The appearance and annihilation of the spin angular momentum for the multi-polar vector optical field in the focal plane

Abstract

Vector optical fields (VOFs) with space-variant polarizations have attracted great attention in various areas, and the VOFs have been applied to study the spin angular momentum (SAM) of the photon, leading to many new effects and applications. Here, we propose the multi-polar coordinate and design and generate the multi-polar VOF (MP-VOF) with an arbitrary even number of singularities. We further find that the SAM appears or annihilates in the focal plane, which means the processes of “0-1” and “1-0” of the SAM can be accomplished in propagation. The corresponding theoretical explanation is also provided, indicating that the SAM appears or annihilates due to the interaction of the fields at central symmetric positions on the wavefront. Moreover, the appearance of transverse SAM (also known as the “photonic wheel”) can also be achieved in tight focusing cases. In this way, we can achieve three cases of SAM under different conditions, including purely longitudinal SAM, purely transverse SAM, and three-dimensional SAM with both components. This new kind of MP-VOF significantly enriches the family of VOFs and provides new insights in studying the focal behavior of the SAM, which can be applied in realms such as spin absorbing particles in a more flexible way.