Abstract
We design and generate the bipolar-variant spin angular momentum (SAM) carried by vector optical field and theoretically investigate the evolution of the bipolar-variant SAM in the tight focusing process. It is found that the longitudinal SAM density annihilates and the purely transverse SAM density appears in the focal plane, and the evolution of the complex singularities of SAM into $V$-point singularities is also studied. We further extend the study to general bipolar-variant SAM, and give the theoretical explanation of the annihilation and appearance of different components of SAM density. We believe the presentation of the bipolar-variant SAM can greatly enrich the study of SAM as well as the singular optics. Meanwhile, the evolution of the bipolar-variant SAM in the focusing process is interesting and important in revealing the focal properties of SAM of the photon, and the purely transverse SAM in the focal plane with a spin axis orthogonal to the propagation direction opens up avenues in optical trapping and manipulation, especially for optically induced rotations.
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