Goos-Hanchen位移数值求解及其在光学教学中的应用

Numerical simulation of Goos-Hanchen shift and its application in optics education

微纳光学中Goos-H?nchen位移是重要的现象,虽然通过稳相法可得其数值结果,但学生很难将求解过程与实际物理现象相联系.针对此问题,本文提出基于角谱理论计算光斑的空间分布及反射光斑与入射光斑之间的位移.由于稳相法适用于有限孔径平面波和傍轴高斯光束,为了与稳相法结果对比,本文以高斯光束入射至近零介电常数介质为例进行计算,相关数值计算步骤可推广至任意均匀各向同性介质、任意模式光束的计算,结果表明当入射角度远离临界角时数值计算与稳相法结果相符,但在临界角附近,稳相法结果中存在相位突变形成的极点,不符合实际情况,而数值结果能够更准确的描述高斯光束的偏移情况.本文提供了另一个角度来观察实际光束的Goos-H?nchen位移,可帮助学生加深对Goos-H?nchen位移的理解,了解稳相法适用条件及光束强度分布的变化.

In micro-nano optics,Goos-H?nchen (GH) shift is an important phenomenon.Stationary phase method is usually utilized to obtain the GH shift,but it is difficult for students to understand the underlying physical essence.In this paper,we study the GH shift from a novel perspective.Incident and reflected light field are calculated based on angular spectrum theory.GH shift can then be expressed by the spot shift before and after reflection.As the stationary phase method can only be applied to the finite-aperture plane wave and Gaussian beam,the incidence of Gaussian beam on an epsilon-near-zero material is numerically calculated for comparing with stationary phase method.The numerical procedure can be further applied in incidence of an arbitrary beam on an arbitrary material.It is shown that numerical results agree well with analytical results when the incident angle is far from the critical angle,but near the critical angle,the present numerical results can be used to describe the GH shift of Gaussian beam more accurately.The numerical approach can be used in the calculation of GH shift of various light beams.The work can be of help to understand the GH shift and the applicable condition of stationary phase method.