  Polarization-dependent photon spectroscopy (dichroism) of the second-harmonic
generation (SHG) response is shown to reveal chiral and magnetic properties of
a sample. Two dichroic signals are allowed with electric-dipole (E1) and
electric-quadrupole (E2) scattering events, and both require circular
polarization in the primary beam. Explicit expressions for electronic
multipoles, which benefit from equivalent electronic operators, in NCD and MCD
of the SHG response are derived using theoretical techniques from atomic
physics.
