Quantifying the coherent interaction length of second-harmonic microscopy in lithium niobate confined nanostructures

Thin-film lithium niobate (TFLN) in the form of x- or z-cut lithium-niobate-on-insulator has attracted considerable interest as a very promising and novel platform for developing integrated optoelectronic (nano)devices and exploring fundamental research. Here, we investigate the coherent interaction length lc of optical second-harmonic generation (SHG) microscopy in such samples, that are purposely prepared into a wedge shape, in order to elegantly tune the geometrical confinement from bulk thicknesses down to approximately 50 nm. SHG microscopy is a very powerful and non-invasive tool for the investigation of structural properties in the biological and solid-state sciences, especially for visualizing and analyzing ferroelectric domains and domain walls. However, unlike in bulk lithium niobate (LN), SHG microscopy in TFLN is impacted by interfacial reflections and resonant enhancement, both of which rely on film thickness and substrate material. In this paper, we show that the dominant SHG contribution measured on TFLN in backreflection is the co-propagating phase-matched SHG signal and not the counter-propagating SHG portion as is the case for bulk LN samples. Moreover, lc depends on the incident pump laser wavelength (sample dispersion) but also on the numerical aperture of the focussing objective in use. These experimental findings on x- and z-cut TFLN are excellently backed up by our advanced numerical simulations.