1：Experimental Design and Method Selection:

The study utilized COMSOL Multiphysics

2：3a simulation software to model a clamped circular graphene membrane under vacuum conditions. The simulation coupled the 'Solid mechanics' module (for deformation sensing) and 'Solid heat transfer' module (for thermal effects) to analyze opto-thermal actuation and resonance characteristics. A 'Swept mesh' was used for element distribution in the thickness direction, and studies included 'Steady state study' and 'Eigen frequency study' to determine resonance behaviors. Sample Selection and Data Sources:

The simulated structure was a clamped circular graphene membrane with parameters such as diameter (50 μm), thickness (

3：35 nm for 10 layers), density (2208 kg/m3), Young's modulus (1 TPa), Poisson's ratio (41), and thermal conductivity (5300 W/(m·K)). Data were generated through parametric sweeps of radius (10–30 μm), thickness (335–35 nm), prestress (103 to 101? Pa), laser output power (1–10 mW), and light spot radius (5–25 μm). List of Experimental Equipment and Materials:

The setup included an optical fiber Fabry-Perot resonant probe with a graphene diaphragm, a distributed feedback (DFB) laser S (wavelength

4：12 nm), an electro-optic modulator (EOM), a lock-in amplifier (HL2FI), an erbium-doped fiber amplifier (EDFA), another DFB laser R (wavelength 72 nm), a 2×1 coupler, a circulator, an optical filter, and a photoelectric detector (PD) with bandwidth 200 MHz and conversion gain 4×10? V/W. An optical spectrum analyzer (AQ6370C, Yokogawa Electric Corporation) was used to confirm cavity length. Experimental Procedures and Operational Workflow:

15 The laser S was modulated by EOM to impose thermal excitation on the graphene membrane, with amplified signals coupled through a 2×1 coupler and delivered to the F-P cavity via a circulator. The detection signal from laser R was filtered and sent to a lock-in amplifier through the PD for resonance signal processing. Simulation involved assigning a Gaussian-distributed heat source based on absorbed heat equations, with temperature and resonance frequency analyzed under varying parameters.

5：Data Analysis Methods:

Data were analyzed using COMSOL simulation outputs, with curve fitting (e.g., linear and polynomial fits) to evaluate relationships between parameters (e.g., temperature vs. radius, frequency vs. prestress). Correlation coefficients and relative errors were calculated to assess fit quality.