**2. Materials and Methods**

The schematic experimental setup is shown in Figure 1, in which the structure of the LNOI sample used in our experiments is also clearly shown. The LNOI sample was composed of a 300-nm thick +Z-cut ion-sliced LiNbO3 thin film, a 100-nm thick Cr thin film, a 2-μm thick SiO2 layer, and a 500-μm thick LiNbO3 substrate, which were all layered or bonded to one another in sequence. The 100-nm thick Cr layer served as a bottom electrode when an AFM-tip voltage was applied on the top 300-nm thick LiNbO3 thin film. Here, different metals may be used as the bottom electrode and different metal-lithium-niobate interfaces may have an effect on the domain poling process, but this is not the main topic of the current paper and will not be explored here.

In the experiments, the top LiNbO3 film was poled directly by applying a DC voltage through an AFM conductive probe tip, contacting the film top surface with the Cr layer being grounded. The dot domains were written under the AFM-tip voltage step by step, and the stripe domain patterns were written using a raster lithography method with graphic templates. The reversed domain structures were characterized by using piezoresponse force microscope (PFM), a versatile and powerful method to image domain structures with nano-size features. The tip radius, *R*, and the resonance frequency, *fR*, of the pt-coated Si probe tip used in the experiments were *R* = 20 nm and *fR* = 100 kHz, respectively. All AFM and PFM experiments were carried out with an MFP-3D Infinity atomic force microscope (Asylum Research, Goleta, CA, USA).

**Figure 1.** Schematic diagram of nano-domain writing in lithium niobate film on insulators (LNOI) under an atomic force microscope (AFM)-tip voltage.

The thermal heat treatments, including the post-poling annealing treatment after the domain writing process and the pre-heat treatment with the virgin LNOI sample without domain structure, were carried out by using an electric drying oven. The sample was heated to a temperature ranging from 90 ◦C to 210 ◦C in air, with a heating rate of 5 ◦C/min from room temperature, and then maintained at the high temperature for a certain time. After that, the sample was moved out from the drying oven and cooled down naturally to room temperature in air with a cooling rate of ∼20 ◦C/min. Note that no oxidation or reduction effect was observed in lithium niobate thin films during the thermal annealing treatment at a temperature of the order of 100 ◦C.
