1. Introduction

Second Harmonic Generation (SHG) is a nonlinear process widely used to access new optical wavelengths not covered by pure laser emission. After its first observation by Franken et al. in 1961 in bulk quartz [1], several noncentrosymmetric media have been developed to improve the conversion efficiency and to reach high power generation at visible wavelengths. Later, quasi-phase-matching (QPM), based on a periodic modulation of the nonlinear polarization, has been introduced to reach larger conversion efficiency in noncentrosymmetric materials [2,3]. The QPM technique is also used in Ge doped silica fibers to obtain SHG by the so called optical poling process: the quadratic susceptibility is induced by the beating between the fundamental wave and its own second harmonic through the real part of the third-order nonlinear susceptibility [4,5]. A static electric field produced by the interaction of the two coherent waves is able to induce a spatially modulated second order optical response [6–9].

$\chi ^{(2)}$ coefficient can also be induced and enhanced in pure glass materials by the mixed action of the temperature and of an external static electric field [10,11]. To enhance the conversion efficiency, the QPM technique has been applied to electric-field thermally poled optical fibers for second harmonic generation [12]. It is important to note that when the SHG signal is electric field induced (EFISH), its strength is proportional to the third-order nonlinear coefficient. Therefore thermo-electric poling (thermal poling) has been developed on new nonlinear glasses as chalcogenides and tellurites, exhibiting strong Kerr effect [13–17]. Recently, very high values of second order nonlinear optical susceptibility (29 pm/V at 1.06 $\mu$m) have been obtained within a thermally micropoled sodo-niobate film: these values can compete with the crystalline lithium niobate second order response [17]. Beyond the $\chi ^{(2)}$ writing process, the implementation of a local static electric field induces changes in linear and nonlinear susceptibilities. More specifically, both the resonant ($\chi ^{(3)}_{R}$) and nonresonant ($\chi ^{(3)}_{NR}$) third-order susceptibilities are affected by the thermal poling process, and the open question remains to evaluate the corresponding variation. While the measurement of the second-order nonlinear susceptibility is easily obtained from the second harmonic conversion efficiency, the quantification of the third-order nonlinear coefficient [8] along the poling process is difficult to obtain and requires sophisticated experiments [18–20]. Consequently, no bimodal systems able to map both $\chi ^{(2)}$ and $\chi ^{(3)}$ relative contributions have been reported so far. It was recently demonstrated how the electronic contribution of the third-order nonlinear optical susceptibility $\chi ^{(3)}_{NR}$ can be retrieved from the nonresonant background (NRB) of a M-CARS measurement. This approach is applicable to cases where the multiphoton absorption can be neglected ($\mathfrak {Im}(\chi ^{(3)}_{NR})=0$) and where the spectral window does not contain vibrational contribution [21].

We show here that this spectroscopic method is compatible with the techniques of microspectroscopy and 2D high resolution imaging as will be shown further. The short acquisition time of M-CARS setup (0.1s per spectrum) permits the fast acquisition of data over a rather large area of a complex sample [22,23]. In this work, we present the spatial mapping of $\mathfrak {Re}(\chi ^{(3)}_{NR})$ in a periodically poled niobium borophosphate (BPN) glass by means of M-CARS microspectroscopy. A systematic reduction of $\mathfrak {Re}(\chi ^{(3)}_{NR})$ is unambiguously detected in the poled areas. Finally, SHG mapping of the sample is additionally carried out using the same setup, leading to fully elucidate the thermal poling impact on the amplitude of $\chi ^{(3)}$ coefficient.

2. Methodology

2.1 Forward M-CARS setup

Figure 1 shows the design of the setup used in our experiment. A Q-switched microchip laser source (Horus Laser, 1064 nm, 1 ns, 20 kHz) generates a linearly polarized beam that is split into two beams by means of a half-wave plate and a Glan-Taylor polarizer. The first beam is injected into a photonic crystal fiber to generate a supercontinuum between 600 nm and 1650 nm. The corresponding output broadband beam is collimated by a parabolic mirror and then filtered by a 1050 nm long-pass filter (Thorlabs, FEL1050) to play the role of the Stokes (probe) wave. The other fraction of the pump beam is synchronized with the Stokes wave by a delay line. Both pump and Stokes waves are combined via a 1064 nm notch dichroic mirror (Semrock, NFD01-1064-25x36) and focused onto the sample by a microscope objective with a high numerical aperture (Olympus, UplanSApo 60x, N.A.=1.2, water immersion) providing high lateral and axial spatial resolutions (0.3 $\mu$m and 2 $\mu$m respectively). A translation stage controls the position of the sample in the $x$, $y$ directions. The generated M-CARS signal is collimated by a second microscope objective (Nikon, S Plan Fluor ELWD 60x, N.A.=0.7) before being filtered by a 1064 nm notch filter (Thorlabs, NF1064-44) in order to eliminate the remaining pump signal. Finally, the signal is analyzed by a spectrometer (Horiba, LabRAM HR Evolution, 600 gr/mm grating, Synapse CCD camera) with a high spectral resolution (<0.8 cm$^{-1}$). The M-CARS spectra are then processed by a deconvolution algorithm known as maximum entropy method (MEM) [24]. This numerical method permits the extraction of the vibrational signatures by estimating the phase of the measured M-CARS spectrum.

 

Fig. 1. M-CARS setup in forward configuration. $\lambda /2$, half-wave plate; GTP, Glan-Taylor polarizer; PCF, photonic crystal fiber.

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2.2 BPN sample

The sample is a BPN glass of nominal composition 0.58(0.95 NaPO$_3$ + 0.05 Na$_2$B$_4$O$_7$) + 0.42 Nb$_2$O$_5$ (commonly labelled BPN42, but also referenced as BPN-10Na in Ref. [25]) periodically poled by thermal poling process, which consists of the application of a static electric field (1.6 kV) using micropatterned indium tin oxide (ITO) anode electrodes under temperature (230$^\circ$ C) [26]. Figure 2(a) shows the position where the electrodes (in red) were located with respect to the glass plate during the microimprinting process, before being completely removed. The depth of the subanodic layer formed under the anode electrodes is about 2 $\mu$m as observed in Ref. [26] for a sample with a slightly different pattern. Surface topology is shown in Fig. 2(b). It can be clearly seen that the poled surface is reshaped with the formation of depleted strips placed below the anode edges: such relief creation does correspond to actual trenches of 200 nm depth induced by the electrostatic process [27–30]. Structural and chemical composition changes after poling process are widely discussed in Ref. [31], where it is stated that the migration of mobile cations such as sodium ions (Na$^+$) that move away from the anodes leads to the creation of a space charge. This is the main cause of the creation of the second-order optical nonlinearity in poled areas. For further discussion concerning finer structure changes, see [31–34]. Figure 2(c) finally shows an optical microscope image of the sample where 3-$\mu$m-wide poled areas alternate with 5-$\mu$m-wide unpoled ones.

 

Fig. 2. Information on the microimprinting process conducted on the BPN42 niobate borophosphate sample. (a) Location of the poled areas in red. (b) AFM surface topology of the glass after microimprinting polarization process and removal of the ITO anodes (c) Bright field microscope image where the area delimitated by the green grid will be mapped further.

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3. Results and discussions

First of all we analyzed both poled and unpoled areas with a LabRAM HR Evolution Raman Microscope (Horiba Scientific, equipped with He-Ne laser, 633 nm, linearly polarized in $y$ direction). The normalized Raman spectra are presented in Fig. 3(a). For both poled and unpoled areas, each displayed spectrum corresponds to the average of five recorded spectra (240s x 2 accumulations per spectrum) in the considered region. Several vibrational modes can be identified: first, the broad envelope in the range 550-950 cm$^{-1}$ is associated with the symmetric stretching of Nb-O bonds when the oxygen is involved in an ionic bond with sodium. This overlays the signature of NbO$_6$ octahedra bridging with PO$_4$ tetrahedral units (750-850 cm$^{-1}$) and that of Nb-O-Nb bonds in a 3D niobate network (600-750 cm$^{-1}$). The shoulder at 900 cm$^{-1}$ corresponds to the symmetric stretching of Nb-O terminal bonds when the oxygen is involved in an ionic bond with sodium. The mode at 950-1030 cm$^{-1}$ is attributed to the symmetric stretching of the tetrahedral phosphate structural units [31,33]. On Fig. 3(a), one can clearly see that the vibrational spectra collected on both poled and unpoled areas are almost identical. This confirms the fact that microimprinting does not seem to induce major changes on the base structure of BPN42, but also underlines the difficulty to reveal tiny differences using the Raman spectroscopy. It is also worth pointing out that only minor structural changes were indeed evidenced by Raman spectroscopy in Ref. [26]. We measured the M-CARS spectra for both poled and unpoled areas with a pump beam polarized in $y$ direction and a randomly polarized Stokes beam. Each displayed specrum corresponds to the average over six recorded spectra (0.1s x 2 accumulations per spectrum). These spectra are shown in Figs. 3(b) and 3(c) before and after data processing by the MEM, respectively. We can identify in the vibrational range (550-1200 cm$^{-1}$) the same main modes previously evidenced with the Raman data. These modes are better visualized with the post-processing of the MEM algorithm (Cf. Fig. 3(c)). Changes in the general shape of the overall spectra between poled and unpoled areas are now more visible. Indeed, one can already notice how the difference between the two normalized M-CARS spectra is more pronounced than difference between the two corresponding Raman measurements. These differences are even far more evident in Fig. 3(c) after MEM processing. As highlighted by the red arrows in Fig. 3(c), the intensity decreases in the poled areas with respect to the unpoled ones related to the Nb-O-(P) and terminal Nb-O bonds located at 820 cm$^{-1}$ and 900 cm$^{-1}$, agrees with the Raman observations previously published [17,25,26,31]. Upon sodium removal from the glass network, the decrease of the band at 900 cm$^{-1}$ linked to Nb-O-Na$^+$ arrangement is expected. As a consequence, the niobate network undergo a distortion to compensate for this loss. Concerning the phosphate network, previous studies [17,31] have shown that it is formed by pyro- and ortho-phosphate structural units. Within the sodium depletion layer, these small units can be more imbricated in the niobate network modifying the Raman mode attributed to Nb-O-P bridges at 820 cm$^{-1}$. Nevertheless, if these differences are clearly the signature of the structural modifications occurring during the poling process [32], our observations also prove the efficiency of the CARS setup, combined with the MEM algorithm. In this regard, no spectral changes were observed for this sample when using a classical Raman measurement.

 

Fig. 3. Recorded spectra of micromprinted niobium borophosphate glass. (a) Normalized Raman spectra recorded with a laser excitation at 633 nm, linearly polarized in $y$. (b-c) M-CARS spectra recorded with an $y$-direction linearly polarized pump beam and a randomly polarized Stokes beam: (b) M-CARS spectra normalized by the mean M-CARS intensities and (c) M-CARS spectra processed by the MEM algorithm with the red arrows highlighting the variation of the vibrational modes between poled and unpoled areas.

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Finally, one can see in Fig. 4(a) the raw M-CARS spectra of both the poled and unpoled areas where the vibrational (550-1200 cm$^{-1}$) and the electronic (1300-1900 cm$^{-1}$) spectral range are displayed. These spectra reveal, after signal optimization conducted on each type of areas, a systematic decrease of the M-CARS intensity in the poled area in the whole recorded spectral range (550-1900 cm$^{-1}$). The core of the current work will be thus to reconstruct some maps of the third order nonlinear optical susceptibility from the integration of the raw M-CARS intensity in 1300-1900 cm$^{-1}$ spectral region, with the aim of evaluating the impact of the thermal poling on the amplitude of $\mathfrak {Re}(\chi ^{(3)}_{NR})$. The first map (Fig. 4(b)) is obtained in the 1300-1900 cm$^{-1}$ spectral range, where the M-CARS signal is composed purely by the electronic response of the material i.e. the NRB signal which can be directly linked to the real part of the nonresonant third-order nonlinear susceptibility $\mathfrak {Re}(\chi ^{(3)}_{NR})$ [21]. It is acquired using the M-CARS setup, by recording spectra while a translation stage is moving the sample. The whole area, delimited by the green grid on the bright field image in Fig. 2(c), is scanned (0.1s x 2 accumulations per pixel) and with a laser mean power of 35 mW (pump power + Stokes power, measured at the sample position). The spatial step of the map is 0.4 $\mathrm {\mu }$m in both $x$ and $y$ dimensions. The effective microimprinted $\chi ^{(2)}$ in the poled area (for which the amplitude is estimated to be around $1.82\times 10^{-12} m/V$ based on the SHG measurements carried out by Dussauze et al. [32]) is also highlighted by recording a SHG map with the same apparatus in forward configuration, by exciting the sample with a 1064 nm linearly polarized laser beam with 17 mW average power. The SHG map is, then, acquired in the same way as for M-CARS map (with also the same spatial resolution, 0.1s x 2 accumulations per spectrum) on exactly the same area of the sample. The reconstituted image is shown in Fig. 4(c).

 

Fig. 4. Mapping of the microimprinted niobate borophosphate glass. (a) Raw M-CARS spectra: maps are recorded from the integration of the raw M-CARS intensity in 1300-1900 cm$^{-1}$ spectral region (delimited by the dashed line). (b) M-CARS map collected in the region 1300-1900 cm$^{-1}$, positioned with respect with a schematical representation depicting the cross-section of the BPN42 sample with the anodes and (c) SHG map recorded at 532 nm, positioned with respect with the M-CARS map.

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From Fig. 4(b) we can see how the maxima of the M-CARS signal follow the unpoled areas with great accuracy. The local minima of the M-CARS signal instead are concentrated in the poled areas. The map displays a reduction of the M-CARS signal by about 18.7 % on average in the poled areas (with respect to the unpoled ones).

In the 1300-1900 cm$^{-1}$ spectral range, the measured M-CARS intensity $I_{aS}$ can be written as $\mathfrak {Re}(\chi ^{(3)}_{NR})\propto (I_{aS})^{1/2}$[21]. Therefore, by taking the square root of the signal level in the map of Fig. 4(b), we can estimate a relative variation of the $\mathfrak {Re}(\chi ^{(3)}_{NR})$ of approximately -9.8 % between poled and unpoled areas. The M-CARS map then clearly reveals how the thermal poling reduces the amplitude of the nonresonant third-order nonlinearity.

We believe that the vast majority of the relative NRB signal variation can be attributed to the sodium depletion within the subanodic zone, which in turn causes a decrease of the matter density and of the linear refractive index [25]. In particular, for the case of BPN42 [25], the density in the poled areas has been calculated to be reduced by an amount of 15.3%.

As expected, the local maxima of SHG intensity are located in the poled areas, especially at the interfaces between poled and unpoled areas. This result is numerically predicted by the modeling shown in Fig. 5, which is derived and calculated from the modeled spatial charge distribution of Fig. 6. The sharp variation of the charge density at the interfaces between poled and unpoled areas induces an abrupt variation of the electric potential causing a strong local field enhancement perpendicular to the poled lines. These figures describe our current configuration (i.e. alternation of poled and unpoled areas having respective width of 3 and 5 $\mu$m), where the two edges of the anode are extremely close. The present configuation slightly differs from the one reported by Dussauze et al. [26] (alternation of poled and unpoled areas having respective width of 8 and 40 $\mu$m), where a similar distribution of SHG intensity is however observed. In view of these combined M-CARS and SHG maps, it is very clear how the presence of a local $\chi ^{(2)}$ susceptibility goes with a local decrease of the $\chi ^{(3)}$ susceptibility and linear refractive index, in agreement with a reduction of the matter density due to the poling process, as observed in Ref. [35], as well as the decrease of the Raman intensity within the poled areas that was previously highlighted in Refs. [25] and [26]. Based on AFM data (Fig. 2(b)), it is also important to stress that such decrease of $\chi ^{(3)}$ in poled areas is not related to the sample topology. As a matter of fact, the minimum of $\chi ^{(3)}$ is observed in the central part of the zone under consideration, which does not correspond to any trench nor any valley but rather to some area where the matter remains still present.

 

Fig. 5. Experimental SHG intensity profile of the sample. The calculated SHG intensities are derived from the electrostatic modeling presented in Fig. 6.

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Fig. 6. Electrostatic modeling of the imprinted electrical static field. Modeled spatial distribution of (a) charge densities and (b) electrical potential. Calculated electric fields in (c) $x$ and (d) $z$ dimensions.

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4. Conclusion

We presented here the interesting capabilities of M-CARS system to provide nonlinear multimodal imaging. As a powerful tool commonly used for vibrational spectroscopy, especially on biological samples such as living cells, we also demonstrated recently that M-CARS can also be used to investigate the electronic contribution of the third-order optical susceptibility of crystals [21]. By exploiting the efficiency of the M-CARS technique (implying a very low acquisition time), a high resolution spatial mapping of the electronic contribution of the third-order susceptibility and of its relative variation have been achieved on a microstructured sample of niobium borophosphate, whose configuration is appropriate to validate our approach. We were able to perform a simultaneous mapping of $\chi ^{(2)}$ and $\chi ^{(3)}$ of the sample. Such approach provides a better spatial resolution than a classical Raman approach, as it involves nonlinear processes. In addition, our results well agree with the experimental data and what is predicted in the literature. Indeed, the M-CARS map has revealed a relative decrease of the NRB signal in the poled areas of the sample of $\chi ^{(3)}$ by 9.8 % with respect to its intrinsic value because of the sodium depletion in the subanodic regions. Finally, the same setup also provided a SHG map that is in full agreement with the data presented in Ref. [26] and the numerical modeling: sharp variations of charge density located at the interface between poled and unpoled areas cause an increase of SHG intensities owing to the local field enhancement. These results show that our M-CARS setup is suitable for a nonlinear multimodal imaging of such type of samples, and could also be an interesting tool to study samples with even more complex structures.