Understanding longitudinal optical oscillator strengths and mode order

A classical way of describing dielectric functions employs sums of contributions from damped harmonic oscillators. We derive the corresponding dispersion relations for the dielectric function and the inverse dielectric function to investigate and establish the relationship between the transversal and longitudinal optical oscillator strengths, which can differ, according to experimental results, by up to three orders of magnitude. We demonstrate that transversal and longitudinal oscillator strengths should be identical for a single oscillator and that the experimental differences are in this case due to the introduction of a dielectric background in the dispersion formula. For this effect we derive an exact correction. Based on this correction we further derive a modified Kramers-Kronig sum rule for the isotropic case as well as for the components of the inverse dielectric function tensor. For systems with more than one oscillator, our model provides oscillator strengths and LO resonance wavenumbers for uncoupled LO modes.