Beta-distributed oscillator model as an empirical extension to the Lorentzian oscillator model: physical interpretation of the ${\beta \_{{\rm do}}}$β_do model parameters.

Abstract

The physical sense of the free parameters of the beta-distributed oscillator (${\beta \_{{\rm do}}}$β_do) dispersion model is discussed. It is shown that the set of six model parameters provides information on central wavenumber, oscillator strength, absorption edge position, asymmetry, as well as homogeneous and inhomogeneous linewidth of a complicated absorption feature. For materials satisfying the Moss rule, the number of independent ${\beta \_{{\rm do}}}$β_do parameters decreases down to five. We also show that the Cody absorption edge shape essentially represents a special case of the ${\beta \_{{\rm do}}}$β_do approach. By making use of the generalized Miller rule, we propose a generalization of the ${\beta \_{{\rm do}}}$β_do model to nonlinear refractive indices and absorption coefficients.