  The quasi-one-dimensional spin ladder compounds, BaFe$_2$S$_3$ and
BaFe$_2$Se$_3$, are investigated by infrared spectroscopy and density
functional theory (DFT) calculations. We observe strong anisotropic electronic
properties and an optical gap in the leg direction that is gradually filled
above the antiferromagnetic (afm) ordering temperature, turning the systems
into a metallic phase. Combining the optical data with the DFT calculations we
associate the optical gap feature with the $p$-$d$ transition that appears only
in the afm ordered state. Hence, the insulating ground state along the leg
direction is attributed to Slater physics rather than Mott-type correlations.
