Theoretical Investigation of the Bending Sensing Characteristics for Four-core Fiber Bragg Grating

Bending characteristics of four-core optical fiber Bragg gratings(MCFBGs) according to bending curvature and bending direction is analyzed using coupled-mode theory and mechanics of materials in this paper. The simulated results show that, bending makes the resonant wavelength of the four-core MCFBGs shift, two FBGs that in the catercorner of square matrix cores have the same wavelength changes(Delta lambda(1) = Delta lambda(3), and Delta lambda(2) = Delta lambda(4)), but have the opposition direction of shift. The wavelength difference of two FBGs at the catercorner of the square matrix (Delta lambda(13) or Delta lambda(24)) is proportional to the bending curvature. The bending sensitivity of the wavelength difference (d(Delta lambda(13))/d rho or d(Delta lambda(24))/d rho) is changed with a different bend-directions. The orientation of the bending was determined by the arctangent of the ratio of the wavelength difference Delta lambda(13)/Delta lambda(21). The sensitivity of the wavelength difference between cores is twice to the sensitivity of the reflection Bragg wavelength changes.