The Poynting vector plays a key role in electrodynamics as it is directly related to the power and the momentum carried by an electromagnetic wave. Based on the Lorenz-Mie theory, we report on the focusing effect of a spherical particle-lens by properly analysing the Poynting vector maps. Conventional two-dimensional (2D) maps showing Poynting vector magnitude and direction in a given plane cannot deliver information on three-dimensional (3D) directivity and vectorisation in key regions of singularities, such as vortexes and saddle points, due to poor expressiveness. In this article, an analytical 3D mapping technology is utilised to track the field-features passing through the singularities of the distribution of the Poynting vector in a spherically dielectric mesoscale particle-lens. We discovered that the spheres with the certain size parameters can stimulate extremely large field-intensity at singularities and then form two circular hotspots around the sphere poles. An astonishing large ‘heart-shape’ 3D Poynting vector circulation, which cannot be predicted by conventional 2D mapping analysis, is found to provide a great angular variation within an enormous range in these spheres. We anticipate that this effect will contribute to the field-enhancement phenomena, such as surface enhances Raman scattering, surface enhances absorption, super-resolution imaging and others.
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