The optical forces of vortex arrays in two-dimensional photonic crystals and slabs

摘要

Applications of optical forces for particle trapping and manipulation would be greatly enhanced if the simultaneous generation of multiple trap sites could be realized "on-chip". We demonstrate that this may be possible through the exploitation of vortex arrays in hexagonal photonic crystals for a band 1 mode at the K point. Flux vortices whose existences are symmetry-required may be located using phasor geometry in the vanishing contrast limit. Direct solution of Maxwell's equations using the Finite Element Method (FEM), for high-dielectric-contrast 2D and 2D-slab geometries, validates the symmetry approach. Optical forces on particles much smaller than the wavelength of light have been calculated using the Lorentz force model, yielding optical gradient and radiation pressure terms. Interestingly, the complementary hexagonal symmetries appear to express optical force distributions of fundamentally different character. The high-index "pillar" geometry has trap sites at Wyckoff A positions for TE modes, while the low-index "hole" geometry has trap sites at Wyckoff B positions for TM modes. Only in the latter case do the trap sites co-locate with the flux vortices that may exert net rotational forces on finite particles. In the former case, the vorticity at a trap site is zero and the net optical force must be purely irrotational.