Brillouin and Raman imaging of domain walls in periodically poled 5%-MgO:LiNbO

supplemental information to “Brillouin and Raman imaging of domain walls in periodically-poled 5%-MgO:LiNbO 3 ” is provided. In particular, we show Brillouin spectra of x- and y-cut bulk domains and compare them with the results of and calculate values according to Eq. (1) of the main we the Brillouin line width and the Brillouin intensity in z-cut line scans crossing over several domain walls (DWs).

In this document, supplemental information to "Brillouin and Raman imaging of domain walls in periodically-poled 5%-MgO:LiNbO 3 " is provided.In particular, we show Brillouin spectra of x-and y-cut bulk domains and compare them with the results of Lejman et al. [1] and calculate values according to Eq. ( 1) of the main manuscript.Furthermore, we show the Brillouin line width and the Brillouin intensity in z-cut line scans crossing over several domain walls (DWs).
In the same way as the bulk z-cut spectra have been acquired, single spectra on x-cut (Fig. S1) and y-cut (Fig. S2) MgO:LNO were recorded.Here, in contrast to z-cut, the polarization direction of the incident light is of relevance as the crystal is birefringent.Therefore, the sample has been rotated in such a way that the polarization of the incident light was aligned to ordinary direction (blue), extraordinary direction (red) and at 45° direction (green).

X-cut Brillouin spectra
For x-cut MgO:LNO, three Brillouin shifts could be observed (cf.Fig. S1): one corresponding to the ordinary refractive index (  = 37.81 ), one corresponding to the extraordinary refractive index (  = 36.49), and one corresponding to the averaged refractive index (  / = 37.15 ).It is noteworthy, that the averaged refractive index can be attributed to a mode conversion effect [1] at which the light polarization rotates by 90°.Thus, light is sensitive to n o on the forward run and to n e on the way back or vice versa, hence, resulting in an averaged value.
The spectra of pure ordinary and pure extraordinary incident light polarization comprise two of the three signals, respectively, whereas the 45° spectrum comprises all three signals.Note that the signal intensities are different to that reported by Lejman et al. [1] which is due to polarization-dependent optics in our setup.

Y-cut Brillouin spectra
For y-cut MgO:LNO, only two Brillouin shifts could be observed (cf.Fig. S2): one corresponding to the ordinary refractive index (  = 39.48 ) and one corresponding to the extraordinary refractive index (  = 38.00).Here, a mixed Brillouin shift is missing which can be explained by the corresponding photoelastic tensor element being zero [1].

Absolute Brillouin shift comparison
The obtained Brillouin shifts for the different measuring geometries are summarized in Table S1 and compared to the results reported by Lejman et al. [S1] (converted to 780.24 nm excitation wavelength) and calculated values.The latter are based on Eq. ( 1) of the main manuscript using the refractive indices for 780.24 nm calculated from [S2] and sound velocities taken from [S3].In general, our Brillouin shifts are in good agreement with literature values and the calculated ones.The difference of ~1.5 GHz compared to Lejman et al. might be ascribed to the fact that we used 5 mol% MgO:LNO rather than undoped LNO.Additionally, the sound velocities for the calculated values are from 7 mol% MgO:LNO, which might explain the small differences to our values.

Brillouin line width and intensity at the DW
During the fitting procedure of the z-cut line scan (cf.Fig. 5 of the main manuscript) not only the Brillouin shift was evaluated but also the Brillouin line width (peak FWHM) and the Brillouin intensity (peak height).Their dependence on the lateral position is shown in Fig. S3.At the DWs, the line width (blue) increases by 0.5 GHz, whereas the intensity (orange) decreases by ~12%.Both parameters clearly mark the positions of DWs, which agrees with the results of the Brillouin shift contrast and the Raman contrast presented in the main manuscript.However, the line width and the intensity curve have a smaller signal-to-noise ratio, which might be due to a higher error susceptibility during the fitting procedure.As discussed in the main manuscript, the extended planar defect theory of Stone and Dierolf [S4] explains the broadening at the DWs, which is visible in the single spectra shown in Fig. 3b, too.A Brillouin intensity (peak height) decrease comes along with the broadening.The total Brillouin intensity, calculated as area under the curve, stays constant over the DWs.

Fig. S1 .
Fig. S1.Brillouin spectra of x-cut MgO:LNO for incident polarization aligned to ordinary (blue), extraordinary (red) and at 45° direction (green), consisting of three different Brillouin shifts which can be attributed to a pure ordinary, a pure extraordinary and a mixed refractive index.

Fig. S2 .
Fig. S2.Brillouin spectra of y-cut MgO:LNO for incident polarization aligned to ordinary (blue), extraordinary (red) and at 45° direction (green), consisting only of two different Brillouin shifts which can be attributed to a pure ordinary and a pure extraordinary refractive index.The mixed signal is missing because the corresponding photoelastic tensor element is zero.

Fig. S3 .
Fig. S3.Brillouin line width (blue) and Brillouin intensity (orange) as function of the lateral position.Whereas the line width increases at the DWs, the intensity decreases.