1
High-energy pulse synthesis with sub-cycle waveform
control for strong-field physics
Shu-Wei Huang
1
, Giovanni Cirmi
1
, Jeffrey Moses
1
, Kyung-Han Hong
1
, Siddharth Bhardwaj
1
,
Jonathan R. Birge
1
, Li-Jin Chen
1
, Enbang Li
2
, Benjamin J. Eggleton
2
, Giulio Cerullo
3
, and Franz X.
Kärtner
1,4*
1
Department of Electrical Engineering and Computer Science and Research Laboratory of Electronics,
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
2
Centre for Ultrahigh Bandwidth Devices for Optical Systems, Australian Research Council Centre of
Excellence, School of Physics, University of Sydney, NSW 2006, Australia
3
IFN-CNR, Dipartimento di Fisica, Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milano, Italy
4
DESY-Center for Free-Electron Laser Science and Hamburg University, Notkestraße 85, D-22607
Hamburg, Germany
Over the last decade, control of atomic-scale electronic motion by non-perturbative
optical fields has broken tremendous new ground with the advent of phase-controlled
high-energy few-cycle pulse sources
1
. The development of close-to-single-cycle, carrier-
envelope phase (CEP) controlled, high-energy optical pulses has already led to isolated
attosecond EUV pulse generation
2
, expanding ultrafast spectroscopy to attosecond
resolution
1
. However, further investigation and control of these physical processes
requires sub-cycle waveform shaping, which until now could not be achieved. Here we
present a light source, utilizing coherent wavelength multiplexing, that enables sub-cycle
waveform shaping with a two-octave-spanning spectrum and 15-μJ pulse energy. It
2
offers full phase control and allows generation of any optical waveform supported by the
amplified spectrum. Both energy and bandwidth scale linearly with the number of sub-
modules, thus the peak-power scales quadratically. The demonstrated system is the
prototype of a class of novel optical tools for attosecond control of strong-field physics
experiments.
Since the invention of pulsed lasers, the ultrafast laser science community has strived
for ever broader optical bandwidths, shorter pulse durations, higher pulse energies, and
improved phase control. Each breakthrough in the generation methods has led to new
scientific discoveries, in a wide range of fields
3-5
. Recent investigations of phenomena at
the intersection of ultrafast and strong-field laser physics, such as high-harmonic
generation (HHG)
6
and strong-field ionization
7
, has demanded that laser sources combine
each of the breakthroughs mentioned above. Investigation and control of strong-field
light-matter interaction simultaneously requires a multi-octave-spanning bandwidth, an
isolated sub-cycle waveform, a peak-intensity above 10
14
W/cm
2
and a full phase control.
Such features would allow arbitrary shaping of the strong electric-field waveform for
steering ionized electron wavepackets
8
and precise control of tunneling and multiphoton
ionization events.
For over two decades, laser scientists have sought to extend laser bandwidths and
achieve sub-cycle optical waveforms by synthesizing multiple laser sources
9
. Attempts
to combine two independent mode-locked lasers have seen some success, e.g., for
frequency metrology
10, 11
, but are challenging because of the differential phase noise
3
beyond the achievable feedback loop bandwidth. This problem was recently
circumvented by coherently adding two pulse trains derived from the same fiber laser,
resulting in the first demonstration of an isolated single-cycle optical pulse source
12
.
This proved the feasibility of pulse synthesis at the nanojoule level, but achieving high
pulse-energy requires synthesis of low-repetition-rate pulses, which is a challenge
because of the environmental perturbations typical of high-energy amplifiers. An
approach to high-energy pulse synthesis based on combining the pump, signal, and idler
of a multi-cycle optical parametric amplifier is being investigated and it shows the
potential to produce multiple single-cycle pulses under a multi-cycle envelope with pulse
separation on the order of a few femtoseconds
13
.
In this paper, we address the challenge of high-energy sub-cycle optical waveform
synthesis. We demonstrate a new approach, based on coherent wavelength multiplexing
of ultra-broadband optical parametric chirped pulse amplifiers (OPCPAs), for the
generation of fully controlled high-energy non-sinusoidal optical waveforms with spectra
spanning close to two octaves. By simulation, we present an example of the unique
features of our source as a driver for isolated strong-field physics experiments: the
confinement of the strong-field light-matter interaction to within an optical cycle and
attosecond control of the interaction. The system coherently combines two CEP-
controlled, few-cycle pulses obtained from different OPCPAs: 1) a near infrared (NIR)-
OPCPA, producing 25-μJ, 9-fs pulses centered at 870 nm; and 2) a short-wavelength
infrared (SWIR)-OPCPA, producing 25-μJ, 24-fs pulses centered at 2.15 μm. The ultra-
broadband OPCPA is the most promising technology for producing wavelength-tunable,
4
high-peak-power and high-average-power, few-cycle optical pulses with good pre-pulse
contrast
14
. Furthermore, an ultra-broadband OPCPA maintains good CEP stability due to
the low thermal load and the small dispersion required to stretch and compress the signals.
Figure 1 shows a schematic of the system. It starts with an actively CEP-stabilized
octave-spanning Ti:sapphire oscillator. Using a single oscillator as front-end for the
entire system ensures the coherence of the two OPCPA pulses to within environmental
fluctuations and drifts on subsequent beam paths. The designs of the OPCPAs follow the
guidelines described in previous studies
15, 16
for simultaneously optimizing energy
conversion, amplification bandwidth, and signal-to-noise ratio. Of note, the inclusion of
an acousto-optic programmable dispersive filter (AOPDF) in each OPCPA allows
independent spectral phase and amplitude adjustment of each pulse, enabling control and
optimization of the synthesized waveform.
Outputs from the two OPCPAs are combined in a broadband neutral beamsplitter.
The overall spectrum spans over 1.8 octaves (green lines in Fig. 2a) and the energy of the
synthesized pulse is 15 μJ. Besides the spectral phases (controlled by the AOPDFs),
three other independent parameters (see Fig. 1) determine the synthesized electric-field
waveform: the CEP of the NIR-OPCPA pulse (φ
1
), the CEP of the SWIR-OPCPA pulse
(φ
2
), and the relative timing between the two OPCPA pulses (Δt). Precise stabilization of
these three parameters is required for coherent synthesis of the two OPCPA pulses, and
subsequent control of each parameter allows precise waveform shaping. While the CEP
of the SWIR-OPCPA is passively stabilized due to the intrapulse difference-frequency
generation (DFG)
17
used to produce its seed, an active feedback loop on the oscillator is
5
implemented to ensure the CEP stability of the NIR-OPCPA. Figures 2d and 2e
demonstrate the CEP stability of the two individual pulses, with r.m.s. fluctuations as low
as 135 mrad and 127 mrad, respectively. Figure 2h characterizes the relative timing
stability. A feedback loop based on a balanced cross-correlator (BCC)
18
is implemented
to synchronize the two pulses, allowing attosecond-precision relative timing stability.
With the feedback control of the SWIR-OPCPA’s path length over a bandwidth of 30 Hz,
the relative timing drift is reduced to 250 as, less than 5% of the oscillation period of the
SWIR-OPCPA (7.2 fs).
Once the BCC-assisted feedback loop stabilizes the relative timing between the two
OPCPA pulses, a two-dimensional spectral-shearing interferometer (2DSI)
19
is used to
measure the frequency-dependent group-delay of the synthesized pulse. Figures 2b and
2c show the raw data of a 2DSI measurement while Fig. 2a plots (black lines) the
extracted frequency-dependent group-delay of the synthesized pulse, which is the
derivative of the spectral phase with respect to frequency. The 2DSI measurement shows
that the two OPCPA pulses are temporally overlapped and each is well compressed to
within 10% of its transform-limited pulse duration.
In our system, the CEPs can be varied by slight tuning of any dispersive element,
including the AOPDFs
20
. The values of the CEP will be determined automatically in situ
when strong-field experiments are conducted
21
and hence CEP tunability is sufficient
from an experimental point-of-view. In summary, our system is capable of stabilizing
and controlling all independent parameters that define the synthesized electric-field
waveform. Figure 3a plots a synthesized electric-field waveform and intensity profile