Analytical Solution of an Induced Fiber Grating Relative Humidity Sensor

In our previous work, a distributed moisture sensor based on the induced long-period fiber grating in the presence of moisture is proposed. The proposed structure is analyzed numerically (Opt Laser Technol 117:126–133, 2019). In this article, due to the axial symmetry and periodic structure of the proposed sensor, the Love’s potential and Fourier series are employed to obtain an analytical solution for the refractive index variation along the sensor versus moisture density. The analytical method reduces the computation time relative to our numerical calculation drastically. The analytical results are in good agreement with those that are obtained by numerical calculations. The analytical method is employed for the analysis and design of distributed moisture fiber sensor.