We investigate the photonic bandgap structure, soliton properties and their stability in a semilinear coupled system where one core has cubic–quintic nonlinearity and is equipped with a Bragg grating, while the other one is uniform and linear. The investigation reveals that three distinct bandgaps, namely the upper, lower and central gaps, exist in the model. It is shown that the model supports two disjoint soliton families which are designated as Type 1 and Type 2 solitons. The soliton families exist only in the upper and lower bandgaps and are separated by a boundary at which no soliton solutions exist. A systematic numerical stability analysis is performed. It is found that vast regions in both the upper and lower bandgaps exist where Type 1 solitons are stable. However, Type 2 solitons are found to be always unstable. The effects of system parameters such as group velocity mismatch between the cores, velocity of solitons, and the coupling coefficient on the stability of solitons are analysed.

我们研究了一个半线性耦合系统中的光子带隙结构，孤子性质及其稳定性，其中一个核具有立方五次非线性并且装有布拉格光栅，而另一个核则是均匀且线性的。调查表明，模型中存在三个不同的带隙，即上，下和中心间隙。结果表明，该模型支持两个不相交的孤子族，分别称为1型和2型孤子。孤子族仅存在于上下带隙中，并被不存在孤子解的边界所分隔。进行了系统的数值稳定性分析。发现在1型孤子稳定的上下带隙中都存在广阔的区域。但是，发现2型孤子总是不稳定的。