Dispersion relation reflects the dependence of wave frequency on its wave vector when the wave passes through certain material. It demonstrates the properties of this material and thus it is critical. However, dispersion relation reconstruction is very time consuming and expensive. To address this bottleneck, we propose in this paper an efficient dispersion relation reconstruction scheme based on global polynomial interpolation for the approximation of 2D photonic band functions. Our method relies on the fact that the band functions are piecewise analytic with respect to the wave vector in the first Brillouin zone. We utilize suitable sampling points in the first Brillouin zone at which we solve the eigenvalue problem involved in the band function calculation, and then employ Lagrange interpolation to approximate the band functions on the whole first Brillouin zone. Numerical results show that our proposed methods can significantly improve the computational efficiency.

翻译：色散关系反映了波通过特定材料时其频率与波矢之间的依赖关系，它揭示了材料的特性，因此至关重要。然而，色散关系重建非常耗时且昂贵。为解决这一瓶颈，本文提出了一种基于全局多项式插值的二维光子带函数高效重建方案。该方法基于带函数在第一布里渊区中关于波矢分段解析的特性。我们在第一布里渊区中选择合适的采样点，求解带函数计算中涉及的特征值问题，然后利用拉格朗日插值在整个第一布里渊区上逼近带函数。数值结果表明，所提方法能显著提高计算效率。