Since its original demonstration over a decade ago, carrier-envelope phase (CEP) control [1,2] of mode-locked lasers has come of age, with a recently demonstrated timing jitter between the carrier and the envelope pushed down to the sub-10-attosecond range [3,4]. Despite such impressive progress, CEP control is still limited to a rather narrow class of lasers, including Ti:sapphire and some other selected broadband solid-state materials as well as some mode-locked fiber lasers. CEP stabilization of high-power Yb systems has proven challenging due to rather long cavities and narrow gain bandwidth as well as the long upper state lifetime of the laser transition [5,6]. Moreover, CEP control becomes increasingly complex for amplified laser sources with energies in the mJ range [7]. Typically, stabilization of a CPA laser source relies on an intricate combination of two servo loops: a fast oscillator loop and a slow amplifier loop [8]. While the second loop is necessary to remove residual phase drift in the amplifier, unfortunately, it also corrupts the residual phase noise in the amplified pulse train due to the limited feedback bandwidth as a consequence of a low repetition rate of the amplifier and a slow readout of a nonlinear phase meter [9]. While oscillators can now be stabilized down to $\approx 10\mathrm{mrad}$ residual CEP jitter [3], 100 mrad stability for an amplified laser source already appears to be a challenge. Here we demonstrate a direct and versatile method to stabilize the CEP of an Yb:KGW MOPA laser system, resulting in sub-100 mrad stability. To the best of our knowledge, this value surpasses most previously measured CEP jitter for Ti:sapphire CPA systems as well as previously reported stabilization of Yb-based laser systems.

Analyzing the problems of the CEP control in amplified lasers, the measurement of CEP after amplification appears to be a major bottleneck [10]. Typically, a spectral-interferometry-based scheme [11] is employed for the purpose which requires averaging over 10 laser shots to avoid detrimental feedback from detection shot noise contributions. The bottleneck in this detection process is the number of useful photons in the narrow second-harmonic generation (SHG) conversion bandwidth of the $f-2f$ interferometer [12,13]. As shot-noise limited CEP detection appears much less challenging [11] for the oscillator heterodyning scheme [13] than for the spectral interferometry scheme used with amplifiers [12], we chose to combine the virtues of both approaches, detecting the CEP of a high-repetition-rate amplifier with the heterodyne scheme that has only been applied to oscillators so far.

In our experiments, we employed a commercial Yb:KGW regenerative CPA system (Light Conversion Ltd.) seeded by a solid-state Yb:KGW Kerr-lens mode-locked oscillator [14], see Fig. 1 for the general setup. The oscillator operates at a repetition rate of $f_{\mathrm{rep}}=75\mathrm{MHz}$. The amplifier repetition rate $f_{\mathrm{amp}}$ can be freely tuned up to 1 MHz. With the latter settings, the amplifier delivers an average power of 6 W and a pulse duration $<190\mathrm{fs}$. Our CEP detection scheme is based on in-line interferometers, as they are customarily used for amplifier measurements but have also been approved for use with oscillators [15]. The optical layout of our in-loop (IL) interferometer is shown in Fig. 2. Supercontinuum is generated in bulk sapphire with $\mathrm{\mu J}$ input energy from the amplifier. The resulting white light is collimated using a spherical mirror. A pair of wedges allows for adjustment of the relative group delay of the $f$ and $2f$ components. The light is then refocused into a BBO crystal for SHG, phase-matched at 530 nm. This results in orthogonally polarized $f$ and $2f$ components. The group delay between these components is then equalized in a 10 mm long birefringent quartz block. Finally, a polarizer heterodynes both polarizations and the beam is spectrally filtered before photo detection. A third $f-2f$ interferometer after the oscillator was used together with a phase-locked loop (PLL) for characterization of the amplifier noise discussed below. This interferometer is not part of the direct amplifier CEP stabilization scheme.

 

Fig. 1. General scheme of the frequency synthesis for the stabilization of a sub-MHz frequency comb from a regenerative amplifier (RA). The dashed box indicates a part of the setup that is necessary only for an in-depth characterization of amplifier noise.

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Fig. 2. Optical scheme of the in-line $f-2f$ interferometer based on white light generation (WLG) in a bulk sapphire crystal for beat-note detection. P, polarizer; SM, spherical mirror.

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The measured CEP beat note frequency $f_{\mathrm{CEO}}$ at the output of the interferometer lies in the range between 0 and 500 kHz. For CEP stabilization, we employed the feed-forward scheme [11]. This scheme employs an acousto-optic frequency shifter (AOFS) which is normally directly driven at the fundamental beat note $f_{\mathrm{CEO}}$. Given that our AOFS has a center frequency of 300 MHz, we have to use a higher-order beat $f_{\mathrm{AOFS}}=N{f}_{\mathrm{amp}}+f_{\mathrm{CEO}}$, with an integer number $N\sim 300$. In this case, direct filtering of the AOFS driver signal becomes very challenging. Detecting the interferometer output with a $>300\mathrm{MHz}$ bandwidth leads to a tightly spaced comb. Compared to a comb signal with $f_{\mathrm{rep}}$ spacing, the energy of the individual beat note is about 2 orders of magnitude lower which leads to a reduction of the electronic signal-to-noise ratio by 40 dB. The solution here is to use a slow photodiode with large detection area and synthesize $f_{\mathrm{AOFS}}$ by mixing the fundamental beat with a suitable harmonic of the amplifier repetition rate. The photodiode used in the experiments exhibits a $13{\mathrm{mm}}^2$ active area (Thorlabs PDA36A, used at $75\mathrm{k\Omega }$ transimpedance). The capacity of the diode in combination with the high gain act as a lowpass filter and limit the bandwidth to $\approx 150\mathrm{kHz}$. This bandwidth is sufficient for measuring the fundamental beat over a significant part of the free spectral range. The noise-equivalent power (NEP) of our photodectector is specified as $\approx 1\mathrm{pW}/\sqrt{\mathrm{Hz}}$. With a measured power of 35 μW on the detector, we therefore expect that shot noise ($\sim 4\mathrm{pW}/\sqrt{\mathrm{Hz}}$) dominates the noise floor. Identical signal strength of the $f$ and $2f$ signal provided and assuming the absence of out-of-band contaminations, these settings should readily enable a beat note visibility of more than 60 dB in a 100 kHz bandwidth which clearly illustrates the potential of our method.

We synthesize the driver signal from the fourth harmonic of the oscillator repetition rate and the amplifier carrier-envelope frequency, i.e., $f_{\mathrm{AOFS}}=4f_{\mathrm{rep}}+f_{\mathrm{CEO}}$. We employ an intermediate frequency scheme to suppress mirror frequencies and other spurious contributions, see Fig. 3. This scheme employs a narrow bandpass filter (RF Monolithics, PX1004-1, 82.2 MHz center frequency, 80 kHz 3 dB bandwidth). In the first mixing step, the fundmental beat is upconverted to the center frequency of the filter using a local oscillator at $\approx 82\mathrm{MHz}$. Figure 4 shows the measured rf spectrum prior to narrow bandpass filtering. For comparison, Fig. 4 also shows the signal that is obtained when the interference is disabled by inserting a glass plate into the beam path of the $f-2f$ interferometer. The observed visibility of the beat note indicates that residual phase jitters well below 100 mrad are possible [16].

 

Fig. 3. (a) A general scheme of the frequency synthesis for the stabilization of a sub-MHz frequency comb from a regenerative amplifier (RA). (b) The narrowband tunable frequency filter scheme.

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Fig. 4. Radio frequency spectrum after mixer M1, where the signal from the photodetector is upconverted by mixing it with a local oscillator. For comparison, a reference spectrum is shown where the $f$ and $2f$ components are delayed, and the beat note is suppressed. Beat note visibility is 55 dB in a resolution bandwidth of 6 Hz.

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Using out-of-loop characterization with a second inline interferometer, we carefully analyzed the performance of our CEP stabilization scheme, see Fig. 5. This analysis indicates a residual rms jitter of $\sigma =87\mathrm{mrad}$. The inset of Fig. 5 shows a histogram representation of raw spectral interference patterns to further illustrate the surprisingly low phase jitters obtained with our scheme. It should be noted that the bandwidth of our scheme relies on the narrowest filter (80 kHz bandwidth) in the frequency synthesis scheme (Fig. 3). Moreover, the acoustic travel time in the AOFS is of the order of a microsecond and certainly did not limit the obtained performance.

 

Fig. 5. (a) Out-of-loop CEP jitter measurement after the amplifier. (b) Inset: $f-2f$ interferogram fringes. The spectrometer integration time was kept at a minimum and averaging is done over 6 laser pulses.

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Generally, CEP noise in an amplified laser system may originate from the oscillator or from the stretcher/compressor pair and the regenerative amplifier (RA) itself. These two contributions, $\mathrm{\Delta }{\phi }_{\mathrm{osc}}$ and $\mathrm{\Delta }{\phi }_{\mathrm{cpa}}$, respectively, are noncorrelated. The total resulting phase jitter amounts to

 

Fig. 6. Phase noise spectrum density (PSD) and integrated phase noise measurement of an amplifier running at repetition rate $f_{\mathrm{amp}}=600\mathrm{kHz}$. The noise floor (gray line) is obtained by delaying the two colors in the $f-2f$ interferometer and represents the measurement sensitivity.

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The measured phase jitter corresponds to $\approx 230\mathrm{mrad}$ which is about three times larger than the value deduced from Fig. 5. Despite the slightly different measurement methods, this finding clearly corroborates the superior noise performance of our novel direct amplifier stabilization approach. In principle, the origin of this noise may either be the low sensitivity of the oscillator $f-2f$ interferometer or a large amount of excess noise in the amplifier. If the latter were true, one would expect to see a structured noise spectrum rather than a flat plateau. In particular, the practical absence of line frequency harmonics implies that we are actually seeing the limitations of the oscillator stabilization here [16]. In any case, it appears challenging to reduce this broadband 230 mrad noise signature with the traditional slow spectral interferometry approach [12] typically employed for amplifier stabilization.

Here we demonstrated unprecedented sub-100 mrad CEP jitter for an amplified ytterbium-based amplifier system. The scheme is currently applicable for intermediate laser pulse energy in the $\mathrm{\mu J}$ range, essentially limited by self-phase modulation and optical damage in the AOFS. Investigations are underway to remove the acousto-optic component from the unattenuated amplifier output which will eliminate the corresponding power limitations. A further constraint arises due to the bandwidth of the noise spectrum of the oscillator [9]. The current scheme enables phase noise removal at frequency components up to $1/2$ of the amplifier repetition rate. Given the advantage of rf heterodyning, the scheme is most effective in laser amplifiers operating at a higher repetition rate, 10 kHz or above. In conclusion, our scheme significantly widens the scope of feed-forward stabilization. High pulse energy $\approx 200\mathrm{fs}$ Yb amplifiers offer an efficient way to attain few-cycle pulses through nonlinear pulse compression schemes and optical parametric amplifiers, with the latter being seeded and pumped by a single Yb laser source. Demonstration of a sub-100-mrad CEP jitter at the Yb amplifier output, therefore, radically simplifies the task of deriving usable CEP-stable few-cycle waveforms from Yb driver lasers. We therefore think that our novel scheme paves a way to combine the efficiency and output power scalability of ytterbium-based materials with the precision previously only obtained with Ti:sapphire-based approaches.