A theoretical model for small-area transverse force measurement based on linearly chirped fiber Bragg grating

When a linearly chirped fiber Bragg grating is subjected to transverse force, there will be some axial extension in the applied area. If the area is the same order of magnitude as the fiber diameter, the influence of the axial expansion cannot be neglected that an extra phase shift is produced in the structure of the grating. The transmission peak of new corresponding spectral is closely related with the location of the phase shift. We consider also the birefringence in the applied area of the grating with transverse force. In this study, based on the mechanical analysis of space elasticity, we present a theoretical sensing model of transverse force in small area by measuring the polarization dependent loss. The results show that the force is exponentially related to the transmission coefficient and linearly related to the peak value of the polarization dependent loss. The peak wavelength of the polarization dependent loss spectrum corresponds to the location and the magnitude of the transverse force. Therefore, we can measure and locate the transverse force with small applied area. In practical applications, the sensitivity of the transverse force measurement can be enhanced effectively by fixing the length of the forced region during packaging. And it can be connected in series forming a transverse force sensor network to locate the sensing position accurately.