论文标题
几何阶段的波描述
Wave description of geometric phase
论文作者
论文摘要
自从Pancharatnam 1956年发现光学几何阶段以及Berry在量子系统中发现几何阶段的发现以来，分析几何阶段的研究人员几乎只专注于使用Jones Colculus或使用POINCARéSphere的球形三角学方法的代数方法。前者的抽象数学以及后者的抽象几何形状掩盖了产生几何阶段的物理机制。我们表明，光学几何阶段完全源自波的叠加和波浪最大位置的偏移。基于波浪的模型提供了一种可视化几何阶段的方法，如何由波之间的关系以及光学元素引起的转换。我们还通过自身的几何阶段与干涉图展示的相之间的关系得出了关系，并提供了两者相互匹配的条件。
Since Pancharatnam's 1956 discovery of optical geometric phase, and Berry's 1984 discovery of geometric phase in quantum systems, researchers analyzing geometric phase have focused almost exclusively on algebraic approaches using the Jones calculus, or on spherical trigonometry approaches using the Poincaré sphere. The abstracted mathematics of the former, and the abstracted geometry of the latter, obscure the physical mechanism that generates geometric phase. We show that optical geometric phase derives entirely from the superposition of waves and the resulting shift in the location of the wave maximum. This wave-based model provides a way to visualize how geometric phase arises from relationships between waves, and from the transformations induced by optical elements. We also derive the relationship between the geometric phase of a wave by itself and the phase exhibited by an interferogram, and provide the conditions under which the two match one another.
