In this study, we used differential geometry to develop an effective field theory to study the behavior of light propagation in distorted photonic crystals (DPCs) of averagely homogeneous refractive index media. To study the light-ray trajectories in DPCs, we derived a geodesic equation based on the principle of least action by defining the metric tensor in terms of the lattice-position distortion. The geodesic equation implies that the lattice-position distortion can curve the trajectory. We present multiple exact solutions for the trajectory for simple distortion under the condition of having the same values of the lattice point filling factor at each unit cell. These solutions explicitly demonstrate that the light is only bent through the introduction of lattice distortion, and that these results are consistent with the finite-difference time-domain simulation results.

中文翻译：

---

畸变光子晶体的有效场论

在这项研究中，我们使用微分几何发展了一种有效的场理论来研究光在平均均匀折射率介质的畸变光子晶体 (DPC) 中的传播行为。为了研究 DPC 中的光线轨迹，我们通过根据晶格位置失真定义度量张量，基于最小作用量原理推导出测地线方程。测地线方程意味着晶格位置失真可以使轨迹弯曲。在每个晶胞的格点填充因子值相同的情况下，我们为简单失真的轨迹提出了多种精确解。这些解决方案明确地表明光只是通过引入晶格畸变而弯曲，