  The first-principles calculations of the electronic structures and the
interband optical conductivity (OC) spectra have been performed for the
stoichiometric Fe$_{2}$MnGa alloy with L2$_{1}$ and L1$_{2}$ types of atomic
ordering. The calculated optical properties of Fe$_{2}$MnGa alloy for the
L2$_{1}$ and L1$_{2}$ phases are complemented by the experimental OC spectra
for bulk and thin film Fe-Mn-Ga alloy samples near the stoichiometry 2:1:1 with
L2$_{1}$ and L1$_{2}$ (for bulks) as well as the body-centered-cubic and
face-centered-cubic (for films) structures, respectively. A reasonable
agreement between experimental and calculated interband OC spectra was obtained
for both phases of the alloy. The experimental data show no significant
difference in the OC spectra with respect to the degrees of atomic and magnetic
orders of the samples.
