabilization of the amplified pulses is essential.

Over the last years, a lot of work has been carried out in order to achieve CEP stabilization of laser systems based on Chirped Pulse Amplification (CPA) [12]. The offer is now quite large, starting with medium energy (less than 5 mJ) lasers, using prisms or transmission gratings based stretcher/compressors [13, 14]. Higher pulse energy, close to or beyond 10 mJ, is now also available using grating-based stretcher/compressors associated with multi-stage amplifiers [15–19]. These latter systems should be scalable to higher energies.

In this paper, we report long-term CEP stabilization of a Titanium: Sapphire (TiS) CPA laser operated at 1 kHz with a large stretching factor. After detailing the laser system, we will describe the original CEP stabilization scheme that we implemented. This scheme, that we proposed recently [20], is based on the linear electro-optic effect in a LiNbO₃ crystal. With this system, we reduced the shot to shot residual CEP noise down to 440 mrad rms at 20 mJ pulse energy (before compression). At lower energies, in the mJ range, the rms CEP noise is kept around 300 mrad. These results are, to the best of our knowledge, the first experimental demonstration of long term CEP stabilization using this technique.

2. Laser system description

Our CEP stabilized laser system has been developed within the IMPULSE laboratory which is a common R&D laboratory associating CEA Saclay and Amplitude Technologies. It relies on the use of a diffraction-grating based pulse stretcher–compressor system and regenerative and multi-pass amplifiers (Fig. 1 ).

 

Fig. 1 Schematic of the CEP-stable 20W range kHz laser. The electro optic device for CEP control uses a LiNbO3 crystal.

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The seed oscillator is a 20 fs-Synergy CEP stabilized oscillator from Femtolasers GmbH that delivers 11 fs pulses (spectral width: 65 nm, non-gaussian distribution) with an average power of 650 mW at 74 MHz. A XPS800 Menlo Systems f-0 interferometer is used for locking the CEP of the oscillator [3] leading to an in-loop residual noise between 100 mrad and 150 mrad rms.

The CEP stabilized pulses are seeded through a specifically designed Öffner stretcher with reduced path length. The dispersion of the stretcher is about 6 ps/nm. The stretched pulse duration is long enough to allow pulse amplification up to 100 mJ with limited B-integral effects. The overall beam path is approximately 6 meters long. The specific design of the mechanical mounts lowers the sensitivity of the stretcher to vibrations and thus insures a better CEP stability.

The stretched pulses are then sent through the Electro Optic CEP control device (EOCEP) which allows us to compensate most of the slow CEP drifts occurring in the whole laser system. It is composed of an AR coated 4 cm-long, 4 mm-thick LiNbO₃ crystal coupled to a High Voltage (HV) amplifier [20]. At this step, the average power of the stretched oscillator is 40 mW.

The first amplification stage is a standard regenerative cavity. A pulse picker reduces the repetition rate to 1 kHz prior to amplification and two KD*P Pockels cells are used for seeding and dumping the cavity. Finally, a pulse cleaner is used at the regenerative amplifier output. The regenerative amplifier is pumped with 6.5 W of a 1 kHz frequency-doubled Q-switched Nd:YLF laser. Saturation is achieved after 12 cavity roundtrips leading to an average power of 0.5W after the pulse cleaner.

The pulse is then amplified in a 4-pass butterfly-like amplifier, pumped with 11 W, leading to a power of 3.5 W with a standard deviation as low as 0.15%. This amplified pulse can either be sent to the compressor to perform CEP measurements at “low” energy or be seeded in an additional “high” power cryo-cooled 4-pass butterfly like amplifier. This stage is pumped with 3 Q-switched Nd:YLF lasers with a 60 W total pump power. The TiS crystal is mounted on a vibration free 100W cryo-cooler head. The energy of the amplified pulses reaches 20 mJ with a standard deviation of 0.3%. After compression the energy is 13 mJ with 40 fs pulse duration.

This laser system is installed on the first floor of a conventional building and is therefore subject to a high level of vibrations. In order to reduce the resulting disturbances due to vibrations, the optical table of the laser system is mounted on specific anti-vibration rubber sheets. The different parts of the laser shown on Fig. 1 are maintained inside separate boxes and a final overall cover is set on the whole optical table to minimize the CEP disturbance caused by air flow.

3. CEP stabilization

The CEP drift was measured using an in-house developed collinear f-2f interferometer [21]. Spectral broadening is performed in a 2 mm-thick Sapphire plate and we use a 1 mm-thick BBO crystal (type I) for frequency doubling at 1 µm. The spectral f-2f fringes are detected using an Acton-SP2356i (300 mm focal length) spectrometer coupled with a line-scan camera (Aviiva SM2 CL 2014).The acquisition repetition rate can be as high as 5 kHz. Our software, including the fringe pattern processing for CEP value calculation, allows continuous single-shot acquisition at 500 Hz or a burst–mode acquisition of 2500 successive single-shots at 1 kHz with an idle time of 300 ms between consecutive burst acquisitions. In order to minimize the latencies, we disabled all non-necessary programs and drivers in our Windows operating system. However, this cannot guarantee a perfectly constant repetition rate of our software. When using the software controlled feedback loop described later in this paper, the acquisition frequency drops down to 100 Hz. Due to the operating system latencies, the data acquisition repetition rate can be lowered to about 50 Hz.

The CEP stabilization was carried out with an original slow feedback loop based on the linear electro-optic effect (EO loop). We have shown [20] that a pulse going through the crystal undergoes a CEP shift that varies linearly with the voltage applied to the crystal. The laser pulse has to be polarized in the same direction as the electrical field in the crystal resulting from the applied high voltage (HV). The induced phase shift Δϕ_CEP is proportional to the crystal length L and to the electrical field E, depending also on the extraordinary refractive index n_e, on the electro-optic coefficient r₃₃ and on the carrier frequency λ₀. It can be written as:

In the set-up we implemented here, the crystal was placed after the stretcher and was used in a two-pass configuration. The dynamic range for the correction was thus increased by a factor of two. The HV amplifier we used could scan a range between ± 4 kV leading to a possible CEP correction up to ± 24.8 rad. The maximum repetition rate of this HV amplifier without saturation is 100 Hz.

The linear dependency of the induced CEP shift as a function of HV exhibits for a single pass a 3.5 rad/kV slope [20] at 800 nm. The CEP measurements are performed with our fast f-2f and it is possible to convert, in the software, the measured CEP value to a corresponding voltage V_m. A software controlled PCI card sends this voltage to a 100 kHz bandwidth external Proportional-Integral-Derivative controller (PID SRS SIM960). The setpoint value V_T is fixed with the PID controller which determines the error ε = V_T - V_m, between the target value V_T and the measured one V_m. The correction voltage V_C is obtained from the error ε using:

P, I and D are respectively the proportional, integral and derivative gain coefficients that can be independently enabled or zeroed as well as the Offset value. The correction voltage V_C is then sent to the HV amplifier which applies the appropriate HV to the LiNbO3 crystal in order to correct the CEP variations and set the CEP at the chosen target value. In the experiments we used only the P and I gain coefficients. This sequence is performed for successive f-2f acquisitions in the single shot mode as well as in the averaged one. It constitutes then the slow feedback loop applied on the LiNbO3 crystal, independently from the oscillator fast feedback loop. Voltage V_m is sent by the software to the PID device at roughly 100 Hz but its coefficient I lowers the correction rate to an expected correction bandwidth of about 0-20 Hz. A schematic layout of the CEP stabilization system is shown in Fig. 2 .

 

Fig. 2 Schematic layout of the CEP stabilization system including both fast and slow feedback loops. F_rep and F₀ are respectively the repetition rate and the Carrier Envelope Offset of the oscillator.

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The measured CEP variation after the two first amplifiers (3W output) is displayed on Fig. 3 for different configurations. In the upper part (a), one can observe the large slow variation of the CEP of the amplified laser when no slow loop is applied. The red curve is for shot-to-shot measurement; grey dots are CEP measurements averaged over 10 ms (10 shots). The variation of the CEP over 10 minutes spans a ± 15 rad range. When applying the EO loop (b), after optimizing the P and I coefficients using the closed-loop Ziegler-Nichols method [22], the CEP is regulated. This works typically over a period of half an hour: the residual rms noise drops down to 320 mrad and 130 mrad respectively for the shot to shot and 10 ms averaged measurements. Both statistical distributions of the stabilized CEP values are Gaussian.

 

Fig. 3 Shot to shot (red dots) and 10 ms averaged (grey dots) measurement of stabilized CEP drift over 10 min of amplified pulses at 3 W output (a) without slow feedback control. (b) with EO feedback loop over 25 min leading to rms CEP noise of respectively 320 and 130 mrad and (c) over 7 min of amplified pulses at 20 W output leading to rms CEP noise of respectively 440 and 250 mrad.

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Measurements have also been performed at higher output power using a cryo-cooled amplifier leading to 20 W output power before compression. The remaining rms CEP noise was found to be about 440 mrad rms (single shot) at this high energy yield. The statistical distribution is still Gaussian in the 20 W case, even if the rms noise is significantly higher (Fig. 3c). This CEP noise is therefore significantly higher than what we obtained at 3 W but the EO loop is still as efficient as at a lower power output. On the one hand, the degradation seems not to result from small vibrations of the cryo-cooler head or cooling system. It is to be noticed that when the cryo-cooler is set ON and the beam is not going through the last amplification stage (3 W output), there is no perturbation on the CEP. This shows that the vibrations due to the cooling system are correctly isolated from the optical table. On the other hand, the beam pointing instabilities in the Brewster windows of the vacuum chamber and the TiS crystal can induce small changes in the optical path length and, consequently, can cause a degradation of the CEP stability. A higher pointing instability in the compressor can also cause such a CEP noise increase. We have performed calculations of this pointing instability effect which could confirm those effects. Another possibility could be a higher f-2f detection noise due to the energy instability which is two times higher at 20 W. Nevertheless, the residual CEP noise of 440 mrad rms (single shot) for an output power as high as 20 W still corresponds to an interesting level of stabilization.

Finally, for the shot-to-shot as well as for the 10 ms averaged measurements, one can observe independently of the output power, a very good stabilization with a very regular shape of the slow CEP drift over a large time scale. The Power Spectral Density (PSD) corresponding to the shot-to-shot measurements without and with EO feedback loop at 3W output are shown in Fig. 4 . The acquisition frequency window is limited to 50Hz as described above. Without the EO feedback loop, one can see two peaks between 10 Hz and 20 Hz. When applying the EO correction loop, the PSD is globally lowered up to 15 Hz and the main peak at 12 Hz disappears. This correction bandwidth is consistent with the 0-20 Hz expected. However, this data is mostly indicative since only in-loop measurements have been performed. An out-of-loop analysis would be necessary to be more precise. This result is connected to the wide phase correction range, close to ± 25 rad that is achievable with this method. It is significantly larger than the one obtained when we apply the slow loop on the oscillator. Indeed, when the slow feedback loop applied on the oscillator has to correct large CEP drift, we observed that it could deteriorate the operation of the fast feedback loop and increase the remaining CEP noise.

 

Fig. 4 Power Spectral Density of the shot to shot measured CEP noise at 3 W output (no cryo-cooler) without EO feedback loop (black line) and with EO feedback loop (red line). The blue arrows show the CEP perturbation peaks when the EO loop is set OFF.

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4. Conclusion

We have presented the CEP stabilization of a chirped pulse amplified laser system using a large stretching ratio together with regenerative and cryo-cooled amplifiers. Despite an environment which was not optimized for CEP stabilization, we obtained a residual CEP noise as low as 320 mrad rms shot to shot at 3 mJ output and 440 mrad at 20 mJ output. These results have been obtained with a new method for the stabilization of the CEP based on the linear EO effect allowing a fast and efficient slow feedback loop. This is the first experimental demonstration that EO effect in a linear crystal can be used in order to correct the CEP drift of an amplified system over a long time. This original technique has many advantages. For instance, its implementation is straightforward and it allows correcting the CEP drift over a very large range. In our double-pass configuration, the correction range was as large as ± 25 rad but it can be further increased since it depends linearly on the crystal length and the applied voltage.

The correction was achieved at a repetition rate lower than 15 Hz. This was mainly due to our HV amplifier and to the digital acquisition and processing of the CEP drift. The short response time of the EO device allows efficient CEP drift correction for higher repetition rates. We are confident that this technique will be used in the future for faster CEP correction and we are currently studying this topic in the laboratory.