基于模式耦合理论, 采用基于光纤布拉格光栅(FBG)的二层圆光波导模型, 通过转移矩阵法实现数值仿真得到升余弦变迹FBG在几种典型非均匀温度场下的反射谱。处于非均匀温度场下的FBG其纤芯、包层的有效折射率及光栅周期都会发生非均匀变化, 因此其反射谱结构也会发生相应变化。仿真结果表明: 非均匀温度场中升余弦变迹FBG反射谱与其温度梯度系数ΔTmax有很大关系, 与均匀温度分布相比, 其反射率明显下降, 反射带宽明显展宽, 反射峰出现分裂以至振荡; 最大反射率随ΔTmax的增加呈非线性减小, 其对应波长与温度梯度系数ΔTmax成正比, 且不同的温度场对应不同的变化率, 如线性温度场中其变化率约为0.004nm/℃, 中心对称二次方分布温度场中变化率为0.0065nm/℃。研究结果对于升余弦变迹FBG实现非均匀温度场的测量有重要意义。

Based on the theory of mode coupling, using a two-layer circular waveguide model, the reflection spectra of raised cosine apodized FBG under several typical non-uniform temperature fields were obtained by using transfer matrix method. Under non-uniform temperature field, the effective refractive index of core and cladding of FBG will present inhomogeneous change. Therefore, the response of FBG reflective spectrum will change accordingly. Simulation results show that the reflection spectrum of raised cosine apodized FBG in non-uniform temperature field is closely related to the temperature gradient coefficient ΔTmax, compared with the case of the uniform temperature distribution, its reflectivity decreases obviously and the reflection bandwidth is significantly broadened, and the reflection peak shows splitting even oscillation. Maximum reflectance decreases non-linearly with increasing temperature gradient coefficient which is proportional to the corresponding wavelength, and different temperature fields have different change rates, as the change rate is 0.004nm/℃ and 0.0065nm/℃ in linear temperature field and centrosymmetric quadratic temperature field, respectively.