# Versatile Femtosecond Laser Synchronization for Multiple-Timescale Transient
IR Spectroscopy

Jan Helbing and Peter Hamm  Department of Chemistry, University of Zurich,
Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
*corresponding author<EMAIL_ADDRESS>
###### Abstract

Abstract: Several ways to electronically synchronize different types of
amplified femtosecond laser systems are presented, based on a single freely
programmable electronics hardware: Arbitrary-detuning asynchronous optical
sampling, as well as actively locking two femtosecond laser oscillators,
albeit not necessarily to the same round-trip frequency. They allow us to
rapidly probe a very wide range of timescales, from picoseconds to potentially
seconds, in a single transient absorption experiment without the need to move
any delay stage. Experiments become possible that address a largely unexplored
aspect of many photochemical reactions, in particular in the context of photo-
catalysis as well as photoactive proteins, where an initial femtosecond
trigger very often initiates a long-lasting cascade of follow-up processes.
The approach is very versatile, and allows us to synchronize very different
lasers, such as a Ti:Sa amplifier and a 100 kHz Yb-laser system. The jitter of
the synchronisation, and therewith the time-resolution in the transient
experiment, lies in the range from 1 ps to 3 ps, depending on the method. For
illustration, transient IR measurements of the excited state solvation and
decay of a metal carbonyl complex as well as the full reaction cycle of
bacteriorhodopsin are shown. The pros and cons of the various methods are
discussed, with regard to the scientific question one might want to address,
and also with regard to the laser systems that might be already existent in a
laser lab.

##  I Introduction

Many photochemical processes are initiated by the electronic excitation of a
photo active molecule, which reacts extremely quickly on a femto- to
picosecond timescale; this is the realm of femtochemistry.[1] The initial
process is followed by a cascade of events that may cover all timescales up to
seconds or even longer. An understanding of these processes in their entirety
requires a full coverage of all relevant timescales, ideally under identical
conditions in a single experimental setup.

One example in this regard are photoactive proteins, in which a chromophore
isomerizes after electronic excitation typically within a few 100
femtoseconds, thereby perturbing the protein, which eventually leads to its
function. For instance in the case of bacteriorhodopsin, which is probably the
best studied photoactive protein, a proton is channeled via a sequence of
amino acid side chains, and eventually through the membrane.[2, 3, 4, 5, 6, 7,
8, 9] Other rhodopsins with a plethora of functions have been described as
well,[10, 11] and show an equally complex cascade of responses. Other examples
are photo-receptors that regulate the physiology of higher plants, microalgae,
fungi and bacteria in response to environmental light conditions.[12, 13, 14],
or protein conformation changes induced by an artificial photo-switch.[15, 16,
17, 18]

Kinetics on multiple timescales is also encountered in photocatalytic systems
that mimick natural photosynthesis. Some of their most relevant applications
relate to water splitting, i.e., water reduction and oxidation,[19, 20, 21,
22, 23, 24] as well as CO2 reduction.[25, 26, 27, 28, 29, 30] In analogy to
natural photosynthesis, these systems typically separate the function of light
absorption and initial charge separation in a so-called photosensitizer – the
reaction center in the natural system – from the actual catalyst, that
oxidizes/reduces the substrate. Several electron relays connect different
components of the overall system. Since the latter are bimolecular reaction
steps of species at low concentration, they are slow, out to the seconds
timescale.[24] While the ultrafast photophysics of the initially excited
compound in these molecular systems is typically well understood from
“conventional” femtosecond pump-probe experiments, studies of the complete
reaction cycles are extremely scarce due to the lack of appropriate
experimental setups that would be able to investigate them in their entirety
under identical conditions and with constant sensitivity.

Figure 1: (a) Generation of an arbitrarily short or long pump and probe delay
time, that is composed of an integer-multiple of the oscillator round-trip
time, $n\cdot t_{rep}$, plus the delay time between the two laser oscillators
$t_{osc}$. (b) Overall laser setup, showing optical pathways of pump and probe
pulses in blue and red, respectively, and electrical ones in black. (c)
Schematics of the synchronisation electronic, which is explained in details in
the text, and (d) picture of a prototype.

Quite some time ago, we presented an approach that can achieve that task by
electronically synchronizing two femtosecond laser systems,[31] a concept that
has been taken over by a few other groups.[32, 33] To understand the idea, one
needs to recap that femtosecond laser systems used for these experiments
consist of two components: a laser oscillator, which delivers a high-
repetition frequency train of femtosecond pulses (typically many 10’s of MHz,
determined by the roundtrip time of the oscillator), and a regenerative
amplifier, which picks individual of these pulses at a much lower repetition
rate and amplifies their energy by many orders of magnitudes. In Ref. 31, the
resonator length of one femtosecond Titanium:Sapphire (Ti:Sa) oscillators
could be tuned with the help of a piezo actuator until its round-trip
frequency locked to that of the other one. Furthermore, the relative phase of
the oscillator pulse trains could be adjusted, and thereby the delay time
$t_{osc}$ (see Fig. 1a). For pump-probe delays longer than the round-trip time
$t_{rep}$ of the Ti:Sa oscillators, the two Ti:Sa regenerative amplifiers were
triggered in an appropriate manner to pick pulses separated by an additional
integer-multiple of the oscillator repetition time, $n\cdot t_{rep}$. Similar
solutions have been proposed to synchronize femtosecond lasers to a
synchrotron or X-ray free-electron lasers.[34]

Alternatively, one may seed two amplifiers from one common oscillator, which
however requires a long (12.5 ns $\triangleq\approx$ 4 m) mechanical delay
line to scan $t_{osc}$.[35, 36] This approach has high demands on alignment
and the mechanical stability of the delay line and introduces a significant
dead time in the measurement, since moving a translation stage over long
distances is slow. A user facility at the Rutherford Appleton Lab is probably
the most advanced instrument in this regard, capable of covering timescales
from $\approx 100~{}$fs to seconds.[37, 38, 39, 40, 41]

A very interesting alternative is arbitrary-detuning asynchronous optical
sampling (ADASOPS).[42, 43, 44, 45, 46, 47] The separation $t_{osc}$ between
pulses from two independent oscillators is continuously changing, but can be
measured, and pairs of pump and probe pulses with the desired time-delay can
be selected for amplification. Particularly interesting in this regard is Ref.
46, which showed how to measure the time-delay purely electronically, thereby
minimizing the complexity of the optical part of the setup. That is, two
standard amplified femtosecond laser systems can be used without any
modification. The concept builds on the fact that inexpensive time-to-digital
converter chips are nowadays available, which have been developed for LiDAR
applications, and which can measure the arrival times of pulses with a
$\approx$10 ps single-shot accuracy (rmsd.) at a measurement rate of 10 MHz.
Femtosecond laser oscillators are intrinsically very stable and do not drift
on a sub-millisecond timescale. Hence, when averaging over 10000 single-shot
measurements (i.e., the period between pulse selection for a kHz amplifier),
an accuracy of the time measurement in the range of 100 fs can be
achieved,[46] sufficient for most chemical applications in time resolved
spectroscopy.

Here, we present and compare several synchronization modes in our labs that
allow us to cover a wide range of timescales: ADASOPS (Mode A, see Sec. II),
synchronisation of two identical Ti:Sa lasers systems (Mode B, see Sec. II),
as well as synchronisation of a 100 kHz Yb-laser system to a Ti:Sa lasers
system (Mode C, see Sec. II). The latter is particularly interesting for
single-pump-multiple-probe experiments, making use of the high repetition rate
of Yb-laser system.[38] All synchronization modes can be realized with one
universal electronics hardware (Sec. II). The pros and cons of the various
synchronization modes will be discussed.

##  II Methods

### Laser Setup and Electronics Hardware

Fig. 1b shows the overall laser setup with two amplified femtosecond laser
systems A and B, each consisting of a laser oscillator and a laser amplifier.
The cavity length of Oscillator B (in our case a Tsunami/Spectra Physics) can
be adjusted by roughly 1% with a motor-driven translation stage (PD1,
Thorlabs) placed inside the mount of one end-mirror. In addition, one of the
resonator turning mirrors is mounted on a piezo actuator (HPSt 150,
Piezomechanik, driven by a KPZ101 piezo amplifier from Thorlabs) for fine
adjustment of the round-trip time (the latter is not needed for the ADASOPS
Mode A).

The central synchronization electronics is shown as schematics in Fig. 1c, and
a picture of a prototype in Fig. 1d. It is conceptually the same as that of
Ref. 46, but quite different in its realisation. The pulse trains from the two
laser oscillators are fed in by optical fibers, with fast photodiodes directly
mounted on the printed circuit board (PCB) to minimize electric noise. We
tested two different diodes, an ultrafast GaAs diode with a specified pulse
response of 29 ps (DX12DF, Thorlabs), and a much cheaper Si PIN diode with a
rise time of 700 ps (FDSP625, Thorlabs). Optionally, the signal can also be
fed in via a 50 $\Omega$ SMA cable, which is required for the laser system
used in Mode C. The input signals are AC coupled into a 280 ps high-speed
comparator (MAX40026, Analog Devices). The amplitude noise of laser
oscillators is quite small, hence, as long as the comparator switches at a
constant level, the rise time of the diode (and probably also that of the
comparator) is not very critical. Indeed, we did not find any significant
difference in overall performance for the two tested diodes.

The time-to-digital converter chip (AS6501, ScioSense) has three clock inputs:
one reference clock as well as two stop channels, whose timings are measured
relative to the reference clock. Initially, we used a separate 10 MHz crystal
oscillator for the reference clock. However, laser oscillators are very stable
oscillators too, and we found that the overall design becomes much simpler,
and the noise performance actually better, when using one laser oscillator
(oscillator B in our case) as reference clock, and measure the second laser
oscillator A relative to it. The maximum reference clock frequency the time-
to-digital converter can handle is $\approx$10 MHz, hence the signal of the
oscillator has to be divided down accordingly, i.e. 1:8 for a 80 MHz Ti:Sa
Tsunami or 1:4 for the Amplitude Tangerine SP system, whose front end seed
oscillator runs at 41 MHz. To that end, we use low-jitter (1 ps) programable
clock dividers (SY89873L, Microchip Technology). The specified single-shot
measurement error of the chip is 10 ps (rmsd.). Applying one and the same
femtoseond laser oscillator to both inputs, we determined a single-shot noise
of $\approx$12 ps, slightly more than the specification of the chip, but that
also includes the jitter of the diodes, the comparators and the clock
dividers. In order to improve signal-to-noise, the two stop channels of the
time-to-digital converter chip are used for two independent measurements per
cycle of the reference clock.

The measured data are transferred to a field-programmable gate array (FPGA,
LMXO2-7000, Lattice Semiconductor Corporation) via two fast serial interfaces.
The two stop events per reference clock cycle are averaged in a first step,
revealing one data point with 17 bit resolution every 100 ns, related to a bit
resolution of ca. 0.76 ps. The time-critical aspects of the subsequent data
evaluation are also done within the FPGA according to the desired
synchronisation mode. The FPGA eventually produces trigger signals for the
laser amplifiers, and transfers results of the data evaluation to a
microcontroller (STM32F427, STMicroelectronics), which in turn transfers them
to a PC via an USB interface (FT232H, FTDI). In addition, for the
synchronisation modes B and C, the FPGA provides a feedback signal for a piezo
actuator via a 12 bit, 10 MHz digital-to-analog converter (DAC, AD5445, Analog
Devices). The integrator needed to close the feedback loop is realised in
analog electronics, to avoid any problems due to the finite bit resolution of
the DAC. The noise at the output of the DAC is larger than its bit resolution,
hence is averaged out by the integrator. We did not attempt to program the
integrator digitally in the FPGA (which would have the advantage that one
could software-control its parameters).

One further, freely programable input of the FPGA is used in Mode A for the
coincidence signal, in Mode B to synchronize the overall laser system to
another device such as a photo-elastic modulator or, in Mode C for the 100 kHz
signal from the Amplitude Tangerine SP system. The MCU has an additional input
“start measure” to be able to relate the transient absorption data recorded by
the detector to the corresponding delay times.

The hardware is assembled on a small $\approx$150*90 mm2 PCB (see Fig. 1d).
The FPGA is programmed in Verilog with the help of the Lattice Diamond
Software (freely available from Lattice Semiconductor Corporation), and the
MCU in C within Eclipse (freeware).

### Synchronisation Mode A: Arbitrary-Detuning Asynchronous Optical Sampling

Figure 2: Principle of ADASOPS. The data directly from the oscillator are
shown in blue, the actually measured ones after division by a factor 8 in red,
and those after unwrapping in black. Unwrapping is performed by adding eight
times the oscillator round-trip time $8\cdot t_{rep}$. In total $n$
measurement points are used to perform a linear fit (black line). The fit can
be extrapolated to predict the time-separation $t_{osc}+m\cdot t_{rep}$ of a
later measurement point with regard to the unwrapped data, that corresponds to
a time-separation between the two oscillators of $t_{osc}$.

The concept ADASOPS based on electronic measurements of time-separations has
been introduced in Ref. 46, and its basic idea is illustrated in Fig. 2. The
time-separation between the pulses from the two oscillators is shown as blue
dots. In this example, oscillator A (probe laser) has a lower repetition
frequency than oscillator B, which is used as a reference clock. Hence, the
time of oscillator A relative to that of oscillator B increases with laser
pulses. Whenever oscillator B overtakes oscillator A, the time-separation
jumps back to 0. However, as explained in Sec. II, the time-to-digital
converter chip cannot handle the repetition rate of the oscillator directly,
hence the pulse train is divided down by a certain factor (8 in the example of
Fig. 2) to reveal the dots shown in red. The slope is the same but fewer pulse
are measured, the maximum time-separation becomes larger, and the rate of
overtaking events is correspondingly smaller. In addition, the data need to be
unwrapped whenever an overtaking event happens for the red data points, by
adding the time period of the reference clock ($8\cdot t_{rep}$), a
calculation step that is performed in the FPGA.

Figure 3: Overview of the timing of the complete cycle between pairwise two
pulses from the Ti:Sa amplifiers. The blue dots sketch the time-separations
between the two Ti:Sa oscillators before division of the clock signal, and the
red ones after division by a factor of 8. Important events in the cycle are
marked, and are discussed in the text.

A certain number $n$ of measurement points is fit to a model function in order
to average out the noise in the single-shot data. We implemented a linear fit
only, since Ref. 46 has shown that higher-order fits, which might account for
drifts in the oscillator frequencies, yield only a minor improvement of the
final accuracy, and only if time-delays longer than the one anticipated here
is used (i.e., 400 $\mu$s corresponding to the 2.5 kHz repetition rate of the
Ti:Sa amplifier). That is, we fit the unwrapped data $t_{i}$ to:

$t_{i}=\widehat{t_{0}}+\widehat{\Delta t}\times i$ (1)

where $i=0,...,n-1$ indexes the measurement, $n$ is the number of measurements
that go into the fit, $\widehat{t_{0}}$ the starting value for the first
measurement point $i=0$, and the slope $\widehat{\Delta t}$ the change of
time-separation per measurement point.

Once the fit parameters are obtained, a pulse $j>n$ can be selected by
extrapolation that minimizes the distance to a desired delay $t_{osc}$. The
corresponding time $t_{j}$ will typically include an integer-multiple of
$t_{rep}$ due to dividing and unwrapping of the raw data, see Fig. 2. Its
index is calculated as:

$j=\frac{t_{osc}+m\cdot t_{rep}-\widehat{t_{0}}}{\widehat{\Delta t}},$ (2)

which is a relatively small, rounded integer number. For example, when the
repetition frequencies of two 80 MHz oscillators differ by 200 kHz, the round-
off error in Eq. 2 corresponds to a time-window of $\approx\pm 15$ ps, i.e.,
it is possible to select oscillator pulse pairs for amplification within that
time window around a desired delay time $t_{osc}$. The size of the uncertainty
interval is inversely proportional to the difference frequency, i.e., it could
be adjusted if needed. In any case, while this interval is relatively large,
the actual time separation for a pulse (whose index may be larger or smaller
than $n$, see fit strategies below) can be obtained by evaluating Eq. 1, and
this can be done with much higher accuracy and bit resolution.

Fig. 3 shows an overview of the timing of the complete cycle between two
pulses from the Ti:Sa amplifiers. Our Ti:Sa amplifiers are optimized for a
repetition rate of 2.5 kHz and they must be triggered by the synchronization
electronic at a rate that is close to this value. We generate the 2.5 kHz
trigger signal by dividing the difference frequency between the two Ti:Sa
oscillators by an integer value, i.e 200 kHz (a rather arbitrary choice)
divided by 80. This results in 10 delay-sweeps per cycle (see red points in
Fig. 3). The next cycle is started when the measured delay exceeds 50 ns.
Despite this being a noisy, single-shot measurement, the approach greatly
helped to stabilize the overall measurement cycle by avoiding that a
measurement is started at a discontinuous overtaking event.

We actually perform the linear fit described above twice, one for the first
$n_{1}$=1024 data points, and a second one for $n_{2}$=3072 data points. The
reasoning for this procedure is the following: The first fit is extrapolated
to predict a laser shot roughly 150 $\mu$s after the beginning of the cycle
with a time-separation $t_{osc}$ according to Eq. 2, which is as close as
possible to a desired value within the uncertainty interval of $\approx\pm 15$
ps. The second fit allows to determine the actual time-separation after the
fact with the help of Eq. 1 with higher accuracy, since it is based on
$n_{2}$=3072 data points (i.e. a potential factor $\sqrt{3}$ improvement), and
since the selected laser shot lies in the middle of the measurement interval,
and not outside (another factor $\approx$2 improvement).

Figure 4: (a) Setup for coincidence measurement between two oscillators and
(b) measurement results. The data are fit to a Gaussian function with a
standard deviation of 1 ps. (c) Pump-probe response of a thin Si-wafer,
showing results for ADASOPS (synchronisation Mode A) in black, those when
synchronizing two identical Ti:Sa laser systems (synchronisation Mode B) in
blue, and those when synchronizing a Ti:Sa laser system to a 100 kHz Yb laser
system (synchronisation Mode C) in red. The data are fit to integrated
Gaussain functions with standard deviations 1.3 ps, 2.9 ps, and 3.2 ps,
respectively.

Fig. 4a shows an experimental setup for a coincidence measurement, overlapping
the two laser oscillators in a BBO crystal. The delay time is set to
$t_{osc}=0$ within the uncertainty interval of $\approx\pm 15$ ps discussed
above. A certain fraction of pulses will nevertheless coincide within
$\lesssim 100$ fs, i.e., the duration of the pulses, and thus generate a sum
frequency signal that is detected and sent to the FPGA. Only for these
coincidence events, the fitted delay times $t_{j}$ are collected in a
histogram shown in Fig. 4b as dots. A fit to that histogram with a Gaussian
function reveals a standard deviation of 1.0 ps, which is considered a measure
of the accuracy of the time-separation measurement. The accuracy is close, but
not quite as good as that reported in Ref. 46, for reasons that are not
entirely clear. We assume that vibration isolation of the laser table becomes
very critical, and our setup is not particularly optimized in this regard.
That is, both laser Ti:Sa systems were on separate laser tables, which were
screwed to each other.

In a pump-probe experiment, we measure transient absorption data for a
sequence of time points. Despite the fact that a set delay is realized only
roughly within an uncertainty interval of $\pm 15$ ps, we can bin the
transient absorption data according to the delay time that is actually
measured with much higher precision. To that end, the electronics that reads
the detector data needs to provide a signal to the synchronisation electronics
to indicate the start of a measurement (see Fig. 1b), in order to be able to
relate both measurements to each other.

Fig. 4c, black, shows the pump-probe response of a thin Si-wafer obtained in
this way, where free carriers are generated by excitation with amplified and
frequency-doubled laser pulses at 420 nm. The resulting change in transmission
was probed by IR pulses at $\approx$2000 cm-1. This experiment now also
includes the Ti:Sa amplifiers as well as an IR-OPA for the generation of Vis
pump and IR probe pulses. ADASOPS defines delay-zero within the time-to-
digital chip, and obviously, both laser pulses take very different pathways
until they reach the sample. Hence, as common in femtosecond spectroscopy,
there will be an arbitrary delay-zero offset, that can be large (many
nanoseconds) and that has to be corrected for. In practice this offest is
simply added to the (list of) delays sent from the measurement software on the
PC to the MCU.

Fitting the experimental data of Fig. 4c, black, to an integrated Gaussian
function reveals a standard deviation of 1.3 ps, slightly longer than that of
the coincidence measurement of Fig. 4b. The data of Figs. 4b and 4c have not
been measured at the same day, and we do not know whether the slight
difference reflects daily performance, or the additional jitter/drifts
introduced by the Ti:Sa amplifiers and the IR-OPA.

In contrast to any other method, ADASOPS does not require any mechanical
motion. Hence, the delay time can be changed in a shot-by-shot manner by
applying a new delay time value for the evaluations in each measurement cycle
shown in Fig. 3.[45] Fast delay scanning can improve the quality of transient
absorption data enormously, as it makes use of the relatively long correlation
times in the noise of typical femtosecond laser systems.

However, when changing the pump-probe delay time by one full round trip time
of the Ti:Sa oscillator ($\approx$12.5 ns), the position of the probe pulse in
the cycle of Fig. 3 moves by $\approx 5\mu$s. As a result, the probe amplifier
will be triggered 5 $\mu$s earlier, i.e. already 395 $\mu$s after the previous
shot instead of 400 $\mu$s (corresponding to the 2.5 kHz repetition rate of
our Ti:Sa laser system). The excited state lifetime of the Nd:YLF laser used
to pump the Ti:Sa amplifier is 500 $\mu$s,[48] hence the excited state is not
saturated after 400 $\mu$s, and a jitter in the separation between amplified
pulses will be translated into energy fluctuations. For the 1 kHz Ti:Sa laser
system used in Ref. 45, this might be much less of an issue, as the laser
active medium in the Nd:YLF pump laser is close to saturation after 1 ms.

Figure 5: Scanning artifacts in ADASOPS. Top: time-separation of consecutive
amplified probe pulses (top arrows) when the pump-probe delay is increased by
1 ns every four laser shots. Bottom: Baseline (transient IR signal with pump
beam always blocked, averaged over all detector pixels) calculated from the
first and second pulses after a delay change (orange) and from the third and
fourth pulses (green).

We found that this effect can cause systematic artifacts. Fig. 5 shows the
baseline (averaged over the full spectrum) recorded for a pump-probe scan
where the delay was increased by 1 ns every four amplifier triggers, but the
pump beam was blocked. This baseline is zero (green line) only when the signal
is calculated from the third and fourth shots after every delay change
(corresponding to pump on and pump off in a regular measurement). When first
and second shots are used, the orange line is obtained, with a significant
offset (equivalent to a signal of $\approx$ 0.5 mOD) for every ns step, and a
12 times larger ’signal’ of opposite sign whenever a full oscillator round
trip time is reached.

These artifacts are huge, despite the fact that we use a reference beam to
normalize for probe-intensity fluctuations. The many non-linear steps needed
for the mid-IR generation probably aggravate the problem. Even larger
intensity changes can be expected for the amplified pump-pulses when we change
the pump-probe delay by many microseconds (see Fig. 3). This is, however, less
critical, because pump-pulse fluctuations only have a small effect on the
already small absorption changes. In any case, within two cycles after a delay
change, the energy of both pump and probe pulses stabilizes.

In our ADASOPS measurements, we therefore scan delay in small blocks of
typically 6 amplified pulses and disregard the first two laser shots in each
block. Pairwise two laser shots are chopped mechanically for referencing probe
pulses with pump on and off. The experiment shown further below (Fig. 6a)
contains 71 delay time setting, resulting in $\approx$6 full delay-time scans
per second, which is sufficient to suppress, for example, thermal laser
drifts.

###  Synchronisation Mode B: Two Identical Ti:Sa Laser Systems

This synchronisation mode is conceptually the same as our early approach,[31]
now realized with state-of-the-art electronics. That is, the time-separations
between the pulses of the two Ti:Sa oscillators is measured in a digital
manner, as described for synchronisation Mode A, which produces an error-
signal that is fed back to a piezo-actuator in one of the Ti:Sa oscillators.
It changes the resonator length of this Ti:Sa oscillator, and hence its
frequency, until both oscillators are locked. An additional number can be
added to the error signal in the FPGA before outputting it to the DAC, hence,
the two oscillators lock with a software-defined time-separation $t_{osc}$
between them.

In the language of electronics, synchronizing two Ti:Sa oscillators is a
phase-locked loop (PLL), where the piezo-controlled Ti:Sa oscillator acts as
the voltage controlled oscillator (VCO), whose frequency changes with the
voltage applied to the piezo-actuator. The theory of PLL’s is well
established, see e.g. Ref. 49. We achieved good performance when setting the
loop natural frequency to 20 Hz with close to critical damping (these values
can be adjusted with R1, R2 and C in the integrator shown in Fig. 1c).
Increasing the loop natural frequency beyond 20 Hz resulted in a $\approx$300
Hz oscillation of the feedback loop, presumably due to additional time
constants introduced into the overall loop filter due to the slow response of
the piezo-actuator.

Fig. 4c, blue, shows the pump-probe response of a Si-wafer measured with two
synchronized Ti:Sa laser systems. The fit reveals a jitter with a standard
deviation of 2.9 ps, about a factor two larger that that of ADASOPS (Fig. 4c,
black).

### Synchronisation Mode C: Ti:Sa Laser System Synchronized to a 100 kHz Yb
Laser System

High-repetition rate Yb-based femtosecond laser systems become more common in
transient IR spectroscopy spectroscopy.[50] This new technology not only
promises better signal-to-noise ratios due to the higher repetition rates and
better stability, but also enables conceptually new experiments. This is in
particular single-pump-multiple probe transient absorption spectroscopy, which
may cover an extremely wide range of timescales from picoseconds to second
with one and the same experimental setup.[38]

To realize such an instrument, we synchronize a Tangerin SP laser system
(Amplitude) to a Ti:Sa laser system (Tsunami/Spitfire, Spectra Physics). The
former produces a train of probe pulses separated by 10 $\mu$s each, the
latter delivers pump pulses at a lower repetition rate, ranging from 1 Hz to
2.5 kHz, which can be adapted to the length of the reaction of the
investigated sample. Within the first 10 $\mu$s, the relative timing of the
two lasers systems needs to be scanned, analogous to the synchronisation
methods described above. Beyond 10 $\mu$s, we get transient absorption data
“for free”, since the Yb-laser produces additional probe pulses.

ADASOPS will not work in this case. Setting the delay time to a desired value
requires that we have a certain freedom to chose which oscillator pulse is
being amplified in both pump and probe lasers. Practically speaking, the
Tangerin SP system does not accept any trigger input. But even if that were
possible, the jitter this may introduce could produce unacceptably high pulse
energy fluctuations, an additional problem beyond that discussed with Fig. 5:
When both lasers run asynchronously, a jitter of at least one oscillator pulse
would necessarily be introduced, even if the desired delay time is kept
constant. This is no longer negligible relative to the repetition rate of the
amplifier.

Figure 6: Demonstration experiments for the three different synchronisation
modes: in (a) with ADASOPS (synchronisation Modes A), in (b) two identical and
synchronized Ti:Sa laser systems (synchronisation Modes B), and (c) with a
Ti:Sa laser system synchronized to a 100 kHz Yb laser system (synchronisation
Modes C). In panels (a) and (b), the photo-induced MLCT and excitetd state
decay of Re(bpy)(CO)3Br in DMSO is measured, in panel (c) the photocycle of
bacteriorhodopsin in D2O. The time range from -10 ps to +10 ps is plotted on a
linear scale, beyond on a logarithmic scale. Negative bleaches are shown in
blue, positive transient bands in red. In the top-left corner, the MLCT in
Re(bpy)(CO)3Br is shown, as well as the photo-cycle of bacteriorhodopsin
including approximate times of the reaction steps. Marker modes of the various
intermediates are indicated in the transient spectra (see text for details).

Synchronisation Mode B will also not work, at least not directly, since the
oscillator frequencies are too far apart. That is, the Yb-oscillator runs at
41 MHz, and the Ti:Sa oscillator at $\approx 80.4$ MHz, the latter tunable by
$\approx\pm 0.2$ MHz with the help of the additional motor-driven mirror
mount. However, both lasers do not need to be locked for each individual laser
pulse, they need to be locked only every 10 $\mu$s, when a pulse from the Yb-
oscillator is picked by the Yb-amplifier. That is, the frequencies of the Yb-
oscillator and the Ti:Sa oscillator can be off by an integer-multiple of 100
kHz, which is within the tuning range of the Ti:Sa oscillator. Hence, the
synchronisation mode described here is a mix of synchronisation Modes A and B,
i.e., we synchronize two asynchronous laser oscillators, locking them to a
defined difference frequency.

To that end, we calculate in the FPGA the unwrapped data shown in Fig. 2,
subtract from them a linear function with properly chosen slope, and output
the result as an error signal to the DAC. The integrator and piezo-actuator in
the Ti:Sa oscillator close the feedback loop just as in synchronisation Modes
B. The same can be achieved much more precisely - albeit with severe
constraints on the laser system and repetition rates, with dual-comb lasers,
which have very recently been used produce amplified fs-pulses at arbitrary
delay[47].

Fig. 4c, red, shows the pump-probe response of the Si-wafer measured in this
configuration. The standard deviation of 3.2 ps is about the same as in
synchronisation mode B. Here it is important to note that both laser systems
were in different (neighboring) rooms on disconnected laser tables, with the
Ti:Sa pump pulse guided through a hole in the wall over $\approx$4 m from one
laser table to the other. The oscillator signal needed for the synchronisation
was sent via an optical fibre. Somewhat surprisingly, we did not see any drift
of time-zero over a period of $\approx$1 h. If drifts became an issue, one
could send the oscillator beam in parallel to the amplified beam from one
laser table to the other, and pick it up in a fibre only then. In that way,
one could compensate for distance drifts between two laser tables.

##  III Results

Fig. 6 shows demonstration experiments for the three different synchronisation
modes. In all of these experiments, the sample was excited with the 2nd
harmonic of a Ti:Sa laser system (Tsunami/Spitfire, Spectra Physics). The
probe pulses were derived from a home-built mid-IR-OPA pumped with an
identical Ti:Sa laser system system in Fig. 6a,b,[51] and a Twin STARZZ
(Fastlite) pumped with a Tangerine SP (Amplitude) in Fig. 6c. For referencing,
in all examples the probe pulses were split into two beams, only one of which
in overlap with the pumped volume of the sample, and imaged onto one line each
of a two-line MCT detector with single-shot readout.[52] To compute absorption
changes, in modes A and B the pump pulses were mechanically chopped at half
the repetition frequency of the pump amplifier. In mode C several probe pulses
were acquired before the arrival of each pump pulse.

Figs. 6a,b show the response of the C=O modes of Re(bpy)CO3Br to photo-induced
metal-to-ligand charge transfer (MLCT), with the focus on the symmetric
stretch vibration. Upon photo-excitation, an electron is transferred to the
ligand, formally oxidizing the Re-center, which causes a characteristic blue
shift of the CO vibrations due to $\pi$-backbonding. Initially, the blueshift
is small, and then increases on a 4 ps timescale due to the resolvation of the
new charge distribution in the charge transfer state.[53] That process is
resolved by both methods, i.e., ADASOPS (Fig. 6a) as well as with the two
synchronized Ti:Sa laser systems (Fig. 6b), but is more distinct in the former
case due to the higher time-resolution. The lifetime of the 3MLCT state is
about 50 ns, hence the plots of Figs. 6 show data up to 150 ns, when the
signal is fully decayed.

Fig. 6c explores the full reaction cycle of bacteriorhodopsin.[2, 6]
Bacteriorhodopsin is a light driven proton pump consisting of an
$\alpha$-helical trans-membrane protein with a retinal molecule bound to the
protein via a Schiff-base. Photo-excitation induces the trans-to-cis
isomerization of the chomophore around one of its C=C double bonds on a 500 fs
timescale.[4] It then proceeds through a sequence of intermediates commonly
denoted as J to O. The Schiff-base is deprotonated during the L-M transition
and the proton is transferred an Asp side chain, and is reprotonated from
another Asp during the M-N transition. Thermal back-isomerisation of the
chromophore occurs during the N-O transition, and deprotonation of the Asp
sidechain completes the catalytic cycle.[6] Most transient IR studies have
been performed with “slower” spectroscopic techniques, such as step-scan FTIR
spectroscopy[3, 54, 55, 5, 7, 8] or more recently with the help of quantum
cascade lasers,[56, 57, 58, 59] while the fs-ps timescale has been addressed
separately.[60, 61]

Synchronisation Mode C allows us to cover all timescales at once, see Fig. 6c.
The dominant feature in the transient absorption spectra is the negative
(blue) bleach of an ethylenic stretch vibration of the retinal chromophore
(labeled BR in Fig. 6c). This band exhibits the strongest response, since it
is affected directly by its photo-isomerization.[62] The band shifts to
different frequencies in the various states of the photo cycle, showing up as
positive (red) bands in Fig. 6c. The time resolution of the experiment,
$\approx$3 ps (see Fig. 4c, red), is sufficient to resolve the earliest J
state, whose lifetime is $\approx$3 ps.[63, 60] All subsequent states, i.e.,
state K through state O, reveal characteristic marker modes that are indicated
in Fig. 6c. The final state O relaxes back to the resting state BR on a 10 ms
timescale. Consequently, the repetition frequency of the pump pulses has been
set to $\approx$30 Hz in this experiment to assure that subsequent pump pulses
hit a fully relaxed sample. To do this without affecting laser performance, we
only adjusted the Pockels cell triggers of the Ti:S amplifier, but did not
change the 2.5 kHz repetition rate of its YLF pump laser. The sample was not
exchanged on a shot-by-shot basis, but we found that it bleaches on a minutes
timescale, hence the sample cuvette was slowly rasterized.

Table 1: Summary of features of the various synchronisation modes |  Mode A ADASOPS |  Mode B pump-probe |  Mode C single-pump-multiple probe
---|---|---|---
Probe rep. rate $f_{probe}^{amp}$ |  $\approx$ 2.5 kHz | 2.5 kHz | 100 kHz
Modification of pump oscillator | none | motor+piezo | motor+piezo
Pump oscillator frequency $f_{pump}^{osc}$ | freely running | locked to $f_{probe}^{osc}$ | locked to $f_{probe}^{osc}+kf_{probe}^{amp}$
At set delay |  $\approx$ every 5 $\mu$s | always | every 10 $\mu$s
Time resolution | 1.3 ps | 2.9 ps | 3.2 ps
Scan range |  $\approx 40~{}\mu$s |  $\approx 40~{}\mu$s |  $>1$ s
Fast scanning | yes | no | for delays $>10~{}\mu$s

##  IV Discussion and Conclusion

Table 1 compares some of the features of the various synchronisation modes.
They are complementary to a certain extent and have their pros and cons. For
example, since the absolute timing is variable within certain limits, but does
not change when changing the delay times in synchronisation Mode B, the two
amplifiers can be synchronized to yet another device, such as a photo-elastic
modulator (PEM) used for polarisation control with its own fixed resonance
frequency.[64]

On the other hand, ADASOPS (synchronisation Mode A) can work without any
modification of the laser systems. We derive the repetition frequency of the
Ti:Sa amplifiers from the difference frequency of the two oscillators by
division through a certain factor. The exact repetition frequency is not
critical (as long as it stays constant) and could be adjusted for any given
laser system by changing that division factor. Having a motor-driven
translation stage in one of the oscillators to adjust its round-trip time is
convenient, but not required, and neither is the piezo actuator. We anticipate
that this capability will be the most important application of ADASOPS.
Furthermore, since ADASOPS involves no moving parts, not even the micrometer
motion of a piezo actuator, it enables fast (i.e., shot-by-shot) scanning of
the pump-probe delay time (with the limitation discussed in Sec. II), which is
advantageous in terms of signal-to-noise of transient data. Finally, the time
resolution is better with ADASOPS.

Unfortunately, ADASOPS is not easily compatible with Yb-laser systems, as it
requires a certain freedom with regard to selecting the oscillator pulse that
is sent to the amplifier; the high repetition rate of these lasers is rather
restrictive in this regard. We see the biggest potential of high-repetition
rate Yb-laser systems in single-pump-multiple probe experiments that allow one
to cover all chemical relevant timescales,[38] ranging from the initial
photochemical trigger of the photoactive part of a molecular system until it
reaches its final state, which often spans a time range from picoseconds to
seconds. Synchronisation Mode C enables such experiments.

The focus in our lab lies on transient IR spectroscopy, which is sensitive to
chemical structure. However, since nonlinear optical processes can be driven
with high yields due to the high peak power of amplified femtosecond laser
systems, other spectroscopic regimes, ranging from THz to X-ray, are equally
accessible. At least for transient IR spectroscopy, the somewhat reduced time
resolution of 1-3 ps is not limiting, as perturbed-free induction decay
typically limits the response time of vibrational transitions to that time
regime.[65, 66]

One important prerequisite that makes these concepts possible is modern FPGAs,
which render hardware software-programmable. The style of programming of FPGAs
is quite different from “regular” programming languages, but is learnable for
anybody with programming experience (some experience in “conventional” digital
electronics helps as well). To learn how to program FPGAs, we recommend to
start from a small development board, such as tinyFPGA.

In our current realisation, we implemented synchronisation Modes A and B into
one FPGA with a software switch to select them without the need to re-plug any
cable in the laser setup. Switching between the two synchronisation modes is
thus a matter of minutes. Mode C, which we use in a different laser lab, is
currently implemented in another FPGA, yet utilizing the same electronics
hardware. One can consider Mode B a special case of Mode C with difference
frequency 0, and implementing all 3 modes in a single FPGA would certainly be
possible. In any case, the universal implementation of the three methods
allows us to freely select the most suitable method for a certain problem. In
fact, all three data sets shown in Fig. 6 were acquired on a single day. The
flexibility of the FPGAs make it possible to adapt the synchronisation
electronics to other laser configurations and/or other synchronisation modes
with only a limited programming effort.

To conclude, we consider the synchronisation electronics shown in Fig. 1d a
very versatile tool for all sorts of timing and synchronisation tasks of
femtosecond laser systems. In particular, many femtosecond labs that acquire a
new high-repetition rate laser system can probably recycle the old Ti:Sa laser
it replaces; the older the better since a non-integrated construct, such as
the Tsunami oscillator from Spectra Physics, makes it easier to add the motor-
driven translation stage and piezo-actuator needed to tune its round-trip
time. With rather limited effort, they may combine old and new laser systems
into a (still) quite unique spectrometer that can address a largely unexplored
time-window of photochemical reactions.

Conflict of Interest: The authors have no conflicts of interest to disclose.

Data Availability Statement: The data used in this article are available on
Zenodo (https://doi.org/10.5281/zenodo.8085588). Upon a reasonable request,
hardware and software of the synchronisation electronics will be made
available in the framework of a collaboration.

Acknowledgement: We thank Kerstin Oppelt and David Buhrke for providing
Re(bpy)CO3Br and BR samples, respectively. The work has been supported by the
Swiss National Science Foundation (SNF) through Grants 200020B_188694/1 and
200020_192240.

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