Thin film lithium niobate is of great recent interest and an understanding of periodically poled thin-films is crucial for both fundamental physics and device developments. Second-harmonic (SH) microscopy allows for the non-invasive visualization and analysis of ferroelectric domain structures and walls. While the technique is well understood in bulk lithium niobate, SH microscopy in thin films is largely influenced by interfacial reflections and resonant enhancements, which depend on film thicknesses and the substrate materials. We present a comprehensive analysis of SH microscopy in x-cut lithium niobate thin films, based on a full three dimensional focus calculations, and accounting for interface reflections. We show that the dominant signal in back-reflection originates from a co-propagating phase-matched process observed through reflections, rather than direct detection of the counter-propagating signal as in bulk samples. We can explain the observation of domain structures in the thin film geometry, and in particular, we show that the SH signal from thin poled films allows to unambiguously distinguish areas, which are completely or only partly inverted in depth.
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