This study presents a theoretical model that enables a fast and precise calculation of a sampled apodized fiber Bragg grating and the related sensor. Transfer matrix method was used since there is no analytical solution due to the complex refractive index profile. Errors brought by the uniform refractive index profile approximation were compensated, which allows a smaller number of divided segments and therefore a fast and memory efficient simulation. This compensation method realizes a high speed and high precision simulation. The theoretical spectra of both the grating and the sensor agrees well with those given by the experiments. According to the experiment, the sensitivity of the moisture sensor is-0.6165 pm/ppm in mineral oil. This theoretical model provides a new choice for the researchers and developers to design and optimize the sensing structure instead of a blind try and error process.
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