Hidden Symmetry and Invariance in Optical Forces

Like any physical quantity whose symmetry properties mimic its source, the optical force acting on a neutral spherical particle has a symmetry that mimics the incident field. The optical force consists of the gradient force and the scattering force. Here, we explicitly show that in optical lattices, the in-plane gradient force and scattering force have additional even and odd symmetries upon 2N-fold rotation, respectively, which are not shared by the incident field that is N-fold discrete rotationally symmetric. Similar hidden symmetries, namely, even and odd symmetries upon reflection about the focal plane, are also found in particles illuminated by a Gaussian beam, suggesting that it is a general property of the optical force. These are verified numerically in multiple examples and analytically for three incident plane waves, by which we also discover that the profiles of the gradient force and the scattering force are invariant with respect to material composition and particle size for a spherical particle. As such, one can tune the polarization to almost completely "turn off' either gradient force or scattering force, leaving behind a purely irrotational or solenoidal force field, opening a new freedom to control the conservativeness of optical forces.