通过模式耦合理论, 建立了基于长周期光纤光栅(LPFG)的二层圆光波导模型; 结合传输矩阵法, 仿真得到了外部介质折射率呈线性分布情况下LPFG的透射谱。仿真结果表明: 该结构下的LPFG透射谱特性强烈依赖于外部介质折射率梯度, 当外部介质折射率梯度升高, 透射谱的损耗峰深度逐渐降低, 损耗峰3dB带宽逐渐增加, 且增加量与折射率梯度的增加量呈较好的线性关系; 当外部折射率梯度由1.111 1×10-7 riu/mm增加到1.111 1×10-5 riu/mm时, 其梯度灵敏度可达到2.2×107 nm·mm/riu。这一结果使折射率梯度的高灵敏度测量成为可能, 为设计和制作基于LPFG的折射率梯度传感器提供了一定的理论依据,并有望用于生化反应中微小尺度下折射率呈梯度分布的液相介质的测量。

A two-layer circle waveguide model based on Long-period Fiber Gratings(LPFG)was established according to the coupling theory. The transmission spectrum of a LPFG in external media with linear Refractive Index(RI) gradient distribution was obtained by using the transfer matrix method. Simulation results show that the transmission spectral characteristics of the LPFG are strongly dependent on the RI gradient distribution of external media. When the RI gradient of external media increases, the loss depth of the transmission spectrum decreases, the 3dB bandwidth increases, and there is a good linear relationship between bandwidth and RI gradient increment. When the RI gradient of external media increases from 1.1111 × 10-7 riu/mm to 1.111 1 × 10-5 riu/mm, the gradient sensitivity can reach 2.2×107 nm·mm/riu. This result allows the high sensitivity measurement of refractive index gradient to become possible, and provides a theoretical basis for the design and production of the RI gradient sensors based on LPFGs. It may be potentially suitable for application to the measurement of biochemical reactions in the small scale liquid refractive index(RI) gradient distribution.