  The optical conductivity [$\sigma(\omega)$] spectra of alkaline-earth-filled
skutterudites with the chemical formula $A^{2+}M_{4}$Sb$_{12}$ ($A$ = Sr, Ba,
$M$ = Fe, Ru, Os) and a reference material La$^{3+}$Fe$_{4}$Sb$_{12}$ were
obtained and compared with the corresponding band structure calculations and
with calculated $\sigma(\omega)$ spectra to investigate their electronic
structures. At high temperatures, the energy of the plasma edge decreased with
the increasing valence of the guest atoms $A$ in the Fe$_{4}$Sb$_{12}$ cage
indicating hole-type conduction. A narrow peak with a pseudogap of 25 meV was
observed in SrFe$_{4}$Sb$_{12}$, while the corresponding peak were located at
200 and 100 meV in the Ru- and Os-counterparts, respectively. The order of the
peak energy in these compounds is consistent with the thermodynamical
properties in which the Os-compound is located between the Fe- and
Ru-compounds. This indicated that the electronic structure observed in the
infrared $\sigma(\omega)$ spectra directly affects the thermodynamical
properties. The band structure calculation implies the different electronic
structure among these compounds originates from the different $d$ states of the
$M$ ions.
