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Negative experimental evidence for magneto-orbital dichroism - supplemental information

A light beam can carry both spin angular momentum (SAM) and orbital angular momentum (OAM). SAM is commonly evidenced by circular dichroism (CD) experiments {\em i. e.} differential absorption of left and right-handed circularly polarized light. Recent experiments, supported by theoretical work, indicate that the corresponding effect with OAM instead of SAM is not observed in chiral matter. Isotropic materials can show CD when subjected to a magnetic field (MCD). In Ref. ~\onlinecite{Mathevet2012} we report a set of experiments, under well defined conditions, searching for magnetic orbital dichroism (MOD), differential absorption of light as a function of the sign of its OAM. We experimentally demonstrate that this effect, if any, is smaller than a few $10^{-4}$ of MCD for the Nd:YAG $^4I_{9/2}\rightarrow^4F_{5/2}$ transition. This transition is essentially of electric dipole nature. We give an intuitive argument suggesting that the lowest order of light matter interaction leading to MOD is the electric quadrupole term. We give here more experimental details and extra measurements.