A general fundamental condition for flat gain optical amplification: Application to Er3+-doped glasses and glass ceramics

Investigating the fundamental basic condition that rules gain flatness in an Er-doped glass optical amplifier, a reduced number of involved parameters have been obtained by drastic simplifications. The most important of them are stressed: level positions are described in assuming icosaedral point site symmetry and a one crystal field parameter description; transitions between excited Stark levels are shown to be mainly homogeneous even at low temperature and are simply linked with their relative position in a given multiplet. Finally a general gain flatness condition for rare-earth-doped glasses is obtained. It contains two parts: a general one for all transitions except the ‘0–0’ one. The electron–phonon coupling (as defined in text) for the considered materials has to be larger than 2/3. When the considered amplification bandwidth includes the ‘0–0’ transition, a weak modulation of the main condition, inversely proportional to the square root of the crystal field strength, appears.In order to examplify these conditions, they are calculated for silicate, fluoride and oxyfluoride glass ceramics, which have been shown to display respectively non-flat and flat gain behavior.