Extraordinary spin density and energy back-flow under interference.

A novel phenomenon was reported recently that the "local optical spin density" based on the Poynting vector might be counter-intuitively opposite to the integrated spin orientation while the one related to the gauge-invariant canonical expression might not [Phys. Lett. B779, 385 (2018)]. However, the "local optical spin density" of the gauge-invariant canonical expression can also be counter-intuitively opposite to the integrated spin orientation under the interference of plane waves, even if all of the plane waves possess the same polarization state. Moreover, the interference fields might acquire a transverse spin density (perpendicular to the propagation plane), which can have more well-controlled relations with the polarization. Additionally, the Poynting vector shows counter-intuitive back-flow and a circular motion (vortex) in the propagation plane locally, which implies a transverse local "orbital" angular momentum density related to the polarization.