  First-principle study of bismuth-related oxygen-deficient centers
($=$Bi$\cdots$Ge$\equiv$, $=$Bi$\cdots$Si$\equiv$, and $=$Bi$\cdots$Bi$=$
oxygen vacancies) in Bi$_2$O$_3$-GeO$_2$, Bi$_2$O$_3$-SiO$_2$,
Bi$_2$O$_3$-Al$_2$O$_3$-GeO$_2$, and Bi$_2$O$_3$-Al$_2$O$_3$-SiO$_2$ hosts is
performed. A comparison of calculated spectral properties of the centers with
the experimental data on luminescence emission and excitation spectra suggests
that luminescence in the 1.2-1.3 $\mu$m and 1.8-3.0 $\mu$m ranges in
Bi$_2$O$_3$-GeO$_2$ glasses and crystals is likely caused by
$=$Bi$\cdots$Ge$\equiv$ and $=$Bi$\cdots$Bi$=$ centers, respectively, and the
luminescence near 1.1 $\mu$m in Bi$_2$O$_3$-Al$_2$O$_3$-GeO$_2$ glasses and
crystals may be caused by $=$Bi$\cdots$Ge$\equiv$ center with (AlO$_4$)$^-$
center in the second coordination shell of Ge atom.
