Convolution Models for the Dielectric Function of Glass

Peter A. van Nijnatten

doi:10.4028/www.scientific.net/AMR.39-40.199

Paper Titles

Study of Lithium-Lead Phosphate and Borophosphate Glasses
p.181

Some Physical Properties of Li₂O-TiO₂-TeO₂ and BaO-TiO₂-TeO₂ Glasses
p.185

Y₂O₃ – Al₂O₃ Binary Glass Microspheres: Synthesis and Characterisation
p.189

Correlation of Surface Characteristics and Thermal Conductivity of High Silica Glass Fibre Materials
p.193

Convolution Models for the Dielectric Function of Glass
p.199

Magnetic Properties of Amorphous Fe₂O₃-R₂O₃ (R=La, Gd and Tb) Thin Films Fabricated by Sputtering Method
p.207

Spectral, Radiation-Optical and Shielding Properties of Phosphate Glasses with High Lead Content
p.213

Formation and Passive Q-Switch Performance of Glass-Ceramics Containing Co²⁺-Doped Spinel Nanocrystals
p.219

Influence of Technological Parameters on Nanosecond Laser-Induced Surface Damage of Optical Multimode Fibers
p.225

HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 39-40Convolution Models for the Dielectric Function of...

Convolution Models for the Dielectric Function of Glass

Abstract:

Spectral behaviour of the real and imaginary parts of the optical constants of glass has been widely investigated to obtain band structural parameters of optically induced transitions. Curve fitting procedures for obtaining a classical oscillator fit to reflectance and/or transmittance data play an important role in this application. The present form of the dispersion model that is widely used to describe disordered media like glass uses a convolution of the Lorentzian oscillator function and the Gaussian Probability Density Function. This model is capable of describing symmetrical band shapes only. In this paper a convolution model is proposed based on using the Beta function as PDF. The maximum of the PDF, which corresponds to the frequency with the highest probability, corresponds to the central frequency of the particular oscillator species in the convolution model. For a certain value of the parameter that describes the degree of asymmetry, the new model is equivalent with the present convolution model and the remaining parameters have an identical meaning yielding practically identical values. The new model also solves a problem related to the infinite integration intervals of the Gaussian PDF based convolution model.