  In this study, we investigate the nonlinear optical phenomena emerging from
the interaction of vortex and vector beams with achiral nanoparticles or
nanostructures. We reveal the conditions under which linear or nonlinear
dichroism can be observed. Despite the achiral symmetry of the nanostructure,
the interplay between the symmetries of the vortex beam, the nanostructure, and
the crystalline lattice of the nanostructure material may result in circular
dichroism in the nonlinear regime. We derive a formula that describes the
conditions for the appearance of circular dichroism across a broad range of
scenarios, taking into account all the symmetries. Building on these findings,
we have determined the conditions for both linear and nonlinear dichroism when
illuminated by vector beams. We believe that this work provides important
insights that can enhance the design of chiral sensors and optical traps,
making them more versatile and effective.
