  We present the classical electromagnetic theory framework of reflection of a
light beam carrying Orbital Angular Momentum (OAM) by an in-plane magnetic
structure with generic symmetry. Depending on the magnetization symmetry, we
find a change in the OAM content of the reflected beam due to magneto-optic
interaction and an asymmetric far-field intensity profile. This leads to three
types of Magnetic Helicoidal Dichroism (MHD), observed when switching the OAM
of the incoming beam, the magnetization sign, or both. In cases of sufficient
symmetries, we establish analytical formulas which link an experimentally
accessible MHD signal up to $10\%$ to the Magneto-Optical Kerr Effect (MOKE)
constants. Magnetic vortices are particularly enlightening and promising
targets, for which we explore the implications of our theory in the joint
publication XX XXX XXXXXX.
