Experimental and theoretical studies of spectral properties of chalcogenide Ge-S and As-Ge-S glasses and fibers are performed. A broad infrared (IR) luminescence band which covers the 1.2-2.3~$mu$m range with a lifetime about 6~$mu$s is discovered. Similar luminescence is also present in optical fibers drawn from these glasses. Arsenic addition to Ge-S glass significantly enhances both its resistance to crystallization and the intensity of the luminescence. Computer modeling of Bi-related centers shows that interstitial Bi$^+$ ions adjacent to negatively charged S vacancies are most likely responsible for the IR luminescence.
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