Curvature and Angle Sensor Based on LP21 Mode Reflected by a Four-Mode Fiber Bragg Grating

A fiber curvature and angle sensor based on LP21 mode reflected by a fiber Bragg grating (FBG) inscribed in a four modes fiber (FMF) has been developed. Modal coupling efficiency was calculated as a function of curvature radius, and LP21-LP01 coupling was revealed to be more sensitive to fiber bending compared with LP11-LP01 and LP02-LP01 coupling. Simulation analysis of mode electric field distribution in a bent FMF demonstrated that modal coupling efficiency was consistent with an overlapping integral, i.e., an overlapping area between the two involved modes. A verification experiment was carried out and the signal intensity of LP21-LP01 coupling first decreased and then increased during bending, keeping consistent with the calculation results. The sensitivity is −46.13 and 38.15 dB/
$\text{m}^{-{1}}$
in the curvature range of 3.96–4.20 and 4.26–4.49
$\text{m}^{-{1}}$
, respectively. The sensor also brings about an angle sensitivity with a maximum difference of 12.03 dB in the angle of
$0- 2\pi $
. Due to the simple structure, ease of fabrication, and reliable response performance, the proposed sensor is believed to have potential application prospects in curvature and angle detection fields.