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Abstract
The arrival time jitter and drift of the photocathode drive laser has an important impact on the performance of a Free-Electron-Laser (FEL). It adversely affects the beam energy jitter, bunch length jitter and bunch arrival time jitter, which becomes especially important for pump-probe experiments with femtosecond time resolution. To measure both parameters background free and stabilize the drift of the Yb:CaF2 based laser we use a well designed balanced optical cross correlator. In this paper we present our results using this device and focus particularly on the performance of the amplifier. We achieve a laser drift of less than 200 fs during 60 h, a 4.5 fs rms jitter of the amplifier relative to its seeding oscillator and 11 fs rms for the whole laser relative to a reference clock integrated from 2 mHz to 100 Hz.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
SwissFEL is a relatively compact hard x-ray free electron laser operating in the self-amplified spontaneous emission mode. It runs with two beam lines named Aramis and Athos as outlined in Fig. 1. Aramis has been in operation for users since 2018 delivering photons in the wavelength range 0.1 – 0.7 nm. Athos went into operation in 2020 covering the wavelengths between 0.65 nm and 5 nm [1,2]. In order to get such a FEL ready for precision experiments, a high reliability and very high accuracy is needed for many components und subsystems in space and in time. In case of Aramis for example the nominal 4.7 mm gaps between the 1060 permanent magnets in each of the 13 undulators, the amplifiers of a free electron laser, have to be aligned with a precision better than 1 $\mu$m [1]. Additionally, sub-10 ps UV optical laser pulses release electron bunches from a CsTe$_2$-photocathode with a repetition rate of up to 100 Hz. Those bunches are then accelerated, compressed longitudinally by about a factor 100 and accelerated again, in case of Aramis by a total of 32-radiofrequency stations until they finally radiate in the undulators femtosecond scale photon pulses. This performance needs an outstanding timing of all involved components. Therefore, the question arises how much timing jitter and drift can be accepted in order to keep the entire machine within specified limits?
Fig. 1. Schematic drawing of SwissFEL. The picture, slightly modified, was taken from [7]. The total length of this machine is 740 m. The photocathode laser beam, injected at the left, delivers sub-10 ps pulses on a CsTe$_2$ cathode. The FEL emits fs-scale x-ray pulses at the end. Their drift and jitter in space, energy and time has to be minimized.
Beutner and Reiche [3,4] gave the answer to this multi-parameter problem. They made start-to-end simulations of the whole machine where they demanded limits for arrival time-, current- and energy- jitter for electron bunches before they enter the first undulator [5]. Geng et al. [6] experimentally confirmed the simulated findings and showed that the machine has even less jitter in arrival time and energy than demanded, but not in current which they attributed to a few of their radio frequency stations. For the optical drive laser pulses at the cathode the simulated results give an acceptable timing jitter of about 40 fs rms under nominal operation conditions.
In this paper, we discuss the timing stability of our photocathode drive laser together with a well designed balanced optical cross correlator. We show that the probe beam and the reference beam of this cross correlator can be made collinear without sacrificing the signal to background ratio even though they have the same color. At the same time, it will be shown that the pulse jitter of the laser stays well below the demanded limit of 40 fs rms, which corresponds to seven percent of its pulse width FWHM. In addition it will be seen that drifts over long time periods can efficiently be removed even under harsh conditions.
2. Photocathode laser setup
The laser setup is visible in Fig. 2. The advantage for choosing this photocathode laser is its low maintenance cost which is accompanied by compactness, simplicity and excellent passive stability [8]. The setup begins with an Origami10 oscillator (OneFive GmbH (now NKT Photonics), Switzerland) based on a Yb-doped gain medium. The oscillator is designed for stable long-term operation with ultra-low phase noise as can be seen in Fig. 3. The only moving part in this laser is a mirror on a piezo transducer which provides a resonator tuning range of 100 Hz. Approximately 1.8 kHz/$^{\circ }$C can be added by temperature tuning. The additional parameters are as follows: center wavelength: 1042.3 nm, repetition rate 71.4 MHz, transform limited pulse width: < 200 fs, main output power: 150 mW. The output pulses and the spectrum have a clean shape (no pedestals). The pulse amplitude noise is exceptionaly low, $0.2 \%$ rms, and the timing jitter is 17 fs rms (integrated from 10 Hz to 10 MHz indicated as well in Fig. 3) if phase locked via it’s 42nd harmonic to the 21st harmonic of a low phase noise reference, an OneFive Origami15 the clock of SwissFEL [9]. To measure the phasenoise about 3mW are tapped from the oscillator and guided via fiber to an EMCORE 2651E photodiode. A narrowband band-pass filter centered at 2998.8MHz filters the 42nd harmonic out of the frequency comb. This filter has an insertion loss of about 1.2dB. Two radio frequency (RF) amplifiers raise the low RF signal to an level which can be measured by the phasenoise analyzer Holzworth HA7062C. The two amplifiers are an ZX60-53LNB-S+ and an ZRL-3500+ from Minicircuits. The noise figure of the first amplifier is about 1.4dB. In combination with the insertion loss of the bandpass filter about 2.6dB of signal-to-noise ratio are lost. The measurements with the Holzworth phasenoise analyzer are done with 100 cross-correlations in order to obtain a good signal-to-noise ratio. The reference is a ultra-low noise RF source SMA100B from Rohde and Schwarz with the option SMAB-B711N (ultra-low phasenoise option) set to 2998.8MHz. To the best of our knowledge this is currently the lowest phasenoise RF source available on the market.
Fig. 2. Setup of the photocathode laser. The Laser Arrival Monitor (LAM) includes the cross correlator. It allows us to measure timing jitter and to feedback timing drift.
Fig. 3. Phase noise power spectral density of the Origami10 oscillator laser pulse train. Blue: oscillator free running, Brown: oscillator in lock, Green: the low phase noise signal generator SMA100B from Rhode $\&$ Schwarz, the radiofrequency source of the FEL common clock, for comparison. Integration of the spectra gives, after Parseval’s theorem, the rms timing jitter which is 552 fs rms for the free-running , 17 fs rms for the locked oscillator and 15 fs rms for the SMA100B within 10 Hz to 10 MHz. The measurment was done with a carrier frequency of 3 GHz.
The pulse picker can select pulses with any repetition rate from single shot to 100 Hz. Picked pulses seed an Yb:CaF$_2$ based chirped pulse regenerative amplifier (Amplitude Systems, s-Pulse HP), that amplifies them to an energy of up to 3 mJ and increases the pulse width to 550 fs FWHM. Part of an amplified pulse is guided to the Laser Arrival time Monitor (LAM) where it overlaps with one oscillator pulse out of the residual pulse train from the pulse picker. The main part of the amplified pulse is converted to 260 nm with an efficiency of around 10$\%$, mode cleaned, stretched to any desired value between 3 ps and 10 ps FWHM, top hat cut by an iris and imaged to the photocathode [10]. The relatively large fluorescence lifetime of 2.4 ms [11] makes the Yb:CaF$_2$ crystal a very effective storage medium. But the real advantage of Yb:CaF$_2$ laser crystals used as laser amplifying media for sub-ps lasers is that they can be pumped by diode laser stacks at 980 nm, which results in a high quantum efficiency making the laser very compact and cost-effective. By comparison, titanium sapphire lasers for example suffer currently from the lack of direct diode laser pumping and therefore need other comparatively complicated and expensive pump lasers itself. However, there is also a drawback: the single pass gain of the Yb:CaF$_2$ crystal is small and therefore the buildup time of the regenerative amplifier is 4 $\mu$s which is equivalent to a travel distance of 1.2 km. For comparison again a titanium sapphire amplifier shows up with a buildup time of only around 100 ns which is equivalent to a travel length of 30 m. The long propagation distance makes the Yb:CaF$_2$ laser amplifier highly susceptible to changes in environmental parameters like temperature, pressure and humidity as well as mechanical vibrations (see section 6). This can cause the amplifier laser jitter and drift easily exceed that of the oscillator whereas within the titanium sapphire laser user community the contribution of drift and jitter from the amplifier is usually neglected (for comparison: drift and jitter between oscillator and amplifier of the SwissFEL experimental titanium sapphire lasers (oscillator: Vitara, amplifier: Legend, both from Coherent Inc., parameters: repetition rate: 100 Hz, max. energy/pulse: 27 mJ, pulse width: 30 fs, one regenerative amplifier (12 passes), two one pass post-amplifiers [12]) amount to 0.8 fs/mbar/m (drift) and 5 fs rms (jitter)).
We will show further on, that even with a laser pulse buildup time inside the regenerative amplifier of the photo cathode laser as long as 4 $\mu$s, the laser pulse drift and jitter from the amplifier can, with a careful design, be kept well below of those from the oscillator (see section5).
A measurement of the free running laser amplifier drift in reference to its seed oscillator is visible in Fig. 4(a). Fig. 4(b) presents the dependence of the FEL photon pulse energy on the laser timing delay. A delay of one ps can cause a photon energy drop of 30$\%$ which makes the demand for a laser timing stabilization obvious. This is even more stringent in case of pump-probe experiments where an x-ray pulse and an optical laser pulse is involved.
Fig. 4. a.) Laser arrival time drift at the output of the laser amplifier, measured during 20 days relative to an oscillator pulse without active feedback. b.) FEL x-ray pulse energy dependence on the photocathode laser timing delay without additional timing feedbacks. The FEL was setup to deliver a photon energy of 11 keV. The delay was initiated by a mirror on a translation stage (green dots) and measured in addition via an electron beam arrival time monitor (red curve) [13]. Unfortunately the delay does not show a stair case function because the available delay stage was too coarse for this scan. Nevertheless, since the encoder was appropriate the visible reading is correct.
3. Single color collinear balanced cross correlator
3.1 Setup
Laser arrival time monitors are used to compare the relative timing of short pulses emitted by a probe laser to short pulses emitted by a reference laser. If it is intended to measure temporal fluctuations with upmost precision one has to detect them independently of amplitude fluctuations and drifts of both the probe beam and the reference beam. This can either be done by spectral encoding [14,15] or by balanced detection [16,–22,25,26]. A cross correlator based on spectral encoding translates a temporal delay into a spatial deviation via time to frequency (chirp) and frequency to space (dispersion) mapping. Here the beam of the reference laser gets correlated with a selected color of the beam from the probe laser. This works only if at least one laser has sufficient spectral bandwidth and pulse energy. Since in our case both laser beams have a narrow bandwidth (amplifier $\sim$3 nm, oscillator $\sim$7 nm) this approach is not possible. Thus the natural choice was the balanced detection method. Moreover, as can be seen later, this technique perfectly serves the required capture range and resolution for the laser temporal jitter as well. The setup of the cross correlator is shown in Fig. 5. The cross correlation is performed via sum frequency generation (SFG). The general idea here is to generate two preferably identical and symmetric signals with a certain delay. Taking the difference of these two signals results in the so called S-curve which has a zero crossing to which the laser gets stabilized (see inset in Fig. 5). The signals are obtained via a delay scan of the seed pulses after the pulse picker relative to the pulses of the residuals which are not picked (see Fig. 2). One pulse out of the residual oscillator pulses overlaps with one amplified seed pulse in the nonlinear crystal. The fixed delay is obtained by inserting $\alpha$-BBO ($\alpha$-BaB$_2$O$_4$) crystals with different thickness into both channels (see Fig. 5, for a detailed analysis see section 3.3). LBO (LiB$_3$O$_5$) is used as nonlinear medium together with type-2 phase matching. LBO is known to be very effective in generating green light (here 521 nm) from near infrared light (here 1042 nm). With a crystal thickness of $l=5~mm$ the phase matching bandwidth is 7.5 nm @ 1042 nm which is the FWHM of the ${Sinc[\Delta k\frac {l}{2}]}^2$ function where $\Delta k$ is the phase mismatch. This is sufficiently beyond the spectral width of the laser pulse (3.2 nm).
Fig. 5. Setup cross correlator, L : lens, P : polarizer, BS : beam splitter, LBO : Lithium Triborate, F : band pass filter, D1,D2 : detector. Inset: Sum frequency signals and S-curve between amplifier pulse and oscillator pulse from the two channels obtained after a scan. For a Gaussian signal shape the delay for max. steepness is given by 0.85*FWHM. The delay is fixed by the optical path length difference between the two $\alpha$-BBO crystals which have a different thickness.
3.2 Optimum parameters for a strong and steep S-curve signal
To enable an optimum timing feedback for reducing the low frequency fluctuations and eliminating the timing drift of the laser pulse it is important to have the S-curve as steep as possible. In case the cross correlator delivers Gaussian signal shapes from its both channels the zero crossing of the S-curve has its steepest value if the delay between the two SFG-signals is 2$\sigma$ where at the deviation $\sigma$ the intensity of the Gaussian signals drops to 1/e of their maximum value. This is equivalent to $1/\sqrt { 2 Ln2} = 0.85$ times the individual signal width (FWHM) which can be seen in Fig. 6 (compare with inset of Fig. 5 as well). If one would refer to incoming Gaussian shape laser pulses before sum frequency generation one has to consider the convolution in the crystal and the optimum delay would be $2\sqrt {{\sigma _1}^2 +{\sigma _2}^2}$ as indicated in [20] where here $\sigma _1$ is the pulse width of the reference and $\sigma _2$ that of the probe incident laser pulse.
Fig. 6. Slope (a) and peak to peak height (b) of the S-curve as a function of delay/pulse-width for a Gaussian and a Sech$^2$ cross correlation signal shape. The vertical lines show the delay for maximum slope.
3.3 How to avoid background with strong pulses, mono color and collinear beams
In the foregoing section it has been shown how to generate a signal with a cross correlator. But more important than having a strong signal is to have a large signal/background ratio. Where the background comes from and how to minimize it will be presented in the following.
The background can come from any laser light incident on or generated by the nonlinear crystals as long as it can pass through the band pass type optical filters mounted in front of the photo detectors. Most of the cross correlators described in the literature are built for two lasers with different wavelengths, which has the big advantage that one can completely filter out the color of interest from any background light. But in the special case given here the reference laser beam and the probe laser beam have the same wavelength. Therefore it is evident that the background is generated by Second Harmonic Generation (SHG)-light since this has the same wavelength as the signal which is generated by Sum Frequency Generation (SFG)-light. In addition, the situation becomes even more pronounced since for ease of alignment we want to use a collinear setup for the probe and reference beam. Finally, we do not compare pulses from an femtosecond oscillator with those from another femtosecond oscillator like in [16–21] and [25,26] but pulses from an femtosecond amplifier with pulses from an femtosecond oscillator (like in [22–24] where only [22] uses balanced detection). That in addition has a strong influence on the background light.
The integration time for generating a signal is in our case approximately $500~ns$, which is given by the convolution of the bandwidth of the photodiode amplifier and the speed of the high resolution Analog to Digital Converter (ADC) we use. In this time interval two 100 MHz oscillators would contribute 50 correlation signals but the 100 Hz amplifier pulse train correlated to such an oscillator pulse train can at most contribute only one. In order to get the same signal level the amplifier pulse therefore has to have 50 times the energy of an oscillator pulse. The background SHG-light energy goes with the square of the incident pulse intensity. Therefore one encounters 25 times more background from the amplifier pulse than from the pulses of two oscillators during the above mentioned integration time if in both cases the signal pulses can be gated properly by an boxcar integrator. This value can even increase in reality since one is tempted to increase the focal size of the amplified beam (and therefore as well the incident energy to keep the same intensity) relative to the one of the oscillator beam in order to decrease the influence of pointing jitter.
There are two known ways to circumvent this problem: One can use a non-collinear setup [22] or one can use type-2 phase matching, which employs perpendicularly polarized beams (see [18,20] and even more advanced [25] where laser timing jitter was measured on a 14 as level (above 10 kHz) or in [26] where a noise floor of 122 ys/$\sqrt {Hz}$ was reached using a combination of balanced optical cross correlator and cross-spectrum techniques). In the ideal case of type-2 phase matching there should be no SHG-light under perfect conditions which means first of all perfect linearly polarized laser beams. In reality, however SHG-light can easily have the same signal amplitude as SFG-light especially for a collinear setup. The reason for this behavior is stress birefringence in the optical elements, which adds to the initially well linear polarized light a weak amount of elliptical polarized light. Because of this effect we found the traditional type-2 matching technique alone as not being sufficient for us. In order to avoid SHG-light we implemented two methods: First we placed Glan polarizers directly in front of the beam splitter/combiner for the two beams (see Fig. 5, BS). These polarizers are known to have an extinction ratio of at least $10^{-5}$ which cleans up the polarization at this point. This leaves only the beam splitter as a depolarizing source before sum frequency generation in the LBO crystals takes place. In order to compensate for the latter we add an $\alpha$-BBO crystal into both arms just in front of the LBO crystals. Alpha-BBO is the high temperature phase of BBO and has a different crystal structure than $\beta$-BBO. The crystal is birefringent but centrosymmetric and therefore SHG, SFG and difference frequency generation are forbidden. The delay bandwidth for the crystal is quite large. Across the bandwidth of the laser beam ($\pm$ 1.6 nm) there is only a $\pm$ 0.3 fs additional delay between the ordinary and extraordinary beam due to dispersion. This makes that crystal a perfect piece of fixed delay between orthogonal polarized beams for the here encountered conditions. The thickness difference between the crystals in the two arms gives an independent parameter to optimize a fixed delay for generating the S-curve. The crystal birefringence adds already a big delay in zero order dispersion to the perpendicular polarized probe and reference beams as given by $\Delta t=d/c (n_0- n_e )$ so that one mm generates already a sufficient delay for the 550 fs FWHM long pulse. Here d is the thickness of the crystal, c the speed of light, $n_0$ the ordinary and $n_e$ the extraordinary index of refraction. Additionally each crystal adds a delay between the two polarization axes (see Fig. 7) of each pulse itself so that SHG can be avoided if the crystals are thick enough. Finally we choose d = 4.95 mm for one channel and d = 6.23 mm for the other channel. No SHG background could be detected anymore within the sensitivity of the ADC.
Fig. 7. The polarization of the amplifier pulse has a horizontal and a vertical component due to depolarization in optical components. The picture shows the pulse delay of the originally time overlapping components after a thin $\alpha$-BBO (a) or a thick $\alpha$-BBO (b) crystal. Just adding a thin crystal in only one arm would repeat the situation given in [16] i.e. a fixed delay causing the S-curve. What makes our setup unique is that we generate in addition a polarization dependent delay for each single pulse which avoids the background coming from the strong amplifier pulse as indicated in (b). There is no pulse overlap between the two amplifier polarization components anymore and therefore no SHG. The decomposition and delay of the oscillator pulse is not shown. The blue arrow indicates the relative movement of the pulses during a delay scan.
4. Characterization of the optical balanced cross correlator
In this section the experimental results obtained with the balanced cross correlator will be presented which is followed by a profound noise analysis showing its final limitations.
4.1 Signal and signal/noise ratio achieved
In order to understand the details of each individual signal and its background we currently do not use a balanced photodetector for retrieving the signals, but rather take them out of two individual photodiodes. Here one has to make sure that the following data taking indeed measures laser shot synchronous results for both channels. This is given if the total jitter amplitude is two times the jitter amplitude out of one channel since the two channel signals are out of phase by 180$^{\circ }$ (the timing jitter signal is by far the strongest signal as will be seen below).
The low noise variable gain photo receivers of the series OE-300 from Femto Messtechnik GmbH deliver raw signals with a maximum amplitude of 0.5 Volt and a FWHM of 300 ns. The signals are well adapted to an IOXOS 16 bit multichannel ADC (ADC$\_$311-A0) running at a sample rate of 286 MHz. The trigger and the sampling clock for the ADC are provided externally and both signals are locked to the SwissFEL common clock. To improve the signal to noise ratio a software based boxcar integrator including gated background subtraction is used. The ADC’s alone contribute an equivalent background noise of 0.05 fs rms while taking the difference signal. Together with the photo detectors the equivalent background noise level reached is 0.3 fs rms. This turned out to be the baseline since the optical measurement is background free, as explained in section 3.
Fig. 8(a) shows the cross-correlation signals from both channels. Each signal data point is obtained by integrating the corresponding raw signal over its pulse shape. The delay of the seed pulse is obtained by scanning a mirror on a translation stage in front of the laser amplifier and this delays the amplified pulse. The oscillator reference stays fixed. The actuator for the delay scan or the delay feedback is a roof top mirror mounted on a linear piezo driven translation stage with nanometric resolution, operating via the so called "piezo walk technic" (Physik Instrumente L.P., stage N-565.360). The difference between the two signals, the S-curve, is visible in Fig. 8(b). The ratio of the distance between the extrema of the S-curve (indicated in the figure as S) and the background (indicated as N) is as high as 1430 confirming the low noise conditions. Since the S-curve is the discrimination signal for the laser arrival feedback one has to make it as steep as possible but still keep the timing jitter related signal within the linear region around the zero crossing. This way a slope of 43 counts/fs has been achieved. The measured jitter during 600 s between amplifier and oscillator is shown as an inset on the zero crossing of the S-curve. It stays well within the linear region, but still gives enough signal amplitude. The origin of the small bumps on the right side of the cross-correlation signals (Fig.9a) is unknown, but fortunately, they do not interfere with the standard operation at zero crossing (Fig.9b).
Fig. 8. Measured ADC channel signals (a) and their difference (b) obtained by scanning the oscillator seed in front of the amplifier. The oscillator reference stays fixed. The laser pulse jitter is shown as an overlay on the S-curve.
4.2 Total amplifier pulse jitter and the final limitations of the cross correlator
The purpose of using a LAM is to measure timing fluctuations and drifts. By employing balanced detection it is assumed that the difference signal between the two channels cancels all amplitude fluctuations so that only timing fluctuations are left. With the same arguments one can argue that the sum signal of the two channles cancels all timing fluctuations so that only amplitude fluctuations are left. We want to examine now how well this becomes true for our system.
Fig. 9(a) shows the laser amplifier timing jitter signal relative to the seeding oscillator measured at zero crossing of the S-curve during 10 min at a laser repetition rate of 100 Hz (outer red signal) which is the result of the difference between the two channels. The inner green trace shows the fluctuation of the sum of the two channels. Here the ordinate unit is converted from counts to fs via the measured S-curve slope of 43 counts/fs. Taking the root mean square values this results in 4.5 fs rms for the difference and 1.43 fs rms for the sum fluctuations. 4.5 fs rms is the timing jitter of the amplifier relative to the oscillator. This is 0.8$\%$ of the FWHM of the Gaussian shape amplified laser pulse. After taking the difference between the two channels of the LAM it turns out that the timing jitter adds coherently. This confirms that the single shot synchronous detection works as mentioned above.
Fig. 9. Difference signal (red) and sum signal after subtracting the mean value (green) out of the two channels; time record and spectrum. The difference signal decreases towards frequencies below 2 Hz because of an applied feedback which eliminates laser drift and slow timing fluctuations (see section 5). The limited bandwidth is given due to the heavy actuator which is a roof mirror mounted on a translation stage.
The sum trace contains several contributions such as electronic fluctuations, laser pulse energy jitter, possible laser beam pointing jitter and remaining timing jitter mismatch. The reason for the latter is that the rising slope of the measured laser pulse is a little steeper than the falling slope making perfect balancing quite cumbersome or even impossible. Fig. 9(b) shows the amplitude spectrum of both jitters indicating how important it is to use balanced detection not only to eliminate pulse energy drifts but also to cancel amplitude fluctuations especially at low frequencies. The drop of the difference spectrum towards lower frequencies is due to an applied feedback to eliminate laser pulse timing drift and low frequency fluctuations.
Since the photodetector noise is small (0.3 fs-rms) and also pointing fluctuations are small (the travel length for the beams is relatively short and the cross section of the amplifier beam is slightly larger than that of the oscillator beam) the question arises whether the 1.43-fs-rms measured for the sum trace really represent solely amplitude fluctuations (since the pulse energy corresponds to the signal amplitude both expressions are used synonymously here).
To get the energy jitter (or amplitude jitter) of the laser pulses one has to measure the jitter at the signal maximum of each single channel since there the timing jitter (horizontal jitter) is flat and generates no signal in first order and so the amplitude jitter (vertical jitter) is left. This can be seen in Fig. 10. The scan was obtained by taking 81 delay steps of $5~\mu m$ each. After each step the jitter was measured for about 8 seconds which delivers about 800 data points for each step. Taking the rms values of the difference between the two channels gives the rms jitter along the S-curve (see inset b). It is obvious that the maximum sensitivity for a jitter measurement is given at the cross point of the two channel signals which is equivalent with the zero crossing of the S-curve. The rms values for each step along the single channels can be seen in the insets on the left (a) and right (c). Indeed the jitter curves show a minimum at the maximum amplitudes of the scanned signals (see as well the projected jitter curve on the bottom of the figure) and the root mean square values corrected by the photodetector noise reads 44 counts rms for channel 1 and 35 counts rms for channel 2. This is the amplitude jitter which shows as well a slight mismatch. The cross point is at 57$\%$ of the signal maximum which converts the amplitude jitters to 25 counts rms and 20 counts rms respectively at zero crossing of the S-curve. By using the known slope at the S-curve at zero crossing one can convert these values finally to equivalent timing jitter values of 0.59 fs-rms for channel 1 and 0.47 fs rms for channel 2. Since these values are much smaller than the jitter of the sum of the two channels it is obvious that there is a given timing jitter mismatch from the cross-correlator. A good estimate of it can be obtained by subtracting the energy jitter of the laser pulses from the sum signal:
where the laser pulse energy jitter at the S-curve zero crossing adds coherently. This ends up finally with a timing jitter asymmetry of around 1 fs rms which is 22$\%$ of the total timing jitter rms value. This value is coming from a difference between the rising and falling slope of the signals as mentioned above and as can be seen from the rms-jitter curves shown in Fig. 10 (insets a and c). These curves map the derivative of the signals and they are indeed asymmetric. The channel with the steeper slope gives more signal than the channel with the shallower slope. The reason for such an asymmetry can be an asymmetry of the laser pulse itself or a walk off effect in the rather thick LBO (d = 5 mm) crystals. The latter could be ruled out already by testing LBO crystals with 3 mm thickness which did not improve the situation but led to a decrease of the signal amplitude down to 30$\%$ of its previous value. After all one can conclude that the timing jitter mismatch adds an error bar to the jitter measurement but it does not impair cancelation of amplitude drifts which is the main purpose of using balanced detection.Fig. 10. Timing jitter step- scan along both signals. The scan is taken with 81 steps of $5~\mu m$ (equivalent to 33 fs) delay each collecting data at 100 Hz during about 8 s. On the floor is shown the projected jitter of the difference between the two signals above. The inset on the top shows the rms of this projected jitter for each step. The insets on the left and right show the rms of the projected jitter for the individual channels.
The amplitude jitter indicated in Fig. 10 is about $0.3~\% ~rms$ of the total sum frequency generated signal and this includes a maximum value of $0.2~\% ~rms$ jitter of the oscillator pulses (according to the data sheet). Without going into the details on this topic, it follows from this result that the amplitude jitter of the amplifier relative to its seeding oscillator is less than $0.2~\% ~rms$. The amplitude jitter shows as well a mismatch as mentioned above, but fortunately its contribution to the timing jitter mismatch is an order of magnitude less than the timing jitter mismatch itself.
5. Low frequency arrival time jitter and drift of laser amplifier and oscillator
The signal from the cross correlator can be used to apply a feedback to the delay actuator in order to eliminate timing drifts and slow timing fluctuations of pulses out of the amplifier (see Fig. 2). The feedback is software based having a proportional and integral part operating within a bandwidth of about 0.5 Hz. The result of the jitter spectrum up to the Nyquist frequency (whose maximum value is half of the laser repetition rate) is shown in Fig. 11(a). Taking the square root over the integrated power spectrum or alternatively the time record (here over 10 min.) delivers finally the jitter of the laser amplifier relative to the oscillator which is, as already mentioned, 4.5 fs rms. Without feedback the integrated jitter amounts to 5 fs rms. By employing a faster translation stage one could probably lower this result another 1 fs rms by increasing the feedback bandwidth beyond 3 Hz (see the low frequency bump in Fig. 11(a)).
Fig. 11. Left(a): Relative timing jitter spectrum between amplifier and oscillator. The feedback has a bandwidth of about 0.5 Hz. Right(b): Spectrum of total fluctuations between the laser (oscillator + amplifier) against a second identical oscillator locked to the same clock. The origin of the peaks in this spectrum still has to be investigated.
SwissFEL can run at a repetition rate up to 100 Hz. To determine the contribution of the photocathode laser on the electron beam timing jitter one has to consider as well the timing fluctuations of the laser oscillator relative to a common clock which is the reference of all timing relevant components. In section 2 the jitter of the oscillator was already presented in the frequency range 10 Hz - 10 MHz measured by a phase noise signal analyzer. To investigate the fluctuations of the oscillator as well in the lower frequency spectrum and compare them with those of the amplifier it is easier to use an optical method which is given by the LAM. In addition one gets as well the drift of the laser. Accordingly the laser amplifier was locked to its seeding oscillator via the presented LAM and another part of the amplified beam was sent into an identical second LAM fed by a second identical oscillator phase locked to the same clock. In order to keep the pulse overlap a second motorized delay stage together with a second feedback is used for the second oscillator to keep the overlap of one of its pulses with the pulse from the amplifier. The result for the jitter is shown in Fig. 11(b) and for the drift in Fig. 12. A total jitter of 15 fs rms was measured during 10 minutes with a data rate of 100 Hz for both systems. With the known jitter between amplifier and its oscillator (4.5 fs rms) the conclusion is that both oscillators jitter with 10 fs rms between 2 mHz and 100 Hz ($\sqrt {\frac {(15^2-4.5^2)}{2}}=10$) and further on that the whole laser jitters with 11 fs rms in this frequency range ($\sqrt {10^2+4.5^2}=11$). Furthermore the photocathode laser shows a drift of less than 200 fs during 60 hours as given by Fig. 12. The impact of the residual timing drift of the whole laser system on the FEL-performance is currently included and therefore counteracted in a multi parameter random walk optimizer [27]. The timing sensor for this optimization is a electron beam arrival monitor linked to the common clock [13]. In future this drift will be measured and compensated by a dedicated UV-LAM positioned close to the FEL cathode [28].
Fig. 12. Drift of the whole locked laser measured relative to an second oscillator phase locked to the same clock. Outer signal (red): random move of the measuring LAM due to the signal jitter. Inner signal (blue): smoothed signal showing the laser drift.
6. Effect of environmental parameters on the amplifier measured with the LAM
Variations of pressure, humidity and temperature can change the optical path length anywhere within the laser system and therefore the laser arrival time. With the feedback between amplifier and oscillator in lock one can gain information about the sensitivity of the amplifier to these parameters by recording them together with the delay stage movement in the feeback loop. In order to discriminate the influence of the different environmental parameters on the laser drift it turned out very useful that the feedback of the air conditioner for temperature and humidity was slightly oscillating during the time of measurement (period 37 min for the temperature and 1 h for the humidity).
6.1 Impact of pressure variations
The pressure in the laser laboratory is not stabilized and therefore a pressure change can be the overwhelming parameter causing drift of the relative arrival time. From local weather forecasts, it is known that during a stormy day the environmental pressure can easily change by 10 mbar within a couple of minutes. Fig. 13(a) shows the compensating action of the translation stage as a function of pressure change during two days. Evaluating the data results in a sensitivity of 1.06 ps/mbar with an residual error of 1.6 $\% ~rms$. The ripple on the curve measured stems from temperature changes as will be explained in the following.
Fig. 13. On the left(a): amplifier sensitivity on pressure change (blue) together with the LAM motor position (red) converted to ps. A linear least square fit of the motor position on the pressure change results in a sensitivity of 1.06(2) ps/mbar. The residuals show the quality of the fit. On the right(b): Amplifier sensitivity on air temperature change. The red curve shows the temperature variation in the laboratory with time and has a period of 37 min. The black curve provides the measured amplifier pulse delay and is obtained by filtering out the slow variations from the residuals shown in the inset of the figure in a.) and fitting amplitude and phase on the red curve.
6.2 Impact of temperature changes in the laboratory
Temperature and humidity in the laboratory are stabilized by an air conditioner. This way a temperature stability of 0.025 K peak to peak is reached (without feedback-oscillation it is rather 0.01 K peak to peak), where the temperature is rising and falling following a triangular function with a period of 37 min (red curve in Fig. 13(b)). This period is seen as well on the translation stage movement of the LAM (Fig. 13(b) black curve, for a detailed view see inset). This curve is obtained by filtering out the slow variations of the residuals shown in Fig. 13(a) and fitting the amplitude and phase on the red curve in Fig. 13(b). From this data a sensitivity of the amplifier on the laboratory temperature of 9.2 ps/K was measured. With the given temperature stability of 0.025 K one can conclude that the LAM has to stabilize an amplifier drift of 233 fs peak to peak during 37 min.
6.3 Impact of humidity changes
The laboratory air conditioner keeps the relative humidity constant on a $0.2\%$ peak to peak level. Its feedback follows almost a sinusoidal pattern with a period of one hour (see Fig. 14 and lower inset). In contrast to the temperature modulation discussed with Fig. 13(b) the humidity changes are not at all visible in the LAM-feedback (see upper inset on Fig. 14). Indeed as [29] indicates the operation wavelength of 1042 nm hits exactly a water window. We can conclude that the sensitivity of the infrared part of the laser to water absorption or dispersion is beyond a value we can measure.
Fig. 14. The relative humidity in the lab. oscillates with a period of one hour (see spectrum and lower inset). Visible are as well two harmonics. The sensor shows also a slight signal at the temperature oscillation period of 37 min. The laser amplifier is not sensitive to humidity changes according to the response from the LAM (upper inset).
6.4 Impact of water cooling
Another parameter disturbing the laser is the water cooling. This cooling is carried out for the amplifier laser crystal, the pump laser diode and the Pockels-cell switching electronics in series with a water flow of about three liters per minute from one chiller. In order to get the impact of the cooling temperature on the laser stability the temperature of the chiller was changed back and forth by 0.15 K every three minutes making sure that the system will thermalize to at least 97$\%$. This resulted in a small modulation of the LAM signal. Subtracting the slow drift (mostly due to environmental changes) leads to the result shown in Fig. 15(a). By fitting the LAM-motor movement (blue curve) on the water temperature curve (in red) results in a sensitivity of the laser timing on the cooling water temperature of 268(38.5) fs/K within the measured range from 20.4 $^{\circ }$C to 20.55 $^{\circ }$C. With a given chiller temperature variation of up to $\pm$ 0.01 K it is obvious that this effect is negligible for the laser system. The impact of vibration related jitter caused by the water flow on the other hand is not at all negligible. By replacing the original chiller (SMC HECR008) by a much smaller one which is equipped with a centrifugal pump (ThermoTEK T257P) it turned out that the laser timing jitter decreased by a factor of three as shown in Fig. 15(b).
Fig. 15. Left (a): Laser pulse timing drift dependence on chiller temperature. The temperature was increased and degreased by 0.15 K every three minutes. The LAM-motor position (converted to fs) changes accordingly. Right (b): Amplifier pulse jitter for two different laser chillers. The flow rate was set to $3~l/min$.
Thus we can infer that the effect of environmental parameter changes on our laser system can easily exceed it’s demanded stability by two orders of magnitude if no measures are taken to minimize and counteract them. The main cause of timing jitter are chiller generated vibrations originating from its water pump which therefore has to be carefully selected or if possible even avoided.
7. Conclusion
We described a single color balanced cross correlator able to stabilize the timing of a mJ level Yb-CaF$_2$ regenerative amplifier to its seeding oscillator. We showed that even in a collinear setup SHG background can be completely avoided. With this device we measured the performance of the SwissFEL photocathode laser. We eliminate the timing drift due to several environmental parameters by an active feedback down to an acceptable value. We reach a jitter of 4.5 fs rms between amplifier and oscillator and 11 fs rms for the whole laser within 2 mHz and 100 Hz relative to a common clock for all SwissFEL systems. With this laser we stay well below the maximum nominal photocathode jitter allowed for stable operation of SwissFEL.
Acknowledgments
We especially thank Albert Romann, Marta Divall and Stefan Hunziker for their contributions at an earlier stage of this project. We are indebted to Vladimir Arsov, Martin Paraliev, Maik Kaiser, Uwe Kolb, Markus Heiniger and Sven Reiche for many valuable discussions and support.
Disclosures
The authors declare no conflicts of interest.
Data availability
All data are available from the corresponding author on request.
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