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.

本研究提出了一个理论模型，可以快速准确地计算采样的切趾光纤布拉格光栅和相关传感器。由于复数折射率分布没有解析解，因此使用了传递矩阵方法。由均匀折射率分布近似带来的误差得到补偿，这允许较少数量的分割段，从而实现快速且内存高效的模拟。这种补偿方法实现了高速、高精度的模拟。光栅和传感器的理论光谱与实验给出的光谱非常吻合。根据实验，水分传感器在矿物油中的灵敏度为-0.6165 pm/ppm。