Polar domain walls are currently at the focus of intensive research owing to their unusual and highly localized functional properties, which bear great potential for technological applications. They can present unusual topological features, like swirling polar structures or defect lines. The prediction of possible non-Ising and chiral internal structures of polar domain walls has been a particularly important development in this topic over the past years. This Tutorial highlights the capabilities of non-linear optics to probe these newly discovered aspects in polar non-Ising type domain walls through the second-harmonic generation (SHG) process. Fundamental symmetry properties of domain walls are presented in the context of recent advances on chiral and abnormal polar structures. We introduce the basics of the SHG and its ability to probe the symmetry down to the nanoscale, and we explain how to obtain insight into the non-Ising character of polar domain walls by combining the SHG polarimetry analysis with modeling.

Non-Ising polar domain walls have recently emerged as individual two-dimensional materials exhibiting localized nonlinear optical emission. The analysis of this emitted light often requires focusing with high apertures. As a result, the vectorial properties of light come into play. This study provides an analytic treatment of the vector light fields’ effect on the polarized second-harmonic emission (SHG) arising at polar domain walls. While confined optical fields are expected to alter the SHG polarization response, we identify extrinsic and intrinsic properties capable of canceling focusing effects. We determine a precise combination of the fundamental wave polarization and orientation of the domain walls at which focusing effects are negligible. Furthermore, the perimeter defined by the domain walls intrinsic optical parameters below which focusing effects are negligible is extracted from a systematic focus-dependent analysis. Our study provides the necessary methodology and precautions to probe the internal structure of non-Ising domain walls with confined optical fields, and it can be extended to explore newly discovered ferroelectric topologic nanostructures.

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