Conflict of interest

4.3. Capability for 3D imaging

34 Ferroelectrics and Their Applications

5. Conclusion

As we described above, the scanning of laser focus in the X-Y plane enables us to obtain twodimensional images of ferroelectric domains. Then if we stack a series X-Y plane images recorded at different depths inside the material, we can produce 3D images of domains. This is an advantage that cannot be met by the traditional domain imaging techniques. In Figure 12 we show a number of 3D images of ferroelectric domain patterns, which are formed in a congruent LiNbOb3 crystal [38]. From these images we can see how the initially circularshaped domains transform to hexagons with depth [Figure 12(b)], how defects were formed during the domain inversion process [Figure 12(c)], and how the neighboring domains merge to form a bigger one [Figure 12(d)]. Revealing these details is essential for a full understanding of domain inversion and growth processes. This is also very useful for improving the quality of

ferroelectric domain patterns, which is critical for a wide range of future applications.

domain structures for advanced photonic applications.

Acknowledgements

We have investigated the nonlinear optical interactions that are strongly dependent on the existence of ferroelectric domain walls, i.e., the spatial variation of the second-order nonlinear coefficient In particular, we have discussed the so-called nonlinear Čerenkov radiation focusing on two special cases including the signal generation from a single and multiple ferroelectric domain wall(s). We have shown that the localized spatial change of nonlinearity constitutes a sufficient condition for strong Čerenkov second harmonic generation. The emitted Čerenkov signals arising from multiple walls can interfere with each other, resulting in the strong dependence of the strength of the overall Čerenkov beams on the wavelengths. Furthermore, the emission from regular periodic domain pattern gives rise to another type of nonlinear interaction, namely, the nonlinear Raman-Nath diffraction. We have derived analytical formulas that govern the emission process and discussed factors that influence the strength of the nonlinear diffraction, including the duty cycle, thickness of the crystal, randomness in domain size, as well as the beam width and wavelength of the fundamental wave. We also utilized the effect of Čerenkov second harmonic generation from a single-domain wall for direct 3D imaging of the antiparallel domains in ferroelectric crystals with sub-diffraction limit resolution. Our studies are important for a better understanding of nonlinear diffraction from ferroelectric domain structures. The nonlinear optical microscopy forms a very powerful tool that will further inspire the design and development of new and sophisticated ferroelectric

The authors thank the Australian Research Council and Qatar National Research Fund (Grant No. NPRP 8-246-1-060) for financial supports. Mr. Xin Chen thanks China Scholarship Council (PhD Scholarship No. 201306750005). The authors thank Dr. Vito Roppo, Dr. Ksawery There is no conflict of interest for this work.
