1：Experimental Design and Method Selection:

The study used the full-vectorial finite-difference method to calculate the single-mode conditions, mode sizes, and optical power distribution of the PE channel waveguides. The FD-BPM was employed to simulate the M-ZI.

2：Sample Selection and Data Sources:

The material of the device studied was an x-cut LN thin film bonded to a SiO2 layer deposited on an LN-substrate.

3：List of Experimental Equipment and Materials:

The thicknesses of the LN thin film and the SiO2 layer were 0.5 μm and 2 μm, respectively. The structures were cladded with 2-μm-thick SiO2 layers after the PE waveguides and electrodes were fabricated.

4：5 μm and 2 μm, respectively. The structures were cladded with 2-μm-thick SiO2 layers after the PE waveguides and electrodes were fabricated. Experimental Procedures and Operational Workflow:

4. Experimental Procedures and Operational Workflow: The study involved simulating and analyzing a proton-exchanged E-O M-ZI modulator in an x-cut LNOI, including the investigation of single-mode conditions, bending losses, and propagation losses.

5：Data Analysis Methods:

The half-wave voltages were simulated using FD-BPM, and the overlap integral of the optical and electrostatic fields was calculated.