Transient photodarkening in amorphous and liquid chalcogenides: fractional dynamics in rheological point of view

Amorphous and liquid chalcogenides exhibit a characteristic response of the optical transmittance with nanosecond bandgap-light excitation. An additional optical absorption is spontaneously generated at the band edge, and its relaxation is observed in a quite wide time domain from 10⁻⁷ to 10⁻² s (transient photodarkening: TPD). In the present study, the TPD is converted into a frequency spectrum (FS). It is found that the FS (or the TPD: time domain) is replicated well by the Mittag-Leffler function (MLF) which is the natural generalization of the exponential function involving the stretched exponential and power law functions. The MLF originates from a concept of the fractional dynamics which is now popularly applied to the viscoelasticity of the polymer system where a complicated structural relaxation may occur in the atomic network system.