Université Paris-Saclay, CEA, CNRS, LIDYL, Gif-sur-Yvette 91191, France.
Grupo de Investigación en Aplicaciones del Láser y Fotónica, Departamento de Física Aplicada, University of Salamanca, Salamanca E-37008, Spain.
Sci Adv. 2023 Mar 24;9(12):eadf3486. doi: 10.1126/sciadv.adf3486.
Symmetries and conservation laws of energy, linear momentum, and angular momentum play a central role in nonlinear optics. Recently, paraxial light fields with nontrivial topology have been attracting a keen interest. Despite not being eigenstates of the orbital and spin angular momenta (OAM and SAM), they are eigenstates of the generalized angular momentum (GAM) operator-a mixture of the OAM and SAM operators with fractional eigenvalues. By driving high harmonic generation with a polarization Möbius strip carrying a half-integer GAM charge and implementing angular momentum characterization methods in the extreme ultraviolet range, we demonstrate the linear scaling of the GAM with the harmonic order, each harmonic carrying a precise half-integer GAM charge. Our work shows that beyond SAM and OAM, the GAM is, in some situations, an appropriate quantum number. It paves the way for finer manipulations and applications of light beams containing fractional-order polarization singularities.
对称性和能量、线性动量以及角动量守恒定律在非线性光学中起着核心作用。最近，具有非平凡拓扑的傍轴光场引起了人们的浓厚兴趣。尽管它们不是轨道角动量（OAM）和自旋角动量（SAM）本征态，但它们是广义角动量（GAM）算子的本征态——OAM 和 SAM 算子与分数本征值的混合。通过用携带半整数 GAM 电荷的极化 Möbius 带驱动高次谐波产生，并在极紫外范围内实施角动量特征化方法，我们证明了 GAM 与谐波阶数的线性比例关系，每个谐波携带精确的半整数 GAM 电荷。我们的工作表明，除了 SAM 和 OAM 之外，在某些情况下，GAM 是一个合适的量子数。它为更精细地操纵和应用包含分数阶偏振奇点的光束铺平了道路。
