The application of the fractional calculus model for dispersion and absorption in dielectrics II. Infrared waves

In the first paper of this series, an empirical formula based on viscoelastic analysis techniques that employs concepts from the fractional calculus originally used to model the dielectric behavior of materials exposed to oscillating electromagnetic fields in the radiofrequency band was applied to do the same for electromagnetic fields oscillating in the terahertz frequency range. The empirical formula was integrated into Maxwell’s equations producing a fractional order Ampere’s law whereof a fractional order wave equation was derived. This wave equation was used to describe the absorption and dispersion of terahertz waves in a dielectric medium. In this work, the empirical formula is extended again for application in the infrared frequency spectrum. The fractional calculus dielectric model is adapted to curve fit the complex refractive index data of a variety of semiconductors and insulators. Following the same procedure used in the first paper of this series, the fractional calculus dielectric model is again integrated in Maxwell’s equations with the same dispersion and absorption analysis performed using the newly derived fractional order wave equation. The mathematical consequences of extending this model into infrared frequencies are also discussed.