In layered media, the solution of the Maxwell equations has discontinuity of the derivative or the function itself at media interfaces. For the first time, finite-difference schemes providing convergence for discontinuous solutions across straight media interfaces are proposed for the one-dimensional formulation of the Maxwell equations. These are bicompact conservative schemes. They are two-point and layer boundaries are taken as mesh nodes. The scheme explicitly accounts for physically correct interface conditions at media interfaces. We propose an essentially new technique which accounts for medium dispersion. All these features provide the second order of accuracy even on discontinuous solutions. Calculation examples, which illustrate these results, are given. The proposed method is verified by comparison with a previously performed experiment on propagation of normally incident plane wave on one-dimensional photonic crystal. Calculated spectrum agrees well with the measured one within experimental error of 2-5%.

在分层介质中，麦克斯韦方程的解在介质界面处具有导数或函数本身的不连续性。第一次，为麦克斯韦方程的一维公式提出了为跨直接介质界面的不连续解提供收敛的有限差分方案。这些是双紧保守方案。它们是两点，层边界作为网格节点。该方案明确说明了媒体接口处物理上正确的接口条件。我们提出了一种基本的新技术来解释介质色散。所有这些功能即使在不连续的解决方案上也提供二阶精度。给出了说明这些结果的计算示例。通过与先前进行的垂直入射平面波在一维光子晶体上传播的实验进行比较，验证了所提出的方法。计算光谱与实测光谱吻合良好，实验误差为 2-5%。