# 185 mW, 1 MHz, 15 fs carrier-envelope phase-stable pulse generation via
polarization-optimized down-conversion from gas-filled hollow-core fiber

Anchit Srivastava  Max Planck Institute for the Science of Light, Staudstrasse
2, Erlangen, 91058, Germany.  Friedrich-Alexander-Universität Erlangen-
Nürnberg, Staudstrasse 7, 91058 Erlangen, Germany.  Kilian Scheffter  Max
Planck Institute for the Science of Light, Staudstrasse 2, Erlangen, 91058,
Germany.  Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudstrasse 7,
91058 Erlangen, Germany.  Soyeon Jun  Max Planck Institute for the Science of
Light, Staudstrasse 2, Erlangen, 91058, Germany.  Friedrich-Alexander-
Universität Erlangen-Nürnberg, Staudstrasse 7, 91058 Erlangen, Germany.
Andreas Herbst  Max Planck Institute for the Science of Light, Staudstrasse 2,
Erlangen, 91058, Germany.  Friedrich-Alexander-Universität Erlangen-Nürnberg,
Staudstrasse 7, 91058 Erlangen, Germany.  Hanieh Fattahi
<EMAIL_ADDRESS>Max Planck Institute for the Science of Light,
Staudstrasse 2, Erlangen, 91058, Germany.  Friedrich-Alexander-Universität
Erlangen-Nürnberg, Staudstrasse 7, 91058 Erlangen, Germany.

###### Abstract

Gas-filled hollow core fibers allow the generation of single-cycle pulses at
megahertz repetition rates. When coupled with difference frequency generation,
they can be an ideal driver for the generation of carrier-envelope phase
stable, octave-spanning pulses in the short-wavelength infrared. In this work,
we investigate the dependence of the polarization state in gas-filled hollow-
core fibers on the subsequent difference frequency generation stage. We show
that by adjusting the input polarization state of light in geometrically
symmetric systems, such as hollow-core fibers, one can achieve precise control
over the polarization state of the output pulses. Importantly, this
manipulation preserves the temporal characteristics of the ultrashort pulses
generated, especially when operating near the single-cycle regime. We leverage
this property to boost the down-conversion efficiency of these pulses in a
type I difference frequency generation stage. Our technique overcomes the
bandwidth and dispersion constraints of the previous methods that rely on
broadband waveplates or adjustment of crystal axes relative to the laboratory
frame. This advancement is crucial for experiments demanding pure polarization
states in the eigenmodes of the laboratory frame.

##  I Introduction

Carrier-envelope phase stable (CEP) broadband sources Baltuška, Fuji, and
Kobayashi (2002) in the short-wavelength infrared (SWIR) and mid-infrared
(MIR) ranges are crucial for many applications where the interaction between
matter and light is sensitive to single oscillations of light, such as in
strong field physics Vozzi, Negro, and Stagira (2012); Schultz  _et al._
(2007); Ghimire and Reis (2019); Chevreuil  _et al._ (2021); Fattahi (2016);
Wendl, Högner, and Fattahi (2018) or field-resolved metrology Keathley  _et
al._ (2023); Hogue  _et al._ (2023); Herbst  _et al._ (2022); Yeung  _et al._
(2023); Zimin  _et al._ (2023); Kempf  _et al._ (2023); Mamaikin  _et al._
(2022); Srivastava  _et al._ (2023). It has been shown that CEP stable pulses
can be generated by actively stabilizing optical oscillators or fiber lasers
Vasilyev  _et al._ (2019); Kowalczyk  _et al._ (2023); Schoenfeld  _et al._
(2022), or by passive stabilization techniques such as frequency down-
conversion Cerullo  _et al._ (2011); Reiger  _et al._ (2024); Ernotte  _et
al._ (2016). Since oscillators generate pulses with low peak power, optical
parametric amplification has been utilized to enhance the energy of the
ultrashort pulses in these spectral regions Elu  _et al._ (2017); Deng  _et
al._ (2012); Alismail  _et al._ (2017); Ishii  _et al._ (2011); Fattahi  _et
al._ (2014). However, parametric amplifiers require high-energy pump sources,
which mostly operate at kilohertz repetition rates. The amplified pulses often
exhibit additional phase jitter in their CEP, stemming from the need for
interferometric stability between the pump and seed pulses Schwarz  _et al._
(2012); Fattahi  _et al._ (2012). Passive CEP stabilization based on
intrapulse difference frequency generation (IPDFG) offers unparalleled
stability and minimal CEP fluctuations, making it the preferred method for
generating CEP-stable, octave-spanning pulses at megahertz repetition rates.

In IPDFG, down-converted passively CEP-stable pulses are generated through
nonlinear frequency mixing of spectral components within a broadband pump
pulse in a $\chi^{(2)}$ nonlinear crystal. Two types of phase-matching can be
used to compensate for the phase velocity mismatch between the interacting
beams. In type II phase-matching, the input pump and IPDFG pulses have
orthogonal polarizations. On the contrary, in type I phase-matching, the input
pump pulses are projected into both orthogonal axes of the nonlinear crystal.
This projection compensates for the phase velocity mismatch between the high-
frequency and low-frequency components of the pump, as well as the IPDFG
pulses. Consequently, enhancing the conversion efficiency in type I phase-
matching requires optimizing the projection of the pump’s spectral components
onto the crystal’s orthogonal axes Fattahi  _et al._ (2013). To meet this
requirement, the optical axis of the nonlinear crystal can be rotated such
that the crystal axes have an angle with respect to the linear polarization of
the pump beam in the laboratory frame. In this case, the polarization of the
newly generated IPDFG pulses has the same angle relative to the linearly
polarized pulse in the laboratory frame, which poses a challenge for
polarization-sensitive applications such as electro-optic sampling,
spectroscopic ellipsometry, polarization spectroscopy, or optical parametric
amplification Kopf  _et al._ (2021); Aspnes (2014); Keiber  _et al._ (2016);
Alismail  _et al._ (2020); Kopf, Barros, and Fickler (2024); Wang  _et al._
(2019, 2017). Broadband half-wave plates present an alternative option for
optimizing the spectral distribution of input pump pulses along the crystal
axes. However, their effectiveness with ultrashort pulses is constrained due
to non-uniform phase retardation across a broad bandwidth and additional
material dispersion. These constraints lead to temporal broadening of input
pump pulses and lower conversion efficiency.

Figure 1: Experimental setup. The experimental setup for IPDFG comprises a
two-stage gas-filled hollow-core fiber setup pumped by a commercial Yb:KGW
amplifier at 1.03 $\mu$m. A half-wave plate is placed before the second fiber
stage to tune the input polarization. The near-single cycle pulses in the
fiber were down-converted in a 0.5 mm-thick BiBO crystal. Electro-optic
sampling was employed for the complete characterization of the generated
pulses. HC:PCF, hollow-core photonic crystal fiber; HWP, half-wave plate; OAM,
90∘ off-axis parabolic mirror; BS, beam splitter; W, wedge pair; EOS, electro-
optic sampling; L, lens; FEL, long-pass filter; FES, short-pass filter; QWP,
quarter-wave plate; WP, Wollaston prism; BD, balanced photodiode.

Gas-filled hollow-core fibers (HCF) are widely utilized to create few-cycle
ultrashort pulses at high peak power and megahertz repetition rates with a
high polarization purity Russell and Travers (2014); Taranta  _et al._ (2020).
In capillaries or single-ring hollow-core fibers with an M-fold symmetry,
where M indicates the number of tiny capillaries, the intrinsic birefringence
is negligible. Therefore, it is anticipated that the nonlinear propagation
dynamics within the fiber remain unaffected relative to the polarization state
of the input pulses Agrawal (2000). In this study, we leverage the inherent
symmetry of HCF to address the challenge of optimizing the spectral intensity
distribution in type I IPDFG. By utilizing a waveplate to adjust the
polarization state of the narrowband input pulses directed into a gas-filled
HCF, we fine-tune the polarization state of near-single-cycle ultrashort
pulses for efficient frequency down-conversion in subsequent stages. Our
findings indicate that the effect of polarization rotation on the nonlinear
dynamics within the fiber is minimal and does not alter the temporal duration
of the generated near-single-cycle pulse. We demonstrate that enhancing the
down-conversion efficiency can be achieved by optimizing the polarization
rotation of the input pump directed to the fiber. The field-resolved
measurement of the IPDFG pulses confirms that this optimization does not
affect the electric field of the generated IPDFG pulses.

##  II Results

The schematic of the setup used to generate and characterize IPDFG pulses is
shown in figure 1 and presented with details in Srivastava  _et al._ (2023).
The frontend was driven by a 1030 nm Yb:KGW amplifier with an average power of
20 W at 1 MHz repetition rate and a pulse duration of 255 fs. Two nonlinear
gas-filled photonic crystal fiber stages were used to generate near-single
cycle pulses. The spectral broadening in the first fiber stage was based on
self-phase modulation, followed by dispersive mirrors to temporally compress
the pulses to 25 fs at the full-width half maximum (FWHM). In the second fiber
stage, soliton-effect self-compression was used to compress the pulses further
to a pulse duration of 4.5 fs at the FWHM. The system ultimately delivered
16.5 W of average power with an overall efficiency of 82% and polarization
extinction ratio of 98%.

### Numerical analysis

Bismuth borate (BiBO) crystal was chosen for frequency down-conversion due to
its wide transmission range from 286 nm to 2500 nm, high damage threshold, and
large effective nonlinear coefficient. BiBO exhibits a higher nonlinear
coefficient compared to other suitable crystals at this range, such as lithium
triborate (LBO), beta barium borate (BBO), and potassium deuterium phosphate
(KDP) Ghotbi and Ebrahim-Zadeh (2004). Numerical simulations were conducted in
a simulation system for optical systems code (SISYFOS) Arisholm (1997) to gain
further insight into the phase-matching process. Both types of phase-matching
were considered for down-conversion of the octave-spanning spectrum in a 0.5
mm-thick BiBO crystal. For the type I phase-matching, the input polarization
was split between the crystal’s orthogonal axes. In this paper, we refer to
these axes as ‘o’ and ‘e’ to represent ordinary and extraordinary crystal
axes, respectively.

Figure 2: Phase-matching simulation for 0.5 mm-thick BiBO. (a) IPDFG spectrum
at various phase-matching angles for the (a) type I and (b) type II phase-
matching, respectively. The broadest bandwidth for phase-matching is at
$\theta$ = 11 o, whereas for type II is at $\theta$ = 55 o.

We assumed a polarization ratio of 95%-5% (o-e) for simulating the type I
phase-matching. The temporal profile of the output pulses from the frontent
was characterized by second-harmonic frequency-resolved optical gating (SH-
FROG) Kane and Trebino (1993). The retrieved spectrum and retrieved temporal
profile of the SH-FROG characterization were used as pump pulses for the IPDFG
simulation. Figure 2-a and figure 2-b compare the spectral bandwidth of the
IPDFG pulses versus the phase-matching angle of $\theta$ for type I and type
II phase-matching. It is seen that the broadest spectral bandwidth is achieved
at $\theta$ = 11 o for type I phase-matching and at $\theta$ = 55 o for type
II phase-matching. The spectra of both phase-matching types at the optimized
angles are shown in figure 2-c. Both spectra are normalized to the energy of
the IPDFG pulses in each case, indicating a broader spectral bandwidth and
higher gain in type I phase-matching compared to type II.

Figure 3: Numerical simulation. (a) Spectral evolution of the generated pulses
over a 1 mm-thick, type I, BiBO crystal at $\theta$ = 11 o. Numerically
simulated temporal evolution of (b) pump pulse propagating and (b) IPDFG
pulses through a 0.5 mm BiBO crystal. (d) Temporal walk-off between the pump
and IPDFG pulse after propagation in 0.5 mm of BiBO crystal. Comparison of the
output (e) o-pump and (f) e-pump at three different crystal thicknesses.

A one-dimensional simulation was performed to study the efficiency and
bandwidth scaling of the IPDFG pulses in type I phase-matching versus crystal
thicknesses. As shown in figure 3-a, for a crystal thickness longer than 0.5
mm, the center of mass of the difference frequency spectrum shifts to higher
frequencies, and the spectral intensity becomes a U-shape. This can be
attributed to the temporal walk-off between the interacting pulses. Inspecting
the temporal overlap of IPDFG and pump pulses indicates the complete temporal
separation between them due to their different group velocity in the crystal,
as shown in figure 3-b, figure 3-c, and figure 3-d. The input pump pulses have
a temporal pedestal, which originates from the residual higher-order phase on
the pump pulses due to the dispersive mirrors and soliton self-compression in
the fiber. The residual higher-order phase caused by the dispersive mirrors is
mainly at the two limits of the input pump spectrum, leading to the generation
of high-frequency wings of the IPDFG spectrum beyond the temporal walk-off of
the interacting pulses (see figure 3-d). Furthermore, soliton self-compression
causes the center of the pump spectrum to carry higher-order phases. These
phases manifest as a temporal pedestal, which in turn leads to the generation
of low-frequency wings in the IPDFG spectrum. Consequently, for crystal
thicknesses greater than 0.5 mm, the spectrum becomes U-shaped.

The energy distribution among the orthogonal components of pump pulses is
crucial for maximizing the efficiency of difference frequency generation in
type I phase-matching. This optimization relies on the principles of energy
and momentum conservation. During the down-conversion process, the energy of
the high-frequency components of the o-pump decreases, as illustrated in
figure 3-e. Conversely, the low-frequency components of the e-pump are
amplified (figure 3-f). Consequently, a series of simulations have been
conducted to investigate the impact of the polarization distribution of pump
energy on the efficiency of the down-conversion process in a 0.5 mm-thick type
I BiBO crystal. The energy of the e-pump pulses was scaled from 2% to 22%,
while the total energy of the pump pulses remained constant. Figure 4-a shows
the generated IPDFG spectra at different pump polarization ratios. This
assumes the placement of an ideal, dispersion-free, broadband waveplate before
the BiBO crystal. The simulation indicates that the conversion efficiency
peaks at a e-pump ratio of 22% and decreases for higher pump polarization
ratios.

Figure 4: Spectral evolution with respect to waveplate angles. (a) Numerically
simulated spectral evolution and (b) experimentally measured spectral
evolution of the IPDFG with respect to the waveplate angle. The measured
spectra are obtained from the Fourier transform of the corresponding EOS
trace.

### Experimental results

As discussed above, employing waveplates or rotating the crystal axes in the
laboratory frame imposes constraints for polarization-sensitive measurement.
Therefore, we took advantage of the fiber symmetry for ideal and dispersion-
free tunning of the polarization state of the octave-spanning pump spectrum. A
half waveplate (Altechna 2-APW-L2-018C) was placed at the relatively
narrowband input of the second gas-filled HCF. A 6-inch focal length parabolic
mirror was employed for focusing the pump to a beam size of 44 $\mu$m (FWHM),
resulting in the peak intensity of 300 $TW/cm^{2}$. A 0.5 mm-thick type I,
BiBO crystal cut in the XZ plane and at a phase-matching angle of $\theta$ =
11 o was used for IPDFG. The crystal was positioned behind the focus to
mitigate damage. Afterward, the IPDFG beam was collimated to a $1/e^{2}$ beam
diameter of 3.2 mm utilizing a 4-inch focal length parabolic mirror. A custom-
designed broadband dichroic beam splitter (UFI BS2214-RC2) separated the pump
and IPDFG beam. A custom-built double-angle chirped mirror compressor (UFI
IR7202) with four reflections was used to compensate for the accumulated
dispersion on the IPDFG pulses due to propagation in the BiBO crystal,
refractive optics and air, yielding 15 fs (FWHM) CEP-stable pulses.

The half waveplate at the input of the second gas-filled HCF was used to tune
the polarization extinction ratio of the pump pulses at the IPDFG szage.
Starting at the system’s overall extinction ratio of 98%- 2% (o-e), the half
waveplate angle was tuned, and the corresponding IPDFG output power was
measured. The average power was measured by placing a thermal power meter
after a holographic wire grid polarizer angled to allow linearly polarized
light with no rotation in the laboratory frame. The power of IPDFG pulses was
85 mW at an extinction ratio of 98%-2% (o-e), with a maximum power of 185 mW
at an extinction ratio of 86%-14%. The electric field of the IPDFG pulses was
characterized via electro-optic sampling (EOS) comprising a 20 $\mu$m BBO
crystal Srivastava  _et al._ (2023); Keiber  _et al._ (2016). The retrieved
spectra from the measured electric field of the IPDFG pulses at various
extinction ratios are shown in Figure 4-b. IPDFG conversion efficiency
gradually increases until the extinction ratio is 86%-14% (o-e). The minor
discrepancy between the measured and simulated optimum polarization ratio
could be associated with the slight birefringence in the fiber due to
fabrication imperfections. The birefringence of the fiber could lead to uneven
phase retardation resulting in elliptical polarization.

Figure 5: Polarization optimisation. The retrieved (a) temporal profiles and
(b) retrieved spectra of pump FROG characterization for two waveplate angles.
(c) The characterized electric field of the IPDFG pulses via EOS at two
extinction ratios and their corresponding spectral intensity are shown in (d).
The dashed line indicates the phase of the spectrum in both (b) and (d). The
legend in (a) applies to all figures.

The temporal profile of the output pulses from the fiber and the generated
IPDFG pulses at two extinction ratios were analyzed to confirm that the
polarization tuning of the input pulses does not affect the dynamics of
soliton self-compression. For this purpose, SH-FROG was employed to
characterize the fiber’s output pulses. Furthermore, to completely
characterize the IPDFG pulses, the electric field was measured through EOS.
Figure 5-a and figure 5-b show the retrieved temporal profiles and retrieved
spectra of the octave-spanning output pulses from the fiber at two
polarization ratios of 98%-2% (o-e) and 86%-14% (o-e). The measurements
indicate that polarization tuning has a negligible impact on the envelope and
spectrum of the fiber’s output. This suggests that the soliton dynamic inside
the fiber remains unaffected due to the minimum birefringence of the fiber.
The corresponding electric field of the generated IPDFG pulses at the two
polarization ratios are shown in figure 5-c. It has been observed that while
polarization tuning enhances the amplitude of the IPDFG waveform, the electric
field of the generated pulses remains unchanged.

##  III Conclusion

Over recent decades, the generation of high-energy, high-power pulses has
increasingly relied on spectral broadening in fibers or multi-pass
compression. IPDFG stands out as a highly promising method for generating
octave-spanning pulses in the SWIR and MIR spectral regions, with unparalleled
CEP stability from these frontends. Type I phase-matching, in particular, is
favored for its superior bandwidth and conversion efficiency, albeit it
necessitates an optimized polarization distribution along the crystal axes.

In this work, we conducted a detailed numerical analysis to identify the
optimal polarization distribution within type I BiBO crystals for the
generation of octave-spanning, CEP-stable pulses in the SWIR region. Prior
approaches primarily utilized broadband waveplates or involved altering the
orientation of the crystal axes with respect to the laboratory frame for
optimizing the down-conversion efficiency. To circumvent the limitations
presented by these methods, we have shown that in ultrashort pulse generation
from gas-filled hollow-core photonic crystal fibers, the efficiency of IPDFG
can be maximized by adjusting the polarization ratio of the narrowband pulses
prior to spectral broadening. By implementing a narrowband waveplate before
soliton compression, we successfully tuned the polarization of octave-
spanning, near-single-cycle pulses for efficient IPDFG without affecting the
soliton dynamics within the fiber. Our findings indicate that the orientation
of polarization relative to the fiber does not impact the duration or the
spectrum of the soliton self-compressed pulses. Additionally, we rigorously
validated our results by directly characterizing the electric field of the
IPDFG pulses, noting that while the polarization rotation of the input pulses
enhances the IPDFG pulse amplitude, their spectral phase remains well-behaved.

The approach discussed in this work is not only applicable to HCF systems but
can be extended to other symmetrical systems like multi-pass geometries, or
multi-stage spectral broadening Nisoli (2024); Fattahi  _et al._ (2016);
Viotti  _et al._ (2022); Lu  _et al._ (2014); Barbiero  _et al._ (2021). These
results are particularly vital for broadband down-conversion of high-power
systems to overtone and fingerprint spectral regions, where the bandwidth and
dispersion characteristics of waveplates present challenges, and in
experiments demanding pure polarization in the eigenmodes of the laboratory
frame.

###### Acknowledgements.

We thank Gunnar Arisholm for his support in the numerical analysis presented
in this work.

## DECLARATIONS

  * •

This work was supported by research funding from the Max Planck Society.

  * •

Conflict of interest/Competing interests: The authors do not declare any
competing interests.

  * •

Authors’ contribution: A.S. and K.S. conducted the measurements. A.S. and A.H.
developed the frontend. A.S. and S.J. performed the simulations. A.S. and H.F
performed the data analysis and wrote the manuscript. All authors proofread
the manuscript.

## DATA AVAILABILITY

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

## References

  * Baltuška, Fuji, and Kobayashi (2002) A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88, 133901 (2002).
  * Vozzi, Negro, and Stagira (2012) C. Vozzi, M. Negro, and S. Stagira, “Strong-field phenomena driven by mid-infrared ultrafast sources: Jmo series: attosecond and strong field science,” Journal of Modern Optics 59, 1283–1302 (2012).
  * Schultz  _et al._ (2007) K. Schultz, C. Blaga, R. Chirla, P. Colosimo, J. Cryan, A. March, C. Roedig, E. Sistrunk, J. Tate, J. Wheeler, _et al._ , “Strong-field physics with mid-infrared lasers,” J. Mod. Opt 54, 1075–1085 (2007).
  * Ghimire and Reis (2019) S. Ghimire and D. A. Reis, “High-harmonic generation from solids,” Nature physics 15, 10–16 (2019).
  * Chevreuil  _et al._ (2021) P.-A. Chevreuil, F. Brunner, S. Hrisafov, J. Pupeikis, C. R. Phillips, U. Keller, and L. Gallmann, “Water-window high harmonic generation with 0.8-$\mu$m and 2.2-$\mu$m opcpas at 100 khz,” Optics Express 29, 32996–33008 (2021).
  * Fattahi (2016) H. Fattahi, “Sub-cycle light transients for attosecond, x-ray, four-dimensional imaging,” Contemporary Physics 57, 580–595 (2016).
  * Wendl, Högner, and Fattahi (2018) M. Wendl, M. Högner, and H. Fattahi, “Theoretical study: High harmonic generation by light transients,” Applied Sciences 8 (2018), 10.3390/app8050728.
  * Keathley  _et al._ (2023) P. D. Keathley, S. V. B. Jensen, M. Yeung, M. R. Bionta, and L. B. Madsen, “Uncovering extreme nonlinear dynamics in solids through time-domain field analysis,” Phys. Rev. B 107, 054302 (2023).
  * Hogue  _et al._ (2023) J. Hogue, P. Cusson, M. Meunier, D. V. Seletskiy, and S. Reuter, “Sensitive detection of electric field-induced second harmonic signals,” Opt. Lett. 48, 4601–4604 (2023).
  * Herbst  _et al._ (2022) A. Herbst, K. Scheffter, M. M. Bidhendi, M. Kieker, A. Srivastava, and H. Fattahi, “Recent advances in petahertz electric field sampling,” Journal of Physics B: Atomic, Molecular and Optical Physics (2022).
  * Yeung  _et al._ (2023) M. Yeung, L.-T. Chou, M. Turchetti, S.-H. Chia, K. K. Berggren, and P. D. Keathley, “Lightwave electronic harmonic frequency mixing,” (2023), arXiv:2307.15145 [physics.optics] .
  * Zimin  _et al._ (2023) D. A. Zimin, I. Cherniukh, S. C. Böhme, G. Rainò, M. V. Kovalenko, and H. J. Wörner, “Electric-field-resolved detection of localized surface plasmons at petahertz-scale frequencies,” (2023), arXiv:2312.11727 [physics.optics] .
  * Kempf  _et al._ (2023) H. Kempf, P. Sulzer, A. Liehl, A. Leitenstorfer, and R. Tenne, “Few-femtosecond phase-sensitive detection of infrared electric fields with a third-order nonlinearity,” Communications Physics 6, 145 (2023).
  * Mamaikin  _et al._ (2022) M. Mamaikin, Y.-L. Li, E. Ridente, W. T. Chen, J.-S. Park, A. Y. Zhu, F. Capasso, M. Weidman, M. Schultze, F. Krausz, and N. Karpowicz, “Electric-field-resolved near-infrared microscopy,” Optica 9, 616–622 (2022).
  * Srivastava  _et al._ (2023) A. Srivastava, A. Herbst, M. M. Bidhendi, M. Kieker, F. Tani, and H. Fattahi, “Near-petahertz fieldoscopy of liquid,” arXiv preprint arXiv:2310.20512 (2023).
  * Vasilyev  _et al._ (2019) S. Vasilyev, V. Smolski, J. Peppers, I. Moskalev, M. Mirov, Y. Barnakov, S. Mirov, and V. Gapontsev, “Middle-ir frequency comb based on cr:zns laser,” Opt. Express 27, 35079–35087 (2019).
  * Kowalczyk  _et al._ (2023) M. Kowalczyk, N. Nagl, P. Steinleitner, N. Karpowicz, V. Pervak, A. Głuszek, A. Hudzikowski, F. Krausz, K. F. Mak, and A. Weigel, “Ultra-cep-stable single-cycle pulses at 2.2$\mu$mµm,” Optica 10, 801–811 (2023).
  * Schoenfeld  _et al._ (2022) C. Schoenfeld, P. Sulzer, D. Brida, A. Leitenstorfer, and T. Kurihara, “Passively phase-locked er:fiber source of single-cycle pulses in the near infrared with electro-optic timing modulation for field-resolved electron control,” Opt. Lett. 47, 3552–3555 (2022).
  * Cerullo  _et al._ (2011) G. Cerullo, A. Baltuška, O. Mücke, and C. Vozzi, “Few-optical-cycle light pulses with passive carrier-envelope phase stabilization,” Laser & Photonics Reviews 5, 323–351 (2011), https://onlinelibrary.wiley.com/doi/pdf/10.1002/lpor.201000013 .
  * Reiger  _et al._ (2024) S. Reiger, M. Mamaikin, D. Kormin, K. Golyari, H. Kassab, M. Seeger, V. Pervak, N. Karpowicz, and T. Nubbemeyer, “Ultra-phase-stable infrared light source at the watt level,” Opt. Lett. 49, 1049–1052 (2024).
  * Ernotte  _et al._ (2016) G. Ernotte, P. Lassonde, F. Légaré, and B. Schmidt, “Frequency domain tailoring for intra-pulse frequency mixing,” Optics express 24, 24225–24231 (2016).
  * Elu  _et al._ (2017) U. Elu, M. Baudisch, H. Pires, F. Tani, M. H. Frosz, F. Köttig, A. Ermolov, P. S. Russell, and J. Biegert, “High average power and single-cycle pulses from a mid-ir optical parametric chirped pulse amplifier,” Optica 4, 1024–1029 (2017).
  * Deng  _et al._ (2012) Y. Deng, A. Schwarz, H. Fattahi, M. Ueffing, X. Gu, M. Ossiander, T. Metzger, V. Pervak, H. Ishizuki, T. Taira, T. Kobayashi, G. Marcus, F. Krausz, R. Kienberger, and N. Karpowicz, “Carrier-envelope-phase-stable, 1.2 mj, 1.5 cycle laser pulses at 2.1 $\mu$m,” Opt. Lett. 37, 4973–4975 (2012).
  * Alismail  _et al._ (2017) A. Alismail, H. Wang, N. Altwaijry, and H. Fattahi, “Carrier-envelope phase stable, 5.4$\mu$j, broadband, mid-infrared pulse generation from a 1-ps, yb:yag thin-disk laser,” Appl. Opt. 56, 4990–4994 (2017).
  * Ishii  _et al._ (2011) N. Ishii, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, “Carrier-envelope-phase-preserving, octave-spanning optical parametric amplification in the infrared based on bib3o6 pumped by 800 nm femtosecond laser pulses,” Applied physics express 4, 022701 (2011).
  * Fattahi  _et al._ (2014) H. Fattahi, H. G. Barros, M. Gorjan, T. Nubbemeyer, B. Alsaif, C. Y. Teisset, M. Schultze, S. Prinz, M. Haefner, M. Ueffing, A. Alismail, L. Vámos, A. Schwarz, O. Pronin, J. Brons, X. T. Geng, G. Arisholm, M. Ciappina, V. S. Yakovlev, D.-E. Kim, A. M. Azzeer, N. Karpowicz, D. Sutter, Z. Major, T. Metzger, and F. Krausz, “Third-generation femtosecond technology,” Optica 1, 45–63 (2014).
  * Schwarz  _et al._ (2012) A. Schwarz, M. Ueffing, Y. Deng, X. Gu, H. Fattahi, T. Metzger, M. Ossiander, F. Krausz, and R. Kienberger, “Active stabilization for optically synchronized optical parametric chirped pulse amplification,” Opt. Express 20, 5557–5565 (2012).
  * Fattahi  _et al._ (2012) H. Fattahi, C. Y. Teisset, O. Pronin, A. Sugita, R. Graf, V. Pervak, X. Gu, T. Metzger, Z. Major, F. Krausz, and A. Apolonski, “Pump-seed synchronization for mhz repetition rate, high-power optical parametric chirped pulse amplification,” Opt. Express 20, 9833–9840 (2012).
  * Fattahi  _et al._ (2013) H. Fattahi, A. Schwarz, S. Keiber, and N. Karpowicz, “Efficient, octave-spanning difference-frequency generation using few-cycle pulses in simple collinear geometry,” Opt. Lett. 38, 4216–4219 (2013).
  * Kopf  _et al._ (2021) L. Kopf, J. R. D. Ruano, M. Hiekkamäki, T. Stolt, M. J. Huttunen, F. Bouchard, and R. Fickler, “Spectral vector beams for high-speed spectroscopic measurements,” Optica 8, 930–935 (2021).
  * Aspnes (2014) D. Aspnes, “Spectroscopic ellipsometry — past, present, and future,” Thin Solid Films 571, 334–344 (2014), 6th International Conference on Spectroscopic Ellipsometry (ICSE-VI).
  * Keiber  _et al._ (2016) S. Keiber, S. Sederberg, A. Schwarz, M. Trubetskov, V. Pervak, F. Krausz, and N. Karpowicz, “Electro-optic sampling of near-infrared waveforms,” Nature Photonics 10, 159–162 (2016).
  * Alismail  _et al._ (2020) A. Alismail, H. Wang, G. Barbiero, N. Altwaijry, S. A. Hussain, V. Pervak, W. Schweinberger, A. M. Azzeer, F. Krausz, and H. Fattahi, “Multi-octave, cep-stable source for high-energy field synthesis,” Science Advances 6, eaax3408 (2020), https://www.science.org/doi/pdf/10.1126/sciadv.aax3408 .
  * Kopf, Barros, and Fickler (2024) L. Kopf, R. Barros, and R. Fickler, “Correlating space, wavelength, and polarization of light: Spatiospectral vector beams,” ACS Photonics 11, 241–246 (2024), https://doi.org/10.1021/acsphotonics.3c01322 .
  * Wang  _et al._ (2019) H. Wang, A. Alismail, G. Barbiero, R. N. Ahmad, and H. Fattahi, “High energy, sub-cycle, field synthesizers,” IEEE Journal of Selected Topics in Quantum Electronics 25, 1–12 (2019).
  * Wang  _et al._ (2017) H. Wang, A. Alismail, G. Barbiero, M. Wendl, and H. Fattahi, “Cross-polarized, multi-octave supercontinuum generation,” Opt. Lett. 42, 2595–2598 (2017).
  * Russell and Travers (2014) P. S. J. Russell and J. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nature Photonics 8, 278–286 (2014).
  * Taranta  _et al._ (2020) A. Taranta, E. Numkam Fokoua, S. Abokhamis Mousavi, J. Hayes, T. Bradley, G. Jasion, and F. Poletti, “Exceptional polarization purity in antiresonant hollow-core optical fibres,” Nature Photonics 14, 504–510 (2020).
  * Agrawal (2000) G. P. Agrawal, “Nonlinear fiber optics,” in  _Nonlinear Science at the Dawn of the 21st Century_ (Springer, 2000) pp. 195–211.
  * Ghotbi and Ebrahim-Zadeh (2004) M. Ghotbi and M. Ebrahim-Zadeh, “Optical second harmonic generation properties of bib3o6,” Opt. Express 12, 6002–6019 (2004).
  * Arisholm (1997) G. Arisholm, “General numerical methods for simulating second-order nonlinear interactions in birefringent media,” JOSA B 14, 2543–2549 (1997).
  * Kane and Trebino (1993) D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE Journal of Quantum Electronics 29, 571–579 (1993).
  * Nisoli (2024) M. Nisoli, “Hollow fiber compression technique: A historical perspective,” IEEE Journal of Selected Topics in Quantum Electronics (2024).
  * Fattahi  _et al._ (2016) H. Fattahi, H. Wang, A. Alismail, G. Arisholm, V. Pervak, A. M. Azzeer, and F. Krausz, “Near-phz-bandwidth, phase-stable continua generated from a yb:yag thin-disk amplifier,” Opt. Express 24, 24337–24346 (2016).
  * Viotti  _et al._ (2022) A.-L. Viotti, M. Seidel, E. Escoto, S. Rajhans, W. P. Leemans, I. Hartl, and C. M. Heyl, “Multi-pass cells for post-compression of ultrashort laser pulses,” Optica 9, 197–216 (2022).
  * Lu  _et al._ (2014) C.-H. Lu, Y.-J. Tsou, H.-Y. Chen, B.-H. Chen, Y.-C. Cheng, S.-D. Yang, M.-C. Chen, C.-C. Hsu, and A. H. Kung, “Generation of intense supercontinuum in condensed media,” Optica 1, 400–406 (2014).
  * Barbiero  _et al._ (2021) G. Barbiero, H. Wang, M. Graßl, S. Gröbmeyer, D. Kimbaras, M. Neuhaus, V. Pervak, T. Nubbemeyer, H. Fattahi, and M. F. Kling, “Efficient nonlinear compression of a thin-disk oscillator to 8.5 fs at 55 w average power,” Opt. Lett. 46, 5304–5307 (2021).