Spontaneous Raman spectroscopy (SR) is a versatile method for analysis and visualization of ferroelectric crystal structures, including domain walls. Nevertheless, the necessary acquisition time makes SR impractical for in situ analysis and large scale imaging. In this work, we introduce broadband coherent anti-Stokes Raman spectroscopy (B-CARS) as a high-speed alternative to conventional Raman techniques and demonstrate its benefits for ferroelectric domain wall analysis. Using the example of poled lithium niobate, we compare the spectral output of both techniques in terms of domain wall signatures and imaging capabilities. We extract the Raman-like resonant part of the coherent anti-Stokes signal via a Kramers–Kronig-based phase retrieval algorithm and compare the raw and phase-retrieved signals to SR characteristics. Finally, we propose a mechanism for the observed domain wall signal strength that resembles a Čerenkov-like behavior, in close analogy to domain wall signatures obtained by second-harmonic generation imaging. We, thus, lay here the foundations for future investigations on other poled ferroelectric crystals using B-CARS.

Lithium niobate (LN) is one of the most widely used materials applied in nonlinear optical devices,1,2 in electro-optic modulators,3–5 and for integrated optics.6–8 The development of thin-film lithium niobate-on-insulator (TFLNOI) platforms gave rise to considerable performance enhancements.9 However, the sophisticated structure of these state-of-the-art devices requires the reliable and fast analysis of structural key factors in the LN crystal.10 Spontaneous Raman spectroscopy (SR) is an established technique for the visualization of domain walls (DWs) in LN.11–13 However, the required long acquisition times greatly limit its applicability in LN-based device fabrication monitoring.

A promising alternative to the SR-based investigation of LN structures is the application of coherent Raman techniques like broadband coherent anti-Stokes Raman scattering (B-CARS).14,15 B-CARS combines the scanning speed of nonlinear coherent imaging, as does second harmonic generation (SHG), with the structural and chemical sensitivity of SR. B-CARS is a four-wave mixing (4 WM) coherent Raman technique, which is established for fast, marker-free chemosensitive imaging especially in biology and medicine.16,17 Due to its nonlinear 4 WM nature, the speed of B-CARS measurements is unmatched by SR and enables fast imaging with short acquisition times. However, B-CARS spectra are not directly comparable to SR spectra, as the SR-like resonant CARS response is distorted due to a non-resonant signal background (NRB). For biological samples, this NRB influence has been addressed through phase retrieval algorithms to evaluate the correct resonant CARS response.18 Recently, our group pointed out specific fundamental aspects of solid-state B-CARS analyses using the example of LN and demonstrated the successful application of the mentioned phase-retrieval approach for this model material.19 

In this work, we build upon these fundamental B-CARS investigations in LN and apply this technique for analysis and hyperspectral imaging of LN DWs. We compare raw and phase-retrieved B-CARS spectra of poled LN with responses obtained by SR and compare the specific spectral DW features, DW signature widths, and imaging capabilities of both techniques. Also, we propose a possible explanation for the strength of the found DW signature in B-CARS measurements. We, thus, use poled LN as the model material to introduce high-speed ferroelectric DW imaging via B-CARS.

The DW signature in standard SR measurements is generally attributed to two mechanisms:20 

  • A relaxation of the selection rules that determine the detected phonon branches is in a selected measurement geometry. This effect is caused by a perpendicularly oriented quasi-momentum induced by the domain wall and results in the detection of phonon modes that are not allowed in the chosen measurement geometry.

  • The influence of mechanical and electric fields in the vicinity of the DW owed to the locally changed atomic order and polarity transition between the two adjoining domains. Under stress, the phonon modes of LN may shift21,22 and, thus, give rise to the DW signature.

For CARS imaging of z-cut LN DWs, contrast mechanisms similar to SR are expected. Phonons are supposed to experience the same frequency shifts under mechanical stress, independent of the detection technique in use. Also, a relaxation of the selection rules in the vicinity of the DW that is comparable to SR is expected for B-CARS. This assumption is supported by the CARS selection rules of LN's crystal point group C3v23 (see Tables S I–S III in the supplementary material). In the measurement geometry z(yyy,y)-z,24 the detection of A1(LO) and E(TO) phonon branches is allowed. Due to the relaxation of these selection rules, additional components of the geometries x(yyy,y)-x and y(zzz,z)-y can be expected that might equally contribute the A1(TO) phonon peak. In the case of the directly measured raw B-CARS spectrum, the influence of the NRB adds a further potential source for a DW signature. According to the selection rules of the 4 WM electronic background (see Tables S IV–S VI in the supplementary material), relaxation of the selection rules allows the detection of an additional tensor element (denoted as f33) for the component with geometry y(zzz,z)-y.

The SR and B-CARS measurements were conducted using a LabRAM HR evolution Raman spectroscope (HORIBA Jobin Yvon GmbH, Oberursel, Germany) in backscattering geometry. For SR measurements, a He-Ne continuous wave laser (Melles Griot) with monochromatic emission at 632.8 nm (17 mW) and a Nikon TU Plan Fluor EPI P 100× microscope objective (NA = 0.9) were used. The pinhole aperture for SR measurements was set to 200 μm, which allows for a depth resolution of approximately 8 μm.25 The detector setup allows a spectral resolution of 0.013 nm (0.28–0.33 cm−1). For B-CARS, a combined pulsed laser system (LEUKOS CARS-SM-30) consisting of a temporally and spatially matched monochromatic pump/probe laser (1064 nm, 100 mW) and a broadband Stokes laser (600–2000 nm, 80 mW) was applied with a pulse frequency of 29 kHz and a pulse duration of 1 ns. A high-pass filter cut off the Stokes laser signal below 1064 nm to avoid interference with the anti-Stokes signal. The microscope objective used for B-CARS measurements is a Nikon CFI APO NIR 40× water dipping objective (NA = 0.8). The spectral resolution of the B-CARS signal reaches 0.05 nm (0.45–0.56 cm−1).

The investigated sample is a 5-mol%-MgO-doped, z-cut congruent LN single crystal (thickness is 200 μm) from Yamaju Ceramics Co., Ltd. (Japan). A domain was dynamically poled into the crystal via near-bandgap illumination and simultaneous application of an electric field with a voltage larger than the sample's coercive field. Details of this process are discussed elsewhere.26,27 The shape of the naturally grown domain is examined via preliminary SHG measurements. (Figure 1; note that the different intensities of the DW signatures arise from the dissimilar DW orientations relative to the incident laser polarization, as has been shown elsewhere.28)

FIG. 1.

Second harmonic generation microscopy image of the investigated z-poled lithium niobate domain showing a clear domain wall contrast. The usual hexagonal domain shape produced by this poling technique is distorted here due to the early termination of the poling procedure in order to obtain a domain of dimensions smaller than 50μm. The red line indicates the location of conducted SR and B-CARS line scans. The virgin and inverted domain are marked with a circled dot or cross, respectively. White arrows indicate the crystallographic axes of LN in the hexagonal coordinate system.

FIG. 1.

Second harmonic generation microscopy image of the investigated z-poled lithium niobate domain showing a clear domain wall contrast. The usual hexagonal domain shape produced by this poling technique is distorted here due to the early termination of the poling procedure in order to obtain a domain of dimensions smaller than 50μm. The red line indicates the location of conducted SR and B-CARS line scans. The virgin and inverted domain are marked with a circled dot or cross, respectively. White arrows indicate the crystallographic axes of LN in the hexagonal coordinate system.

Close modal

To compare SR and B-CARS DW imaging, line scans across the DWs and hyperspectral maps of domain sections were recorded with both techniques in z(yy)-z and z(yyy,y)-z geometries for SR and B-CARS, respectively. A focus depth of 130 μm was chosen for both techniques applied, as the deep focus point aids signal collection in the B-CARS measurement.19 

Line scans of 10 μm length were conducted along the red line indicated in Fig. 1, parallel to the x axis of the crystal in 0.1 μm steps (acquisition times: two accumulations of 1 s/px for B-CARS, two accumulations of 20 s/px for SR). Hyperspectral maps were measured in 0.2 μm steps (acquisition times: 0.05 s/px for B-CARS, 1 s/px for SR). Details about the experimental determination of the acquisition times are given in the supplementary material. With B-CARS, 35 × 35 μm2 maps were generated to image the complete poled domain. The corresponding SR map size was chosen to reach the same total measurement time (1 h 28 min) and, thus, measures only 9 × 9 μm2 in size.

Single spectra shown in this work were extracted from line scans. For isolating the resonant B-CARS signal, the raw B-CARS spectra were post-treated via a phase retrieval process analogously to our earlier work.19 

In a first step, we compare the SR spectra, measured in the virgin LN domain and on the DW with the raw and phase-retrieved B-CARS spectra to determine spectral features that yield a DW contrast. Details about the analysis of spectral features in the SR, raw CARS, and phase-retrieved CARS spectra can be found in the supplementary material.

Figure 2 shows the SR, as-measured (raw) B-CARS, and phase-retrieved B-CARS spectra measured well within the virgin LN domain (polarization ↑), at the LN DW, and the difference spectra of these two locations. Figure 2(a) reveals the intensity of the A1(TO4) peak (ca. 623 cm−1) as the main DW signature in SR, in accordance with previous works.11–13 

FIG. 2.

Spectra of poled bulk lithium niobate in-domain (black), at the domain wall (green), and the difference spectra of these (orange), measured with (a) spontaneous Raman spectroscopy, (b) raw CARS, and (c) phase-retrieved CARS. The asterisk (*) marks a spectral region of (c) in which phase retrieval restores peaks that were previously too dispersive in shape to be analyzed in (b).

FIG. 2.

Spectra of poled bulk lithium niobate in-domain (black), at the domain wall (green), and the difference spectra of these (orange), measured with (a) spontaneous Raman spectroscopy, (b) raw CARS, and (c) phase-retrieved CARS. The asterisk (*) marks a spectral region of (c) in which phase retrieval restores peaks that were previously too dispersive in shape to be analyzed in (b).

Close modal

In the raw B-CARS spectra [Fig. 2(b)], the majority of the phonon peaks up to about 550 cm−1 is hardly discernable because of their dispersive shape and the low intensity as compared to the NRB. The in-domain B-CARS spectrum is massively dominated by the A1(LO4) peak (ca. 868 cm−1). However, in the vicinity of the DW, the signal intensity of the A1(LO4) peak decreases down to about 50% of the in-domain signal. Instead, a second dominating peak at ca. 600 cm−1 is detected. We identify this as the A1(TO4) phonon peak, which is not allowed in this geometry in the absence of a DW, according to the selection rules. These DW signatures are much more distinct than those in SR; however, to elucidate whether these signatures are generated by the resonant B-CARS signal or the NRB, the former must be isolated via the phase retrieval algorithm.

After phase retrieval [Fig. 2(c)], the spectral region below 550 cm−1 (marked with an asterisk in the figure) reveals much more distinct peaks than in the raw spectra. The phase-retrieved in-domain B-CARS peaks resemble the in-domain SR peaks.19 In contrast, the phase-retrieved DW spectrum reveals a massive intensity change of the A1(TO4) peak, much like the raw CARS spectrum. The strong DW signature of the B-CARS measurement, thus, is not caused by the NRB but is inherent to the resonant B-CARS response. Interestingly, we can see intensity changes for other phase-retrieved phonon peaks on the DW as well. Among these, the complete intensity drop of the E(TO8) peak (ca. 580 cm−1) is the most remarkable change. From the current data, it cannot be determined with absolute certainty whether we see a simultaneous intensity decrease in E(TO8) and increase in A1(TO4), or whether this is a case of phonon directional dispersion, i.e., a gradual frequency transition of the peak frequency from E(TO8) to A1(TO4). Phonon directional dispersion between E(TO8) and A1(TO4) has been reported for SR,29 however, not as a DW signature.

Based on the findings for the B-CARS spectra in Fig. 2, the spectral features for B-CARS imaging of LN DWs were chosen with respect to the most significant signal changes between the in-domain and DW spectra: the A1(TO4) phonon peak intensity and the A1(TO4) phonon peak frequency. Like in SR, the A1(TO4) intensity change is the most apparent DW signature in raw and phase-retrieved B-CARS. Additionally, if we assume phonon directional dispersion for the phonon frequency of E(TO8), the frequency transition to A1(TO4) on the DWs is also of interest as a potential DW signature.

Line scans of these spectral features across the DW are shown in Fig. 3. With SR [Fig. 3(a)], we see a clear DW signature, similar to literature data.13 The signature width of 2.4 μm (FWHM of the Gaussian fit) is higher than that given in the literature, where the signature width is diffraction-limited. In our setup and with the focus in the sample (ordinary axis), the diffraction limit is 1.0 μm (Rayleigh criterion). A comparative measurement on the sample surface (see Fig. S2 in the supplementary material) indeed yields a signature width of ca. 1.1 μm, which is of a comparable order of magnitude. However, the deep focusing causes aberrations that distort the illumination volume, therefore reducing the resolution. For the same reason, the DW signature is not of pure Gaussian shape. The fitting is, thus, not optimal, and the FWHM appears wider than the DW signature in SR actually is.

FIG. 3.

Line scans recorded across a domain wall in poled bulk lithium niobate, visualizing the progression of the A1(TO4) phonon peak intensity measured via (a) Raman spectroscopy, (b) raw CARS, and (c) phase-retrieved CARS, as well as (d) the frequency shift of the A1(TO4) phonon peak in phase-retrieved CARS.

FIG. 3.

Line scans recorded across a domain wall in poled bulk lithium niobate, visualizing the progression of the A1(TO4) phonon peak intensity measured via (a) Raman spectroscopy, (b) raw CARS, and (c) phase-retrieved CARS, as well as (d) the frequency shift of the A1(TO4) phonon peak in phase-retrieved CARS.

Close modal

For the same feature in the raw B-CARS measurement [Fig. 3(b)], we obtain a DW signature with considerably less noise than in SR and a better Gaussian fit. Again, the DW signature width (FWHM = 2.0 μm) exceeds the given resolution limit (1.4 μm Rayleigh criterion). After phase retrieval [see Fig. 3(c)], the A1(TO4) peak intensity is comparable to that of the raw spectrum, however, with a narrower signature (FWHM = 1.8 μm). The similarity between the raw and phase-retrieved A1(TO4) signal again shows that the DW signature is inherent to the resonant part of the B-CARS signal.

The fitted peak frequency shift of the E(TO8)/A1(TO4) transition in the phase-retrieved B-CARS measurement [see Fig. 3(d)] provides a DW signature as well, however, with a considerably broader signal (FWHM = 3.1 μm). It can, thus, be assumed that the contrast mechanism for this signature is different from that of the A1(TO4) peak intensity and has a larger response length. Possible mechanisms might be, e.g., a high stress sensitivity that detects long-reaching stress fields or a sensitivity for electric fields. Further experiments are indicated to clarify the mechanisms of this broad signature.

The remarkably stronger DW contrast of the A1(TO4) intensity with B-CARS compared to SR gives rise to speculations about where this divergence might stem from. We propose an effect in analogy to what is known from second-harmonic imaging of LN DWs by the so-called Čerenkov SHG.30 [We, thus, may brand the effect as Čerenkov CARS (see Fig. 4).] This signal enhancement mechanism on LN DWs is associated with a change in phase matching: for a collinear setup, the k-vectors of the incident photons and the generated CARS signal are diametrical with the phase mismatch Δk directed parallel to the incident beam k-vector. For Čerenkov CARS, however, the k-vector mismatch is compensated via the reciprocal lattice vector G, which is directed perpendicular to the k-vectors of the incident beam (in analogy to the quasi-momentum in SR on DWs, see the theory part of this article). The anti-Stokes k-vector is, thus, angled for reasons of momentum conservation. The Čerenkov CARS signal fulfills the phase matching conditions much better than the regular phase matching scheme and allows for the detection of a locally enhanced signal at DWs. Such a Čerenkov CARS signal would only be detectable for z-cut CARS geometries, as the nonlinear Čerenkov process is always longitudinally phase matched.31 Future experiments are indicated to verify this hypothesis.

FIG. 4.

Schematic representation of CARS phase matching in lithium niobate with (a) the collinear phase matching configuration and (b) the proposed Čerenkov CARS configuration on the domain wall in analogy to Čerenkov SHG.

FIG. 4.

Schematic representation of CARS phase matching in lithium niobate with (a) the collinear phase matching configuration and (b) the proposed Čerenkov CARS configuration on the domain wall in analogy to Čerenkov SHG.

Close modal

Based on the contrast mechanisms covered in Fig. 3, hyperspectral maps of the poled LN domain were recorded (Fig. 5). Because of the drastically different acquisition times of the two techniques, the B-CARS map covers 15 times the area of the SR measurement over the same total sampling time. This speed advantage of B-CARS due to its coherent nature is of essential importance for the potential use in LN-based device production monitoring. The comparison of Figs. 5(a)–5(c) shows that the essential information obtained by SR and B-CARS is the same, and the line shape and signal strength of the raw and phase-retrieved B-CARS maps are very similar. Thus, B-CARS can be used as an equivalent to SR in LN DW imaging, and it is not necessary to post-process the raw B-CARS measurements for phase-retrieval to obtain a reliable domain image. Finally, the imaged domain shape of Fig. 5(d) resembles that of the other colormaps and offers a very strong DW signature, while the broader DW signature obscures the actual shape of the imaged domain. This spectral feature might be of interest for potential thin film measurements though, where large frequency shifts might be easier to detect than peak intensity changes.10 

FIG. 5.

Hyperspectral colormaps of the same poled bulk lithium niobate domain as in Fig. 1, visualizing the progression of the A1(TO4) phonon peak intensity measured via (a) Raman spectroscopy, (b) raw CARS, and (c) phase-retrieved CARS, as well as (d) the frequency shift of the A1(TO4) phonon peak in phase-retrieved CARS.

FIG. 5.

Hyperspectral colormaps of the same poled bulk lithium niobate domain as in Fig. 1, visualizing the progression of the A1(TO4) phonon peak intensity measured via (a) Raman spectroscopy, (b) raw CARS, and (c) phase-retrieved CARS, as well as (d) the frequency shift of the A1(TO4) phonon peak in phase-retrieved CARS.

Close modal

We have shown that B-CARS DW analysis in poled LN is a high-speed equivalent to standard SR measurements. After phase retrieval, B-CARS provides the same features like SR on DWs. However, the domain wall signatures in raw and phase-retrieved B-CARS are much more pronounced. We propose that the DW signal is enhanced by a Čerenkov-like mechanism. Imaging can directly be conducted with the raw spectra here, as this DW signature is retained after phase retrieval.

Based on these findings, angle-resolved B-CARS experiments are indicated to investigate the proposed Čerenkov-like signal enhancement on DWs and verify the observed relaxation of selection rules. B-CARS measurements with crystals under uniaxial stress can indicate the influence of stress signatures in the vicinity of the DW. Finally, DW investigations on other ferroelectric materials like lithium tantalate or on ion-doped waveguides can show the versatility of this technique to reliably provide high-speed Raman imaging for ferroelectric poling structures.32 

See the supplementary material for a comparative spontaneous Raman spectroscopy surface line scan across the lithium niobate domain wall, aids for reading the extended Porto notation and selection rules of B-CARS and its non-resonant electronic background in crystals of the C3v point group.

The authors gratefully acknowledge financial support by the DFG through Project Nos. CRC1415 (ID: 417590517), EN 434/41–1 (TOPELEC), INST 269/656-1 FUGG, and the FOR5044, as well as the Würzburg-Dresden Cluster of Excellence on “Complexity and Topology in Quantum Matter”—ct.qmat (No. EXC 2147; ID: 39085490).

The authors have no conflicts to disclose.

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

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Supplementary Material