1：Experimental Design and Method Selection:

The study involved the theoretical investigation of mode characteristics of a fiber with different diameters to determine conditions for two-mode fiber. An on-line grating fabrication system was used to write TM-FBG arrays, which were then investigated for temperature and curvature sensing.

2：Sample Selection and Data Sources:

A fiber preform with a germanium-doped, photosensitive core was used for FBG inscription. The fiber had a diameter of 200 μm to support two transverse modes (LP01 and LP11).

3：1). List of Experimental Equipment and Materials:

3. List of Experimental Equipment and Materials: Equipment included an excimer laser operating at 193 nm wavelength, a phase mask, and a grating interrogator (LGI-100B, Sentek Instrument). Materials included a step-index fiber with a photosensitive core.

4：Experimental Procedures and Operational Workflow:

The TM-FBG array was written on-line during fiber drawing. Temperature and curvature sensing experiments were conducted using the fabricated TM-FBG array.

5：Data Analysis Methods:

The response to temperature and curvature was measured and analyzed. The system's performance for quasi-distributed temperature and curvature sensing was evaluated.