AI 中文总结
研究了复矢量场\(E\)代表的傍轴光学高斯光束的手性连通性，通过双参数族说明其在参数平面除原点外处处手性，绕原点一周手性反转两次且非非手性，分析了与手性相关的矢量和标量性质及度量变化，指出平面场与三维场手性情况。
AI 中文摘要
手性连通性描述了手性结构在从不处于非手性状态的情况下平滑转变为其镜像的情况。用一个表示傍轴光学高斯光束的复矢量场\(E\)的双参数族来说明这一现象。除原点外，\(E\)在参数平面处处是手性的。在绕原点一周的过程中，\(E\)手性反转两次且不处于非手性状态。手性的不同方面与\(E\)的矢量和标量性质相关；它们各自的自然度量及其组合在\(E\)为手性的参数值处改变符号。平面场\(E\)的分析更简单，但考虑三维细节时其手性基本相同。
英文摘要
Chiral connectedness describes chiral structures that transform smoothly into their mirror images while never being achiral. The phenomenon is illustrated with a two-parameter family of complex vector fields E representing paraxial optical Gaussian beams. E is chiral everywhere in the parameter plane except the origin. During a circuit of the origin, E reverses chirality twice without being achiral. Different aspects of chirality are associated with the vector and scalar nature of E; natural measures of each, and their combinations, change sign at parameter values where E is chiral. The analysis is simpler for planar fields E, but their chiralities are essentially the same when the subtleties of three dimensions are included.
Comments13 pages, 1 figure, in press in J. Phys. A: Math. Theor
Journal refJ. Phys. A: Math. Theor. 59, 365202 (2026)
