  Understanding the mechanisms and spatial correlations of crystallographic
symmetry breaking in ferroelectric materials is essential to tuning their
functional properties. While optical second harmonic generation (SHG) has long
been utilized in ferroelectric studies, its capability for probing complex
polar materials has yet to be fully realized. Here, we develop a SHG spectral
imaging method implemented on a home-designed laser-scanning SHG microscope,
and demonstrate its application for a model system of (K,Na)NbO3 single
crystals. Supervised model fitting analysis produces comprehensive information
about the polarization vector orientations and relative fractions of
constituent domain variants as well as their thermal evolution across the
polymorphic phase transitions. We observe an unexpected persistence of the
orthorhombic phase at low temperatures, pointing to the phase competitions.
Besides, we show that unsupervised matrix decomposition analysis can quickly
and faithfully reveal domain configurations without a priori knowledge about
specific material systems. The SHG spectral imaging method can be readily
extended to other ferroelectric materials with potentials to be further
enhanced.
