  The imaginary Poynting momentum (IPM) of light has been captivated an unusual
origin of optomechanical effects on dipolar magnetoelectric particles, but yet
observed in experiments. Here, we report, for the very first time, a whole
family of high-order IPM forces for not only magnetoelectric but also generic
Mie particles, assisted with their excited higher multipoles within. Such
optomechanical phenomena derive from a nonlinear contribution of the IPM to the
optical force, and can be remarkable even when the incident IPM is small. We
observe the high-order optomechanics in a structured light beam with
vortex-like IPM streamlines, which allows the low-order dipolar contribution to
be suppressed. Our results provide the first unambiguous evidence of the
ponderomotive nature of the IPM, expand the classification of optical forces
and open new possibilities for optical forces and micromanipulations.
