# Molecular alignment-assisted spectral broadening and shifting in the near-
infrared with a recycled depleted pump from an optical parametric amplifier

Zhanna Rodnova  1 Tobias Saule  1 George Gibson  1 and Carlos A. Trallero-
Herrero1  1Department of Physics, University of Connecticut, Storrs, CT,
06269, USA
<EMAIL_ADDRESS>
††journal: opticajournal††articletype: Research Article

We demonstrate how the depleted pump of an optical parametric amplifier can be
recycled for impulsive alignment of a molecular gas inside a hollow-core fiber
and use such alignment for the broadening and frequency shift of the signal
pulse at a center wavelength of $\sim 1300$nm. Our results combine non-
adiabatic molecular alignment, self-phase modulation and Raman non-
linearities. We demonstrate spectral shifts of up to 204 nm and a spectral
broadening of more than one octave. We also report on the time delays at which
broadening occurs, which do not coincide with any of the molecular rotational
constants. Further, we encounter that maximum frequency shifts occur when the
signal and pump have perpendicular polarization instead of parallel.

##  1 Introduction

The invention of lasers in 1959 allowed a variety of applications in science
and technology, from spectroscopy [1, 2] and communications [3] to higher-
intensity applications, like studying nonlinear optical processes [4, 5, 6]
and multiphoton ionization [7, 8]. After a series of technological
breakthroughs in laser design, by the 1980s, the highest achievable peak
intensities became limited by self-focusing effects [9]. The invention of
chirped pulse amplification (CPA) [10] by Donna Strickland and Gerard Mourou
in 1985 resolved that limitation, paving the way for shorter laser pulses with
more bandwidth, allowing for higher peak intensities and enabling a variety of
high-intensity applications, from shorter timescale measurements in atomic and
molecular physics [11, 12, 13] and chemical dynamics [14, 15] to attosecond
physics [16, 17, 18].

Applications like these often benefit from frequency conversion from the
extreme ultraviolet (XUV) to the near-infrared (NIR). Optical parametric
amplifiers (OPAs) are a well-established technology for producing frequency-
tunable pulses [19, 20, 21, 22], and the accessible wavelength range can be
further extended with the use of additional non-linear methods.. For example,
difference frequency generation (DFG) is a common way of obtaining mid- and
long-wavelength infrared femtosecond pulses [23, 24, 25, 26, 27]. In this
case, a further wavelength range extension of both the signal and the idler
would be useful for concurrently running experiments at a different set of
wavelengths, therefore allowing for more flexibility. In another example,
degenerate OPAs (DOPAs)can create an extremely broadband gain [28, 29, 21],
but are limited in their wavelength range. Extending their wavelength range
would allow for experimental applications otherwise not available (i.e., pump-
probe experiments or DFG).

Along with the quest for more frequency tunability, much research has been
focused on generating pulses with more bandwidth through spectral broadening.
More conventional approaches to spectral broadening use Kerr-induced self-
phase modulation (SPM) [30],[31] from gas-filled hollow-core fibers (HCFs). In
the past, some research has been done on using molecular alignment for
spectral modulation [32]; recently, this approach has experienced a
renaissance of interest. Recent studies investigated optimizing the pulse
duration to maximize molecular alignment-induced rotational nonlinearities
[33], [34], therefore enhancing spectral broadening. Others focused on the
spectral shaping capabilities of employing molecular alignment for spectral
modulation, where a spectral shift was observed around partial rotational wave
packet revivals [35], with the probe pulse centered around 800 nm achieving a
shift of around 100 nm.

An alternative approach to generating larger bandwidth focuses on waveform
synthesis, a technique based on spatially and temporally combining multiple
pulses with different wavelengths and bandwidths to synthesize pulses with a
spectrum spanning multiple octaves [36, 37, 38, 39, 40, 41, 42]. However,
implementing such techniques requires a sophisticated feedback mechanism to
minimize time jitter between the different arms of the synthesizer. OPAs
present a natural palette for multiple colors, showing immense potential for
waveform synthesis. The depleted pump of an OPA typically possesses poor
spatial mode quality [43] and often gets discarded; however, in the past, our
group has shown [43], that it can be broadened in combination with the signal.
This is advantageous as it produces additional spectral components that are
phase-locked with the signal. In this work, we combine non-adiabatic
($\tau<<T_{rev}$) molecular alignment with SPM- and Raman-induced spectral
broadening. The technique we propose demonstrates a spectral shift of up to
204 nm, as well as broadening enhancement. We show that the recycled depleted
pump from an OPA can be effectively used as an alignment pulse, therefore
enhancing the overall optical efficiency. In addition, we demonstrate that a
depleted pump can be simultaneously broadened with the signal, showing promise
for continuous multi-octave spectrum generation; unlike in [43], our spectrum
contains wavelength components that bridge the spectral gap between the
depleted pump and the signal.

##  2 Experimental setup

Fig. 1 shows a schematic of the experimental setup. The technique employs a
titanium-sapphire (Ti:sapph) laser system, lasing around 800 nm, with 12 mJ
energy per pulse, 1 kHz repetition rate, and pulse duration of 35 femtoseconds
(fs). The laser is used to pump an asymmetric dual bismuth triborate
(BIBO)-based optical parametric amplifier (OPA). Pump power is split between
two arms of the OPA, with 70% pumping the strong arm and 30% pumping the weak
arm. The OPA generates two signal-idler pairs, with signals tunable from 1080
to 1600 nm, pulse duration of 50-80 fs, and idlers tunable from 1600-2600 nm,
pulse duration of 30-100 fs. The power of the strong signal-idler pair is up
to 2.7W, corresponding to a 32% conversion efficiency. Details on the OPA
design can be found in [44]. For the experiments presented here, only the
strong arm of the OPA was used. This experiment was performed using the
depleted pump (DP) and the strong signal from the OPA tuned to a central
wavelength of 1300 nm. In this experiment, the DP, with a pulse duration of
180 fs, was used to align molecules (i.e., N2, N2O, CO2, O2) in a hollow-core
fiber (HCF). We chose these molecular gases due to their wide availability,
their relatively high ionization potential (above 12 eV), and their high
nonlinear index of refraction. The signal has a pulse duration of 75 fs. A
$\lambda/2$ plate (half-wave plate, HWP) was used to control the polarization
of the signal, with the signal polarization initially perpendicular to the
polarization of the DP. Data was taken with polarizations of the DP and the
signal parallel as well as perpendicular. A delay stage with a minimum step
resolution of 1 $\mu$m was used to delay the pump pulses with respect to the
signal pulses. The two beams were spatially recombined, using a dichroic
mirror (DM) that reflects the DP and transmits the signal, and coupled into a
1m-long HCF (few-cycle, Inc.) filled with a molecular gas; unless specifically
mentioned, a 400 µm-core fiber was used. To ensure coupling to the fundamental
EH11 mode of the HCF, beams were focused to a $\frac{1}{e^{2}}$ spot size
$2\omega=0.7a$, where a is the core diameter of the HCF [31, 45, 46]. Gas was
supplied into the HCF using gas inlets on both sides of the fiber setup;
pressure is measured by two pressure gauges, set on both sides of the setup.
All pressures mentioned in the paper are absolute. The fiber setup employed
uncoated fused silica entrance and exit windows to ensure both DP and signal
were transmitted and to prevent spectral modulation of the output spectrum. As
a result of spatial imperfections in the signal mode, coupling losses were the
dominating loss mechanism, resulting in a power loss at the front of the HCF.
The intensity of the signal inside the HCF was kept around $2\cdot
10^{13}\frac{W}{cm^{2}}$ at all times to prevent ionization. The output of the
HCF was split with a wedge, where the transmission of the wedge went through a
long-pass filter with a cut-on wavelength $\lambda$=1000 nm to filter out the
DP. It then passed through a zinc-selenide (ZnSe) crystal, generating a second
harmonic (SH). The SH was necessary due to the wavelength range limitations of
spectrometers available during the experiment. Due to its random quasi-
matching properties (RQPM) [47, 48, 49, 50, 51], ZnSe does not require tuning
of the phase matching angle of the crystal, making it the perfect candidate
for SH generation. The SH spectrum was measured by Spectrometer 1. The
reflection from the wedge, containing the signal and the DP, was measured by
Spectrometer 2. The delay stage was used to scan across various regions of the
rotational structure induced by the DP or signal (depending on the delay), in
particular the partial and full revivals (overlap, ¼Trev, ½Trev, ¾Trev, Trev)
to look for changes in the output spectrum. Experimental data were plotted as
a two-dimensional map of spectra as a function of the delay between the
aligning DP pulse and signal pulse.

Fig. 2 shows two examples of delay-dependent output spectra. Both figures were
obtained by performing a scan over -Trev to Trev for the respective gases. In
both figures, at times before overlap (t0=0 ps), the signal pulse arrives
earlier and has an aligning effect on the DP spectrum. After overlapping, the
DP pulse arrives earlier and has an aligning effect on the signal spectrum. To
determine the time of overlap accurately, the experiment was performed with
the HCF filled with argon (Ar); due to being an atomic gas, argon had a clear
overlap region with the DP and signal intensities adding up at t0 when their
polarizations were parallel. Fig.2(a) shows the output spectra from a 1.36 bar
nitrous oxide (N2O)-filled HCF, whereas Fig.2(b) shows the spectra from an HCF
filled with 1.01 bar of carbon dioxide (CO2). Data in both figures are taken
with signal and DP cross-polarized. In Fig.2(a), a lack of structure at
quarter-revivals (¼Trev, ¾Trev) is evident, characteristic for N2O, due to the
molecule having a 1:1 ratio of even and odd rotational states. On the other
hand, Fig.2(b) shows pronounced quarter-revivals as well as the half-revival
and full-revival of CO2.

Figure 1: Experimental setup. OPA - optical parametric amplifier; HWP -
$\lambda/2$ plate; L1, L2 - lenses for focusing depleted pump (DP) and signal
(S) into the fiber, respectively; DM - dichroic mirror, reflecting the DP and
transmitting the signal; HCF - 1m-long hollow-core fiber (few-cycle, Inc.); W
- wedge; LP - long-pass filter.

Figure 2: Examples of output spectra obtained by Spectrometer 2. The signal of
the OPA was centered around 1300 nm. (a) Output spectrum for 1.36 bar of N2O
(Trev=39.8 ps), signal and DP cross-polarized, (b) Output spectrum for 1.01
bar of CO2(Trev=42.7 ps), signal and DP cross-polarized.

##  3 Results and discussions

Figure 3: Second harmonic (SH) of the output spectra from a fiber filled with
1.7 bar of N2O, signal and DP are cross-polarized. The signal of the OPA was
centered around 1300 nm. The dashed line represents the output spectrum
without DP. The wavelengths specified are center-of-mass wavelengths for each
spectrum. The tunability range of 102 nm in SH corresponds to 204 nm in the
fundamental.

The signal of the OPA was centered around 1300 nm. As the signal interacted
with the molecular gas, it experienced spectral broadening due to Kerr-induced
SPM, changing its central wavelength. However, when scanning over various
delay regions of interest (overlap, ¼Trev, ½Trev, ¾Trev, Trev), we observed
noticeable spectral shifts around the partial revivals along with spectral
broadening. The experimental results are summarized in Table 1, where the
largest experimentally observed center-of-mass (COM) wavelength shift is
given, together with the polarizability difference for each of the four
molecules. The absolute wavelength shift for each molecule was comparable
between different partial revivals (¼Trev, ½Trev, etc.), except in N2. In N2,
the shifts around quarter-revivals (¼Trev and ¾Trev) were half of those around
half-revivals (½Trev and Trev).

Molecule |  $\Delta\alpha(10^{-25}$ cm3) | COM shift, $\perp$ | COM shift, $\parallel$
---|---|---|---
N2O | 28.1$\pm$1.1 [52] | 204 nm | 130 nm
CO2 | 21.09 [53] | 136 nm | 110 nm
O2 | 10.2$\pm$0.4 [52] | 54 nm | 49 nm
N2 | 6.7$\pm$0.3 [52] | 49 nm | 41 nm
Table 1: Largest COM wavelength shift and polarizability differences for N2O,
CO2, O2 and N2 when signal and DP polarizations were perpendicular ( $\perp$ )
and parallel ($\parallel$). The absolute shift was comparable between
different partial revivals for a given molecule, except in N2. In N2, the
shift around quarter-revivals (¼Trev and ¾Trev) was half of that around half-
revivals (½Trev and Trev). The number density of molecules is $N=4.2\cdot
10^{25}$ m-3 for all gases, assuming ideal gas law.

Figure 3 shows a wavelength shift that occurred in 1.7 bar of N2O, with the
COM wavelength of the SH spectrum experiencing a redshift of 42 nm followed by
a blue shift of 60 nm as the delay between the DP and the signal increased.
This shift corresponded to a tunability range of 102 nm in the SH and 204 nm
in the fundamental, which was the largest shift observed. In 1.7 bar of CO2,
the SH COM wavelength experienced a blue shift of 50 nm followed by a red
shift of 18 nm as the delay increased, corresponding to a tunability range of
68 nm in SH and 136 nm in the fundamental. Lastly, the spectral shift in N2O
was studied with DP and signal polarizations parallel, only showing a COM SH
wavelength tunability range of 65 nm, equivalent to 130 nm in the fundamental.
The change of the refractive index of a molecular gas is given by [35]:

$\Delta n(t)=\Delta n_{K}+\Delta n_{R}+\Delta n_{Align},$ (1)

where $\Delta n_{K}=n_{2}I(t)$ \- instantaneous response due to the Kerr
effect, $\Delta n_{R}$ \- delayed contribution due to the Raman effect,
$\Delta n_{Align}$ \- delayed contribution due to molecular alignment. When
the polarization of the signal is parallel to the polarization of the DP, the
change of the refractive index of molecular gas due to molecular alignment is
given by [54]:

$\Delta n_{Align}=\Delta n_{\parallel}(t)=\frac{2\pi
N}{n_{0}}\Delta\alpha(<cos^{2}\theta>_{t}-\frac{1}{3}),$ (2)

where $\Delta n_{\parallel}(t)$ \- change in the nonlinear index in the cross-
polarized case, N - number density of molecules, n0 \- linear refractive
index, $\Delta\alpha=\alpha_{\parallel}-\alpha_{\perp}$ \- the difference
between the parallel and perpendicular components of polarizability,
$<cos^{2}\theta>_{t}$ \- expectation value of the thermally averaged
alignment. When the polarizations of the signal and the DP are
perpendicular[35, 55],

$\Delta n_{Align}=\Delta n_{\perp}(t)=-\frac{1}{2}\Delta n_{\parallel}(t).$
(3)

Based on Eq. (3), we would expect the wavelength shift to be larger when the
DP and signal polarizations are parallel. However, our data consistently
showed a larger wavelength shift for the cross-polarized case. We believe that
to be because our pulse duration is in a regime where Raman and Kerr
contributions to the nonlinear refractive index can no longer be treated and
evaluated independently [52, 56].

After studying the spectral shift that occurred around partial revivals, we
set out to investigate the effect of an aligning pulse on spectral broadening.
We anticipated the largest spectral broadening to occur at the exact temporal
overlap between the DP and the signal, with DP and signal polarizations
parallel and their intensities effectively adding together. However, the
biggest broadening did not occur at t0 but some $\Delta t$ after, indicating a
delayed response of the medium that enhanced the spectral broadening. The
experimental results are summarized in Table 2, where the largest
experimentally observed bandwidths are given, together with the delays where
they were observed.

Molecule | 10 dB, $\parallel$ | $\Delta t_{\parallel}$ | 10 dB, $\perp$ | $\Delta t_{\perp}$
---|---|---|---|---
N2O | 417$\pm$3 nm | 406 fs | 330$\pm$15 nm | 180 fs
CO2 | 393$\pm$4 nm | 253 fs | 225$\pm$16 nm | 213 fs
N2 | 318$\pm$17 nm | 133 fs | 307$\pm$36 nm | 40 fs
Table 2: Largest 10 dB bandwidths for spectra from 1.7 bar of N2O, CO2, O2 and
N2, when signal and DP polarizations were parallel ($\parallel$) and
perpendicular ( $\perp$ ). The signal of the OPA was centered around 1300 nm.
The largest bandwidth was consistently observed in the region of temporal
overlap between the DP and the signal. $\Delta t$ is the exact delay in
femtoseconds from temporal overlap t0 where the largest bandwidth occurs.

Unlike our spectral shift results, we did not see a contradiction with Eq. (3)
in the effect of an aligning pulse on spectral broadening. Our data
consistently showed a larger broadening when the DP and the signal
polarizations were parallel. The largest broadening enhancement was seen in
1.7 bar of N2O, where a 251 nm 10 dB bandwidth was enhanced to 417 nm. In 1.7
bar of CO2, the bandwidth without the DP present was 310 nm, enhanced to 393
nm. The experiment was repeated with 1.7 bar of N2O, with DP and signal
polarizations perpendicular, but that did not yield an increase in bandwidth
as significant as in the same polarization case. Lastly, the setup was tested
with 1.7 bar of argon to confirm the attractiveness of such a technique for
spectral broadening. Ar is one of the more commonly used gases for spectral
broadening due to its availability, relatively high ionization threshold
(above $10^{14}\frac{W}{cm^{2}}$ [57]), and high nonlinear refractive index
n2, resulting in Kerr-induced spectral broadening due to self-phase
modulation. Other commonly used gases, xenon and krypton, are more expensive
and generally less available. In our experiment, 1.7 bar of argon showed a 10
dB bandwidth of 265 nm, which was significantly smaller than the enhanced
broadening from CO2 and N2O. We were only able to see an enhanced broadening
in N2 when we used a smaller fiber with a 300 µm core diameter. In O2, we did
not see a strong enough dependence of spectral broadening on the presence of
an aligning pulse. We believe using a smaller fiber, and therefore, having a
higher peak intensity would have changed that.

Figure 4: (a) Output spectrum from a 400µm fiber filled with 1.7 bar of Ar.
(b) Output spectrum from a 400µm fiber filled with 1.7 bar of N2O. (c) Output
spectrum from a 300µm fiber filled with 1.7 bar of N2. Data in (a) and (b)
were taken with the signal centered around 1300 nm. Data in (c) were taken
with the signal centered around 1200 nm. The dashed colored line is the
spectrum at the time of overlap, t0; $\Delta t$ \- delay from t0. $\Delta
t_{N_{2}O}=$406 fs for N2O, $\Delta t_{N_{2}}=$133 fs for N2. The black line
represents background noise.

After demonstrating the spectral tunability and the spectral broadening
capabilities of the setup, we investigated the potential of using the proposed
scheme for generating continuous broadband spectra, expecting the enhanced
broadening to bridge the spectral gap between the DP and the signal and yield
a continuous spectrum. Fig. 4 shows output spectra from the HCF filled with Ar
(Fig. 4(a)), N2O (Fig. 4(b)) and N2 (Fig. 4(c)). In Fig. 4(b) and (c), the
dashed colored spectrum is the spectrum at the time of overlap, t0. The
spectrum obtained from 1.7 bar of argon (Fig. 4(a)), commonly used for
spectral broadening, produces a significant symmetric broadening,
characteristic for Kerr-induced broadening. However, using the proposed
technique with the HCF filled with 1.7 bar of N2O results in a broader
spectrum; an even broader spectrum can be obtained using a smaller (300 µm)
core diameter fiber filled with 1.7 bar of N2. It can be seen that the
spectrum slightly after ($\Delta t_{N_{2}O}=$406 fs for N2O, $\Delta
t_{N_{2}}=$133 fs for N2) the overlap is significantly broader, demonstrating
the delayed nature of spectral broadening, characteristic of the Raman effect
[33]. To obtain a continuous spectrum, we had to either use a smaller fiber,
resulting in higher peak intensity (Fig. 4(b)), or lower the signal wavelength
to bring it closer to the DP wavelength (Fig. 4(c)). The spectrum in Fig. 4(b)
is continuous and spectrum in Fig. 4(c) is nearly continuous. Our resolution
is limited by the bit depth of the spectrometer used. We believe our spectrum
in Fig. 4(c) is continuous. It can be seen that molecular gases (N2O and N2)
introduce a noticeable red shift of the spectrum, characteristic of Raman-
induced nonlinearities [33, 56], as well as broadening. In Fig. 4(b) and (c),
the output spectrum contains wavelength components around 1100 nm that are
otherwise not present. This allows for a continuous spectrum from 729 nm to
1589 nm in N2 (Fig. 4(b)), spanning more than one octave and showing promise
for continuous multi-octave spectrum generation. To confirm our experimental
results, we performed theoretical simulations to predict spectral broadening
from a gas-filled HCF. The theoretical results agreed with our data in the
case of Ar, a noble gas, whereas for molecular gases no such agreement was
found.

##  4 Concluding remarks

In conclusion, we have demonstrated a flexible technique that recycles a
depleted pump from an OPA to combine non-adiabatic molecular alignment with
Kerr-induced self-phase modulation and Raman nonlinearities, allowing for
spectral shaping, spectral broadening enhancement, and potential continuous
ultra-broadband spectrum generation. We measured an OPA signal shifting in the
center-of-mass (COM) wavelength of the spectrum by up to 204 nm. The COM
wavelength shifts observed around different partial revivals were comparable
for a given gas, except for N2, where the shift around quarter revivals (¼Trev
and ¾Trev) was half of the shift observed around half-revivals (½Trev and
Trev). We expected the shift to be larger when the DP and the signal
polarizations are parallel, but our data consistently showed a larger shift in
the cross-polarized case. We believe our pulse duration is in a regime where
the changes in the refractive index due to the instantaneous and delayed
responses of a molecular medium can no longer be treated separately. We
studied the effect of the delayed Raman response of molecular gas on spectral
broadening, expecting the contradiction to carry over to broadening as well.
However, we found no such contradiction, observing a larger broadening in the
case of parallel polarizations. Lastly, we demonstrated the generation of
additional spectral components around 1100 nm, bridging the gap between the
depleted pump and the signal of an OPA, resulting in a continuous spectrum
from 729 nm to 1589 nm, spanning more than an octave without the need for
additional jitter control. Adding a broadened spectrum of an OPA idler in the
future would allow for extending the spectrum further, making the generation
of an ultra-broadband multi-octave spectrum possible.

Funding Acknowledgments This research was performed under the Office of Naval
Research, Directed Energy Ultra-Short Pulse Laser Division grant
N00014-19-1-2339. T. S. was partially funded by AFOSR, Air Force Office of
Scientific Research grant FA9550-21-1-0387. Z. R. was partially funded by the
Directed Energy Professional Society Graduate Research Grant.

Disclosures The authors declare no conflicts of interest.

Data Availability Statement Data underlying the results presented in this
paper are not publicly available at this time but may be obtained from the
authors upon reasonable request.

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