# Coherent Vibrational Micro-Spectroscopy for High-Speed Investigation of
Single-Crystalline Materials

Franz Hempel<EMAIL_ADDRESS>Institut für Angewandte Physik,
Technische Universität Dresden, 01062 Dresden, Germany  Federico Vernuccio  :
<EMAIL_ADDRESS>Physics Department, Politecnico di Milano, 20133
Milano, Italy  Lukas König  Institut für Angewandte Physik, Technische
Universität Dresden, 01062 Dresden, Germany  Robin Buschbeck  Institut für
Angewandte Physik, Technische Universität Dresden, 01062 Dresden, Germany
Michael Rüsing  Institut für Angewandte Physik, Technische Universität
Dresden, 01062 Dresden, Germany  Giulio Cerullo  Physics Department,
Politecnico di Milano, 20133 Milano, Italy  Dario Polli  Physics Department,
Politecnico di Milano, 20133 Milano, Italy  Lukas M. Eng  Institut für
Angewandte Physik, Technische Universität Dresden, 01062 Dresden, Germany
ct.qmat: Dresden-Würzburg Cluster of Excellence—EXC 2147, Technische
Universität Dresden, 01062 Dresden, Germany

###### Abstract

Broadband coherent anti-Stokes Raman scattering (BCARS) is an advanced Raman
spectroscopy method that combines the spectral sensitivity of spontaneous
Raman scattering (SR) with the increased signal intensity of single-frequency
coherent Raman techniques. These two features make BCARS particularly suitable
for ultra-fast imaging of heterogeneous samples, as already shown in
biomedicine. Recent studies demonstrated that BCARS also shows exceptional
spectroscopic capabilities when inspecting crystalline materials like lithium
niobate and lithium tantalate, and can be used for fast imaging of
ferroelectric domain walls. These results strongly suggest the extension of
BCARS towards new imaging applications like mapping defects, strain, or dopant
levels, similar to standard SR imaging. Despite these advantages, BCARS
suffers from a spurious and chemically unspecific non-resonant background
(NRB) that distorts and shifts the Raman peaks. Nevertheless, the NRB also
serves as a heterodyne amplifier of the resonant signal, making it
particularly beneficial for identifying weak Raman peaks. Post-processing
numerical algorithms are then used to remove the NRB and to obtain spectra
comparable to SR results. Here, we show the reproducibility of BCARS by
conducting an internal Round Robin with two different BCARS experimental
setups, comparing the results on different crystalline materials of increasing
structural complexity: diamond, 6H-SiC, KDP, and KTP. First, we compare the
detected and phase-retrieved signals, the setup-specific NRB-removal steps,
and the mode assignment. Subsequently, we demonstrate the versatility of BCARS
by showcasing how the selection of pump wavelength, pulse width, and detection
geometry can be tailored to suit the specific objectives of the experiment.
Finally, we compare and optimize measurement parameters for the high-speed,
hyperspectral imaging of ferroelectric domain walls in lithium niobate.

broadband coherent anti-Stokes Raman scattering, BCARS, CARS, solid state,
single crystals, phase-retrieval, phase matching

##  I Introduction

Raman scattering is a powerful vibrational spectroscopy technique that
provides rich chemical information on materials and biomedical samples in a
non-destructive and label-free way [1, 2]. Due to its high sensitivity to
changes in the crystal structure, it is particularly useful to detect changes
like defects [3], strain [4], and doping [5]. However, one drawback is the low
scattering efficiency of spontaneous Raman (SR) scattering , which leads to
long pixel dwell times and prevents image acquisition with high spatial
resolution. Coherent Raman scattering (CRS) dramatically increases the
acquisition speed thanks to the nonlinear nature of the optical interaction
between the sample and the impinging electric fields, which generate a
vibrational coherence [6]. In its simplest configuration, single-frequency CRS
employs two picosecond pulses, the pump and the Stokes, at frequency
$\omega_{p}$ and $\omega_{s}$, respectively, that interact with the sample,
thus interrogating a vibrational mode $\Omega=\omega_{p}-\omega_{s}$. Among
the CRS techniques, Coherent Anti-Stokes Raman Scattering (CARS) has emerged
as an advanced, yet quite simple-to-implement method for high-speed
spectroscopy and imaging [7]. The CARS signal derives from a four-wave mixing
process at the sample: first, interactions with the pump and Stokes fields
lead to the population of vibrational states. Then, a probe field reads these
states, generating the blue-shifted anti-Stokes component at frequency
$\omega_{as}$. In most implementations, the pump and probe field are frequency
degenerate since they are delivered by the same train of pulses, leading to
$\omega_{as}=2\omega_{p}-\omega_{s}$. However, narrowband CARS does not
provide the same chemical specificity as SR since it probes only a single
frequency at a time. The solution is Broadband CARS (BCARS), which combines a
narrowband pump with a broadband Stokes pulse and probes all the vibrational
frequencies of the sample. BCARS combines the increase in signal intensity of
CRS techniques with the rich spectroscopic information provided by SR [6].

One prominent feature of CARS is the influence of the so-called non-resonant
background (NRB) signal. The NRB results from non-resonant four-wave mixing
processes in the sample and its surroundings. It coherently mixes with the
resonant response of the investigated material, which results in enhanced
signal intensity, but also in the distortion of both peak shape and peak
position. Several solutions may be adopted to suppress this chemically
unspecific signal, like time-resolved detection [8], polarization CARS [9],
Fourier-transform CARS [10], or angle-resolved measurements of anisotropic
vibrational modes [11]. All these methods, however, increase the setup
complexity and lead to signal degradation. For BCARS, the NRB can be removed
using analytical approaches like the maximum entropy method [12], the time-
domain Kramers-Kronig (KK) transformation [13], or deep-learning-based methods
[14, 15, 16].

Today, BCARS is broadly applied in the biomedical field [17, 18] for cancer
research[19], label-free imaging, and for sample sizes down to nanoparticles
[20]. In addition, recent works have demonstrated excellent performances of
BCARS for the investigation of ferroelectric materials, such as LiNbO_3 and
LiTaO_3[21] as well as imaging of single ferroelectric domain walls [22].

In biomedical imaging, the strong signal allows for fast and label-free
imaging with sub-ms acquisition times. The intensity of specific bands or
modes is used to contrast different types of tissue [23, 24, 25]. The focus is
different for crystalline materials. Knowing and retrieving the exact peak
parameters of the vibrational modes is crucial in solid-state physics, as
changes in the material’s structure, like strain or defects, affect the Raman
spectrum only slightly. Small shifts in peak position or width broadening
indicate defects, strain, dopants, number of layers, and structural changes
[3, 4, 5, 26, 27]. It is critical that differences in experimental setups used
do not change the results of these precise measurements.

Interlaboratory setup comparisons, i.e., Round Robin investigations, have been
made for SR spectroscopy [28], Auger electron spectroscopy [29], mass
spectroscopy [30, 31] and tip-enhanced Raman spectroscopy [32], showing the
reproducibility of their respective techniques and laying the basis for
comparative research and widespread application.

To the best of our knowledge, only one comparison between BCARS spectra of
glycerol taken with two different setups has been reported in literature [13].
Reproducibility is an essential step towards the broader use of this
technology. One key aspect of that is the strong setup dependence of the NRB
due to differences in the spectral profiles of the used laser sources and
detector efficiencies. It is of great importance that these differences are
taken into account in the NRB removal process.

Here, we compare two BCARS setups with greatly different parameters,
evaluating their reproducibility when measuring and employing NRB suppression
algorithms on a range of materials. In addition, we compare measurement
parameters like the forward and backward (epi) detection directions and focal
depth dependence for the application to four crystalline materials of
increasing structural complexity. Finally, we optimize the high-speed imaging
of ferroelectric domain walls.

##  II BCARS Spectroscopy

###  II.1 Inelastic Light-Matter Interaction

The basis of Raman spectroscopy is inelastic light-matter scattering. For SR,
a pump photon of frequency $\omega_{pu}$ scatters inelastically to either lose
(Stokes scattering, figure 1.a) or gain energy (anti-Stokes scattering, figure
1.b) corresponding to the probed vibrational level $\Omega$. The scattering
cross-section for SR is low due to its spontaneous and incoherent nature. In
contrast, BCARS is a nonlinear process where the sample interacts with three
fields with a spatial and temporal overlap. In BCARS, the vibrational levels
$\Omega_{i}$ are populated through coherent excitation at $\omega_{pu}$ and
$\omega_{s}$, whose energy difference corresponds to the vibrational level.
These states are read out by the third field $\omega_{pr}$, resulting in the
emission of an anti-Stokes field $\omega_{as}$. By using a broadband light
source for $\omega_{s}$, a broad range of vibrational modes can be probed,
leading to the generation of a broadband anti-Stokes component (figure 1.c).

Figure 1: Jablonski diagrams of a) spontaneous Stokes scattering, b)
spontaneous anti-Stokes scattering, and c) BCARS.

###  II.2 Extraction of Spectral Information

The measurable BCARS signal $I_{CARS}$ depends on the spectral response of the
sample and the detector response function $\tilde{C}(\omega)$ as follows[13]:

$\displaystyle
I_{CARS}(\omega)\propto|\tilde{C}(\omega)|^{2}|\chi^{(3)}(\omega_{pu},\omega_{s},\omega_{pr},\omega_{as})|^{2}.$
(1)

As BCARS is a third-order nonlinear optical process, the spectral response of
the sample is described by its third-order susceptibility tensor
$\chi^{(3)}(\omega)$[33], which consists of two terms, a resonant and a non-
resonant one:

$\displaystyle\chi^{(3)}$ $\displaystyle=\chi^{(3)}_{R}+\chi^{(3)}_{NR}.$ (2)

The resonant part $\chi^{(3)}_{R}$ is the sum of many complex Lorentzian
functions, and its imaginary part corresponds to the SR-like response of the
sample. The laser excitation stimulates an additional chemically unspecific
background of electronic signals, the NRB. It corresponds to the non-resonant
$\chi^{(3)}_{NR}$, which can be considered purely real under the assumption
that the pump/Stokes frequencies are far from electronic resonances.
Therefore, extracting the imaginary part of the resonant term from the BCARS
intensity is necessary to obtain SR-like spectral features. In this work, we
remove the NRB from the BCARS spectra by adapting the Python-based algorithm
Crikit2 developed by Camp et al. [13], based on the time-domain KK
transformation. The detailed mathematical description can be found elsewhere
[13].

##  III Methods

For our BCARS measurements, we employed two different experimental
configurations: The first one is the CERES setup in Dresden, Germany, which is
a commercial setup optimized for the investigation of crystalline materials
and their lower-shift Raman modes
($\nu\approx$200\text{\,}$-$1100\text{\,}{\mathrm{cm}}^{-1}$$). The second
system is the tailor-made VIBRA setup in Milan, Italy, which is optimized for
high-speed imaging across the entire fingerprint region
($\nu\approx$500\text{\,}$-$1800\text{\,}{\mathrm{cm}}^{-1}$$). Another key
difference is the detection geometry: While CERES operates in epi-detection,
VIBRA can measure in both transmission- and epi-direction.

###  III.1 CERES Setup

The CERES setup consists of a LabRAM HR Evolution commercial Raman microscope
(HORIBA Jobin Yvon GmbH, Oberursel, Germany), as shown in figure 2.

Figure 2:  Layout of the CERES BCARS setup used in this work: The pulsed
incident pump ($1064\text{\,}\mathrm{nm}$) and broadband Stokes laser
($600\text{\,}$-$2000\text{\,}\mathrm{nm}$) are spatially and temporally
matched. Measurements are conducted in epi-detection geometry. ND: neutral
density filter, $\lambda/2$: rotatable half-wave plate, DM: dichroic mirror.

The pump and Stokes pulses are generated by a commercial combined laser system
(LEUKOS CARS-SM-30), which consists of a Q-switched microchip Nd:YAG laser
pumping a photonic crystal fiber to generate a broadband supercontinuum. The
system produces $1064\text{\,}\mathrm{nm}$, $100\text{\,}\mathrm{mW}$ average
power pump pulses and $600\text{\,}$-$2000\text{\,}\mathrm{nm}$,
$80\text{\,}\mathrm{mW}$ average power Stokes pulses, both with a
$1\text{\,}\mathrm{ns}$ pulse length and a $30\text{\,}\mathrm{kHz}$
repetition rate. The Stokes pulses are used in the range of
$1085\text{\,}$-$2000\text{\,}\mathrm{nm}$ covering the BCARS signal range of
$190\text{\,}$-$4000\text{\,}{\mathrm{cm}}^{-1}$. The optical paths are
adjusted to ensure the pulses’ temporal and spatial overlap on the sample. SR
measurements can be performed alongside, using a $632.8\text{\,}\mathrm{nm}$
monochromatic He-Ne continuous wave laser (Melles Griot) as an alternative
laser source. A rotatable half-wave plate controls the laser’s polarization. A
Nikon CFI APO NIR 40$\times$ water-immersion objective ($NA=0.8$) focuses the
pulses on the sample and collects the scattered light in epi-detection. A
dichroic mirror acts as the short-pass filter and transmits the blue-shifted
BCARS signal to the detector, which consists of a spectrometer with a
$600\text{\,}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{m}\mathrm{m}$
diffraction grating, and a Syncerity CCD detection system (HORIBA Jobin Yvon
GmbH, Oberursel, Germany), resulting in a spectral resolution of the detector
of $0.05\text{\,}\mathrm{nm}$
($0.45\text{\,}$-$0.56\text{\,}{\mathrm{cm}}^{-1}$) in the relevant spectral
range.

The sample is mounted on an XYZ translation stage, which enables raster
scanning in three dimensions.

###  III.2 VIBRA Setup

The architecture of the VIBRA BCARS microscope is shown in figure 3 and
described in detail elsewhere [34].

Figure 3:  Layout of the VIBRA BCARS setup used in this work: The incident
laser source is a $1030\text{\,}\mathrm{nm}$,
$2\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$ pulsed laser, which is split by a
beam splitter (BS): The first part is spatially broadened by a YAG crystal and
a long pass filter (LPF) selects the red-shifted part. The second part is
spectrally filtered by an etalon and temporally shifted by a delay-line (DL)
to ensure temporal and spatial overlap at the sample. The BCARS signal can be
detected either in transmission or in epi-detection geometry. DM: dichroic
mirror, SPF: short-pass filter.

A commercial fiber-based ytterbium laser system (Coherent Monaco) provides
$270\text{\,}\mathrm{fs}$ pulses at a $1035\text{\,}\mathrm{nm}$ wavelength
with a $2\text{\,}\mathrm{MHz}$ repetition rate. A beam splitter divides the
laser output into two beams. The first beam generates narrowband pump pulses
through a high-finesse Fabry-Perot etalon to decrease the pulse bandwidth.
This determines the spectral resolution of $10\text{\,}{\mathrm{cm}}^{-1}$
($1.1\text{\,}\mathrm{nm}$ full width at half maximum (FWHM) bandwidth). The
second replica generates a broadband Stokes pulse via white-light continuum
generation by focusing into a $10\text{\,}\mathrm{mm}$-thick yttrium aluminum
garnet (YAG) crystal [35]. A long-wave-pass filter selects the red-shifted
lobe of the Stokes pulse ($1050\text{\,}$–$1300\text{\,}\mathrm{nm}$). In
front of the microscope, the pump and Stokes pulses are collinearly
superimposed through a dichroic mirror and temporally synchronized by a
mechanical delay line. The beams are then sent to a homebuilt transmission
microscope in up-right configuration, equipped with two identical 100x air
objectives of $NA=0.85$ (Olympus LCPLN100XIR). Behind the sample, a short-pass
filter (FESH1000, Thorlabs) rejects the pump and Stokes beams, transmitting
the generated BCARS signal, whose spectrum is then measured with a standard
grating-based dispersive spectrometer (ACTON SP-2150, Princeton Instruments)
using a CCD detector (Blaze 100HR, Princeton Instruments). Additionally, a
movable dichroic mirror (DMLP1000, Thorlabs) is inserted in front of the
illuminating objective, allowing to perform BCARS detection in epi-
configuration. The sample is raster-scanned in three dimensions using a
motorized XYZ translation stage synchronized with the CCD camera of the
spectrometer.

###  III.3 Samples

For our internal Round Robin, crystalline materials constitute ideal reference
samples. They are easily transportable and stable under environmental changes
like temperature, pressure, and humidity, which might differ between
laboratories. Moreover, the sample preparation is reproducible, samples do not
degrade, and they generally have sharp Raman peaks, which is ideal for
measuring minor changes in their spectra. We have chosen four materials with
varying structural complexity to increase the number of detectable Raman modes
and to show the variety of possible applications.

The complexity of the crystals surveyed in this paper is gauged using a
complexity measure introduced by Krivovichev [36] and later expanded by
Hornfeck. The open-source Python script crystIT by Kaussler and Kieslich [37]
is used to calculate the complexity to determine the amount of information in
a crystal unit cell.

##### Diamond

Diamond is a cubic crystal of carbon with space group Fd$\bar{3}$m [38]. Its
unit cell contains eight carbon atoms. However, its configurational complexity
per unit cell is zero because it lacks any coordinational degrees of freedom.
It has one fundamental Raman-active $F_{2g}$ mode [39]. The diamond used in
this study is a polished single-crystal CVD diamond cut along the [100]
orientation with a thickness of
$200\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$ manufactured by Applied
Diamond.

##### 6H-SiC

The 6H polytype of SiC used in this paper is of hexagonal structure and space
group P63mc [40], with eight atoms in its unit cell, resulting in a
configurational complexity of 35. Expected Raman modes are $3A_{1}$, $3E_{1}$,
and $4E_{2}$ [41]. The sample is a z-cut 6H-SiC from MSE Supplies, Tucson
(AZ), USA.

#####  D2K[PO4]

(KDP) is tetragonal with a space group I$\bar{4}$2d [42] and 32 atoms per unit
cell, resulting in a configurational complexity of 68.7. Theroretically
expected Raman modes are 11 $A_{1}$, 13 $B_{1}$, 12 $B_{2}$, and 23 $E$ [43].
The sample used here is a z-cut crystal provided by the Czech Academy of
Sciences, Prague, Czech Republic.

#####  KTiOPO4

(KTP) is orthorhombic with space group Pna21 [44] and 64 atoms in its unit
cell. Its configurational complexity is thus 558.3, constituting a complex ion
conductor with a vibrant Raman spectrum with an astonishing 47 $A_{1}$, 47
$B_{1}$, 47 $B_{2}$, and 48 $A_{1}$ modes. The sample used here is a z-cut KTP
provided by the Czech Academy of Sciences, Prague, Czech Republic.

##  IV Results

###  IV.1 Phase Retrieval

Figure 4:  Transformation steps to retrieve the SR-like spectrum using the
CRIKit2 algorithm demonstrated with the example of 6H-SiC for both the CERES
and VIBRA setup: The NRB (blue) is measured on glass and the raw, epi-detected
BCARS signal (orange) on 6H-SiC. The exposure times are
$500\text{\,}\mathrm{ms}$ for CERES, and $10\text{\,}\mathrm{ms}$ for VIBRA.
The Kramers-Kronig transformed signal (red) is furthermore corrected for phase
errors (purple) and scaling errors (green). Finally, the SR spectrum (cyan)
was measured in CERES ($15\text{\,}\mathrm{s}$ exposure time) for comparison.
The dashed lines indicate zero-intensity levels.

Comparing the raw BCARS spectra between laboratories is challenging, as the
distortion by the NRB is setup-dependent: The NRB shape is substantially
influenced by the spectral profile of the broadband Stokes pulse, the pump
wavelength, the detector response function, and the spectral profile of the
diffraction grating. Additionally, each optical component within the laser
path has a wavelength-dependent influence on polarization and intensity. In
order to compare the results and estimate the reproducibility of BCARS for the
analysis of crystalline materials, one needs to use phase-retrieval algorithms
to properly remove the NRB response and extrapolate the purely resonant
contribution of the sample, independent of the power spectral density of the
sources. Therefore, the first step is the removal of the NRB using the KK
transformation. The multiple steps of transformation are shown exemplarily for
6H-SiC in figure 4. Note that BCARS detects the blue-shifted anti-Stokes
component, exhibiting negative Raman-shift values. For comparison to SR data
and easier readability, we give the absolute values for Raman shifts and peak
positions, i.e., $|$Raman Shift$|$. The Raman shift axes for both setups are
calibrated using emission lines from the same Neon-gas lamp (Model 6032,
Newport Spectra-Physics GmbH, Darmstadt, Germany).

The pure NRB was measured by taking the BCARS spectrum of borosilicate glass,
which shows no distinct Raman peaks. Note that this is not the correct NRB of
the investigated 6H-SiC, as it is impossible to measure only the non-resonant
part of the signal inside a crystal without recording the resonant response of
the sample as well. Both raw and NRB spectra were corrected by subtraction of
a dark spectrum. The BCARS spectra (orange) differ between the two setups but
have a broad and almost constant shape in both cases. An exception is the
VIBRA spectrum at around $500\text{\,}{\mathrm{cm}}^{-1}$, where a broad
intensity peak is measured, mainly due to self-phase modulation occurring
during the supercontinuum generation in the YAG crystal. The phase retrieval
is done with the KK transformation in CRIKit2 using the default parameters.
The retrieved spectra (KK, red) exhibit Lorentzian-shaped peaks and a varying
baseline due to using the NRB on glass as a reference instead of the
inaccessible ”real” NRB. CRIkit2 runs through two steps of error correction to
remove the baseline in the complex phase of the signal (Phase Corr., purple)
and correct the relative intensities of the peaks (Scale Corr., green). For
both steps, the parameters are adjusted individually for CERES and VIBRA. For
the precise values used for all transformation processes, see the Supplemental
Material at [URL will be inserted by publisher] . The scale error corrected
spectrum (green) is closest to an SR-like spectrum and, in the following, will
be used to discuss the phase-retrieved (PR) spectrum.

Table 1: Main peak frequencies $\Delta\tilde{\nu}_{Peak}$ detected in BCARS and SR measurements on SiC, and phonon assignment based on reported phonon frequencies $\Delta\tilde{\nu}_{Phonon}$ by SR [45].  $\Delta\tilde{\nu}_{Peak}$ [cm-1] | Assigned |  $\Delta\tilde{\nu}_{Phonon}$ [cm-1]
---|---|---
VIBRA | CERES | Phonon | (SR) [45]
BCARS | BCARS | SR |  |
767 | 768 | 767 |  $E_{2}$(PO) | 767.5
790 | 791 | 789 |  $E_{1}$(TO) | 788.0
969 | 969 | 966 |  $A_{1}$(LO) | 966.5

After the phase retrieval processing, the spectra from both setups have
Lorentzian-shaped, SR-like peaks, as reported in table 1. CERES could detect
modes at $768\text{\,}{\mathrm{cm}}^{-1}$ ($E_{2}PO$),
$791\text{\,}{\mathrm{cm}}^{-1}$ ($E_{1}TO$) and
$969\text{\,}{\mathrm{cm}}^{-1}$ ($A_{1}LO$), with different relative
intensities. VIBRA measures the peaks at $767\text{\,}{\mathrm{cm}}^{-1}$,
$790\text{\,}{\mathrm{cm}}^{-1}$ and $969\text{\,}{\mathrm{cm}}^{-1}$,
respectively, which are, within error ranges, located at the same positions.
One should note that the retrieved peaks for the VIBRA setup are broader
because of the broader bandwidth of the pump pulse
($10\text{\,}{\mathrm{cm}}^{-1}$ vs. $0.6\text{\,}{\mathrm{cm}}^{-1}$ in the
CERES setup). The absolute signal intensities can best be compared for the raw
spectra, where the resulting relative peak intensities differ: While VIBRA has
almost equal intensities for the $791\text{\,}{\mathrm{cm}}^{-1}$ and
$969\text{\,}{\mathrm{cm}}^{-1}$ modes, CERES detects a slightly more intense
signal at $969\text{\,}{\mathrm{cm}}^{-1}$. These results show that comparable
spectra can be retrieved despite the vastly different raw and NRB data.
Furthermore, the Raman shift axis calibration ensures the comparability of the
peak positions. Finally, the BCARS results align well with SR measurements and
theory, proving the applicability of the technique to solid-state materials
independent of setups.

###  IV.2 Epi- vs. Transmission Detection

For transparent materials or thin films, it is possible to detect the signal
either in the forward (transmission) or backward (epi) direction. However, the
signal strength for these directions differs strongly due to the wave-vector
missmatch $\Delta k$ and the corresponding coherent interaction length
$l_{c}=\pi/\Delta k$. The $l_{c}$ dictates the range over which the signal is
constructively accumulated. In the forward scattered signal, $\Delta
k=2k_{pu}-k_{s}-k_{as}$ is close to zero, resulting in an $l_{c}$ on the
micrometer length scale, which is longer than the confocal parameter of the
focused pump/Stokes beams. Whereas for epi-scattering with a backward
propagating anti-Stokes beam, there is a significant k-vector mismatch $\Delta
k=2k_{pu}-k_{s}+k_{as}$ resulting in $l_{c}$ being a fraction of the anti-
Stokes wavelength [46].

Figure 5:  Comparison of the transmission- (trans, upper row) and epi-detected
signal (epi, lower row) of KDP using the VIBRA setup: Both the NRB (blue) and
the raw BCARS data (orange) show almost the same spectral shape, although in
transmission the intensity is
$6\text{\,}\mathrm{-}$$47\text{\,}\mathrm{t}$imes higher. The phase-retrieved
(PR) data (green) shows the same spectral features, thus rendering both
signals equivalent in information content.

The epi signal is used when imaging heterogeneous biological samples such as
cells and tissues since they feature scatterers whose dimension is much
smaller than $l_{c}$ [46]. Using a high-NA objective provides a range of
k-vectors to always fulfill the phase-matching condition [47, 48, 49, 50].
However, for bulk crystalline samples, the scattering direction is
consequential, and previous results in crystals concluded that there is no
measurable epi-scattered signal. Instead, the back-detected signal is the
strong forward signal reflected on the backside of the sample [21]. This
hypothesis is tested by measuring the BCARS spectra of bulk KDP and measuring
the NRB spectra of a borosilicate glass slide in both directions at the same
position near the backside of the sample. These experiments are done in the
VIBRA setup by introducing an additional dichroic mirror in front of the
illumination objective to collect the back reflected light and send it to the
spectrometer, thus switching between transmission- and epi-detection. The
results are shown in figure 5.

The measured spectra for NRB (blue) and raw BCARS (orange) are similar in
shape, except for some broad features in the NRB epi spectrum at
$1050\text{\,}{\mathrm{cm}}^{-1}$ and $1250\text{\,}{\mathrm{cm}}^{-1}$, and
in the raw transmission spectrum at $900\text{\,}{\mathrm{cm}}^{-1}$ due to
modulation of the broadband Stokes beam. The similarity is expected, as the
same laser source and detector are used. However, the differences in spectral
shape can be explained by the different optical components present along the
two detection paths. For both cases, the transmission signal is stronger - by
a factor of $47\text{\,}$ and $6.8\text{\,}$ for the NRB and the BCARS signal,
respectively. The ratio between transmission- and epi-detected signal strength
might vary between samples, depending on their thickness, transparency, and
surface roughness. The retrieved spectra (green) contain equivalent spectral
information: The $B_{2}$ mode is measured at $911\text{\,}{\mathrm{cm}}^{-1}$
and $910\text{\,}{\mathrm{cm}}^{-1}$ for transmission- and epi-detection,
respectively. This difference is smaller than the spectral resolution of the
setup. The transformation algorithm delivers similar results when given
similar input spectra. The presence of spurious modulations in the
transmission spectrum is due to self-phase modulation processes occurring
during the generation of the white light in the YAG crystal. Further expected
peaks from KDP cannot be measured as their Raman shifts are smaller than the
detection limit of $500\text{\,}{\mathrm{cm}}^{-1}$ of the VIBRA setup. In
conclusion, the forward- and backward-detected signals show the same Raman
peaks. However, the forward scattered signal should be measured to achieve
higher signal intensity if the sample and setup allow it.

#### Focal Depth Dependence

When measuring bulk samples significantly thicker than the laser Rayleigh
range, the dependence of the focal spot position inside the crystal is a
fundamental parameter to consider. Therefore, we performed depth scans on a
diamond single crystal to compare the BCARS signal in forward and epi-
detection depending on the focal position, as shown in figure 6.

Figure 6: BCARS on a diamond single crystal measured with VIBRA. a) Raw BCARS
spectra in transmission (blue) and epi-detection (orange) yield the same
results after phase retrieval processing (green), which is compared to the SR
spectrum (cyan) measured with CERES. b) Focal depth scan through diamond
single crystal: In transmission detection (blue), the integrated signal
intensity is measurable along the whole crystal, from the front- to the
backside. On the other hand, the epi-detected signal (orange) is only
detectable near the backside, where the strong forward scattered signal is
reflected.

Diamond was shown to have an intense CARS peak at the $sp^{3}$ vibrational
resonance [20]. The spectra from VIBRA shown in figure 6 (a) show a single
strong peak at $1336\text{\,}{\mathrm{cm}}^{-1}$. It has an FWHM of
$14\text{\,}{\mathrm{cm}}^{-1}$, with good agreement to the SR comparison
measurements at $1333\text{\,}{\mathrm{cm}}^{-1}$ (FWHM =
$3.1\text{\,}{\mathrm{cm}}^{-1}$) in CERES and the literature value of
$1332\text{\,}{\mathrm{cm}}^{-1}$ (FWHM down to
$1.7\text{\,}{\mathrm{cm}}^{-1}$) [51]. With signal intensities of
$55\text{\times}{10}^{3}\text{\,}\mathrm{c}\mathrm{t}\mathrm{s}\mathrm{/}\mathrm{m}\mathrm{s}$
for transmission and
$1.8\text{\times}{10}^{3}\text{\,}\mathrm{c}\mathrm{t}\mathrm{s}\mathrm{/}\mathrm{m}\mathrm{s}$
for the epi-detected signal, this is two orders of magnitude stronger than any
other material measured in this work. Figure 6 (b) shows the BCARS intensity
upon longitudinal translation of the focal spot inside the material. The
transmission signal shows a linear increase along the depth axis due to lower
scattering and losses of the BCARS signal when focusing closer to the backside
of the sample. The signal in epi-detection shows a strong intensity near the
backside of the sample, indicating that the reflection of the forward signal
on the far surface is measured. A backscattered signal would show a rather
constant intensity across the sample, with a decrease further inside due to
scattering losses. As the same objective is used for focusing the laser and
collecting the signal, the best collection efficiency is achieved whenever the
reflection point at the backside is in focus and the signal beam is not
widened. Therefore, it is advised to measure epi-BCARS near the backside of
the sample.

The signal intensity changes drastically at the surfaces as the laser focus
volume enters or leaves the signal-generating material. The spectral
information is independent of focus depth in a single crystalline material,
except for possible surface phenomena. On the other hand, for quantitatively
comparable measurements, measuring in the same depth and having the same
material thicknesses is essential.

###  IV.3 Setup Comparison

Reproducibility and comparability between different setups are essential
aspects of scientific research. As stated before, this is especially important
for BCARS, as the NRB signal strongly depends on various setup parameters such
as laser source, focusing, and detector response function. As a comparison
study, we have measured the BCARS spectra of the same KTP sample in both the
CERES and VIBRA setups using epi-detection. The results are shown together
with the NRB data from glass in figure 7.

Figure 7:  Comparison of BCARS signals from the same KTP sample measured in
the two different setups: VIBRA (upper row) and CERES (lower row). The NRB
(blue) shows different shapes, which influence the baselines of the raw BCARS
spectra (orange). The distorted KTP peaks can be seen at roughly the same
position but with vastly different shapes and intensities for the two setups.
The PR spectra (green) compare to the SR result (cyan). Again, the spectra
show matching spectral positions but differences in relative intensities and
width.

The NRB spectra show a similar baseline with decreasing intensity for
decreasing wavenumbers. However, the shape differs due to different Stokes
laser profiles and detector response functions for both setups. The raw BCARS
spectra show peaks at a similar position and with BCARS-typical peak
deformation, but they differ in baseline shape and peak widths. Additionally,
CERES has a larger detection range, as its small bandwidth filter allows for
detection down to $190\text{\,}{\mathrm{cm}}^{-1}$, while the VIBRA data is
cut at $500\text{\,}{\mathrm{cm}}^{-1}$. The signal intensity for epi-detected
raw BCARS is on the same scale for both setups. For comparison, the VIBRA
transmission detection yields a ${10}^{3}\text{\,}$ times higher signal
strength. On the other hand, for the NRB, VIBRA achieves a ${10}^{3}\text{\,}$
times greater intensity in counts per second because a thinner glass slide was
used. After phase retrieval processing, both spectra show Lorentzian-shaped
peaks and their positions align with the corresponding SR spectrum measured in
CERES. However, the relative peak intensities differ for both BCARS and SR
spectra. The fitted peak positions and their mode assignment are described in
table 2.

Table 2: Main peak frequencies $\Delta\tilde{\nu}_{Peak}$ detected in BCARS and SR on KTP, and phonon assignment based on reported phonon frequencies $\Delta\tilde{\nu}_{Phonon}$.  $\Delta\tilde{\nu}_{Peak}$ [cm-1] | Assigned |  $\Delta\tilde{\nu}_{Phonon}$ [cm-1]
---|---|---
VIBRA | CERES | Phonon | (SR) [52, 53]
BCARS | BCARS | SR |  |
- | 216 | 215 | $A_{1}$ | 213
- | 262 | 268 | $A_{1}$ | 268
- | 280 | 280 | $A_{2}$ | 284
- | 293 | 293 | $B_{2}$ | 304
- | 340 | 341 | $A_{2}$ | 335
- | 376 | 374 | $A_{1}$ | 378
- | 400 | 400 |  $\nu_{2}$PO4 | 400
- | 491 | 490 |  $\nu_{4}$TiO6 | 509
- | 518 | 517 | $A_{1}$ | 517
- | 549 | 547 |  $\nu_{4}$PO4 | 548
- | 594 | 591 | $A_{1}$ | 598
634 | 624 | 636 |  $\nu_{1}$TiO6 | 632
693 | 673 |  | $B_{2}$ | 673 (IR)
709 | 709 | 701 |  $\nu_{2}$TiO6 | 709
779 | 773 | 764 | $A_{1}$ | 770
836 | 836 | 835 |  $\nu_{3}$TiO6 | 833
975 | 974 | 975 |  $\nu_{1}$PO4 | 974
990 | 991 | 990 | $A_{1}$ | 993
| 1013 | 1013 | $A_{1}$ | 1008
1037 | 1034 | 1034 | $A_{1}$ | 1034
1093 | 1093 | 1093 |  $\nu_{3}$PO4 | 1095
1171 | 1122 | 1120 | $A_{1}$ | 1113

One notable difference is in the peak width, exemplarily shown for the
$1093\text{\,}{\mathrm{cm}}^{-1}$ $A_{2}$ mode: CERES detects an FWHM of
$9.1\text{\,}{\mathrm{cm}}^{-1}$ in BCARS and $6.7\text{\,}{\mathrm{cm}}^{-1}$
for SR. Using a higher-resolution diffraction grating does not decrease the
FWHM of the mode, which indicates that the detector resolution does not limit
its width. In comparison, VIBRA shows an FWHM of
$16.6\text{\,}{\mathrm{cm}}^{-1}$. Due to the broader width, peaks can
overlap, making the distinction between close modes challenging, as seen for
the $836\text{\,}{\mathrm{cm}}^{-1}$ $A_{1}$ mode. The detector resolutions
were tested by measuring a Neon gas lamp spectrum: CERES has a minimum peak
width of $0.25\text{\,}\mathrm{nm}$ or
$2.8\text{\,}$-$3.9\text{\,}{\mathrm{cm}}^{-1}$, which is three times smaller
than the measured peak width. As the spectral width of CERES’
$1\text{\,}\mathrm{ns}$ laser pulse corresponds to a
$0.015\text{\,}{\mathrm{cm}}^{-1}$ spectral resolution, it can be assumed that
the measured peak width corresponds to the actual width of this KTP mode. In
contrast, the VIBRA detector has a minimum peak width of
$1.2\text{\,}\mathrm{nm}$, or $13.8\text{\,}{\mathrm{cm}}^{-1}$. Here, the
spectral resolution is limited by the short laser pulses to
$\approx$10\text{\,}{\mathrm{cm}}^{-1}$$. However, the shorter laser pulses
have a higher maximum intensity, which allows for a higher BCARS signal
intensity and lower pixel dwell time. Additionally, the spectral resolution of
VIBRA can be increased, if needed, by changing the etalon to decrease the
spectral width of the pump signal. In conclusion, both setups can detect equal
spectral information. Depending on the objectives of the conducted experiment,
the setup can be optimized for higher spectral resolution or faster
acquisition by varying the pump and Stokes pulse parameter.

###  IV.4 Imaging

A promising application of BCARS microscopy in crystalline materials is
imaging ferroelectric domain walls, as recently shown for LNO [22]. LNO can be
poled to locally generate inverted order parameters, distinguishing between
original and inverted domains. The boundary region between two domains is
called the domain wall (DW), which has many exciting features and applications
[54, 55]. SR is an established technique for DW imaging and investigation [56,
57, 58], and BCARS can offer increased acquisition speed for better
applicability in LNO-based device fabrication monitoring. Here, the
reproducibility of BCARS DW imaging is tested in the CERES setup using epi-
detection and the VIBRA setup using epi- and transmission-detection. On a
single sample of periodically poled LNO, areas of $50\text{\,}$ $\times$
$50\text{\,}{\mathrm{\SIUnitSymbolMicro m}}^{2}$ were scanned with a step size
of $500\text{\,}\mathrm{nm}$ in both x- and y-direction. The results are shown
in figure 8.

Figure 8:  BCARS imaging of domain walls in periodically poled Lithium Niobate
(PPLN) using the CERES, VIBRA epi-, and VIBRA transmission setup. (a)-(c): The
raw BCARS spectra of the domain wall (orange) exhibit an additional signal at
around $600\text{\,}{\mathrm{cm}}^{-1}$ compared to the LNO domain spectrum
(blue). (d)-(f): The contrast of the domain walls is imaged by calculating the
intensity ratio of the two measured peaks. The out-of-plane arrow symbols
indicate the direction of the crystal order parameter. The single spectra
(a)-(c) are taken from the maps at the positions indicated by the colored
crosses. The PPLN maps were taken with pixel dwell times of
$50\text{\,}\mathrm{ms}$ for CERES, $20\text{\,}\mathrm{ms}$ for VIBRA epi-,
and $1\text{\,}\mathrm{ms}$ for VIBRA transmission detection. In all cases,
the lateral step size is $0.5\text{\,}\mathrm{\SIUnitSymbolMicro m}$.

Panels 8 (a)-(c) show the raw BCARS spectra of the LNO domain (blue) and the
domain wall (orange). In the domain, the spectra detected in this range
exhibit a strong $A_{1}(LO_{4})$ mode at $868\text{\,}{\mathrm{cm}}^{-1}$. At
the DW position, the $A_{1}(LO_{4})$ mode decreases in intensity, while a new
mode appears at $600\text{\,}{\mathrm{cm}}^{-1}$, which is assigned to the
$A_{1}(TO_{4})$ mode [59, 57]. The ratio between the two peak intensities
yields a good contrast for imaging, as seen in panels 8 (d)-(f). The yellow-
green color indicates the DWs, which delineate the poled domains. The same
vertically aligned cylinder shape can be imaged for all three measurement
modes. The scan region was chosen to show the endpoints of the domains and an
area of virgin LNO. The lateral resolution of the DW signal is comparable for
all three images. Although the DWs have a thickness of only a few unit cells,
the detected signal is broadened to the diffraction-limited spatial
resolution.

As the $A_{1}(TO_{4})$ mode substantially varies in intensity, the contrast is
visible even for low signal-to-noise ratio (SNR), allowing for fast
acquisition speed. For CERES, the SNR of $13\text{\,}$ for DW and
$17\text{\,}$ for the domain spectrum limit the pixel dwell time to a minimum
of $50\text{\,}\mathrm{ms}$ while using the maximum laser power of
$100\text{\,}\mathrm{mW}$ for the pump- and $80\text{\,}\mathrm{mW}$ for the
Stokes laser. In the VIBRA setup, the SNR is higher both in epi-
($29\text{\,}$-$69\text{\,}$) and transmission direction
($231\text{\,}$-$337\text{\,}$). The VIBRA epi measurement was done with
$20\text{\,}\mathrm{ms}$ acquisition time and laser powers of
$100\text{\,}\mathrm{mW}$ and $10\text{\,}\mathrm{mW}$ for pump- and Stokes-
laser, respectively. The VIBRA transmission measurement has the highest
intensity and fastest pixel dwell time of $1\text{\,}\mathrm{m}\mathrm{s}$,
which is limited by the detector read-out speed. Additionally, the pump laser
power was reduced to $40\text{\,}\mathrm{mW}$ not to saturate the detector.
Ignoring the detector limitations and using the nonlinear relation between the
signal intensity and the laser power of $I_{CARS}\propto I_{pu}^{2}I{s}$, the
pixel dwell time in transmission mode at $100\text{\,}\mathrm{\char 37\relax}$
pump power could be reduced to $3.6\text{\,}\mathrm{\SIUnitSymbolMicro s}$ and
still reach CERES’ levels of SNR. At a pulse rate of $2\text{\,}\mathrm{MHz}$,
this translates to eight pulses per pixel. In conclusion, both setups and
detection directions show the capability of high-speed imaging of domain walls
in LNO. The spectra are reproducible and contain equivalent information.
Furthermore, the higher intensity in the forward direction allows for faster
imaging, which is limited by detector read-out speed and scan stage movement
rather than signal intensity or SNR.

##  V Conclusions and Outlook

In this work, we have conducted an internal Round Robin by comparing BCARS
from two different setups and two different detection modes for analyzing
single crystalline materials with increasing complexity: diamond, 6H-SiC, KDP,
and KTP. The NRB correction is shown to work equally well for all cases and
can remove the setup-dependent influences from the laser source and detector
response function. As a result, the phase-retrieved spectra are comparable,
reproducible, and in good agreement with SR measurements and literature
values. Both forward- and epi-detected signals contain essentially the same
spectral information. The epi-detected signal is shown to be the reflection of
the forward signal, as the backward signal is non-detectable due to the phase
mismatch between the pump/Stokes and the BCARS signals. The transmission
signal is more intense and has a better SNR. Therefore, it is advised to use
transmission detection whenever the setup and the sample system allow for it,
meaning transparent materials or samples on transmissive substrates. Epi-
detection is shown to be equal in information value but can only be used for
transparent materials as well, as the reflection of the scattered signal on
the backside of the sample is needed. The comparison of setups showed
differences in spectral resolution and signal intensity, depending on the
laser system. Furthermore, the imaging of ferroelectric domain walls in LNO
was compared in both setups showing the possibility for even faster
acquisition speed using transmission detection.

###### Acknowledgements.

The authors gratefully acknowledge financial support by the Deutsche
Forschungsgemeinschaft (DFG) through projects CRC1415 (ID: 417590517), INST
269/656-1 FUGG and FOR5044 (ID: 426703838; http:
www.For5044.de), as well as the Würzburg-Dresden Cluster of Excellence”
ct.qmat” (EXC 2147), LASERLAB-EUROPE (grant agreement no. 871124, European
Union’s Horizon 2020 research and innovation program), and the European Union
project CRIMSON (grant agreement no. 101016923). The authors thank Jiří Hlinka
of the Czech Academy of Sciences, Prague, Czech Republic, for providing
samples.

The authors F.Hempel and F.Vernuccio equally contributed to this work.

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