从任意解基中显式构造Floquet-布洛赫态
Explicit Construction of Floquet-Bloch States from Arbitrary Solution Bases of the Hill Equation
AI总结：
本文提出从任意线性无关解对直接构造Floquet-布洛赫态的方法，通过单调矩阵将任意基映射到对应的布洛赫基，适用于一维光子晶体，无需规范归一化解。
摘要：
对于描述一维周期系统的一阶方程，本文开发了一种构造性方法，直接从任意线性无关解对生成Floquet-布洛赫态。一维光子晶体作为具体示例，显式闭合公式通过单调矩阵将任意基映射到对应的Floquet-布洛赫基，包括通用的Jordan带边情况，无需依赖规范归一化解。该构造可直接用转移矩阵表达，使残余表示自由度透明，并提供了一个适用于分析和数值研究周期系统的方法框架。
英文摘要：
For the Hill equation describing one-dimensional periodic systems, a constructive formulation is developed for generating Floquet-Bloch states directly from arbitrary pairs of linearly independent solutions. One-dimensional photonic crystals are used as a concrete illustration. Explicit closed-form formulas map an arbitrary fundamental system to the corresponding Floquet-Bloch basis via the monodromy matrix, including the generic Jordan band-edge case, without reliance on canonically normalized solutions. The construction can be expressed directly in terms of the transfer matrix, making the residual representation freedom transparent and providing an implementation-ready framework for analytical and numerical studies of periodic systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
