The Kramers-Kronig Relations: Validation via Calculation Technique

Abstract

The historical aspect of the discovery of the Kramers-Kronig dispersion relations is considered. A calculational technique is shown for investigating the validity of the Kramers-Kronig relations. The dielectric susceptibility function is constructed as a classical linear response function in the framework of two equations of charge motion of the microscopic Lorentz theory. It is shown that the Kramers-Kronig relations can be satisfied in the presence of poles in both the upper and lower half-planes simultaneously. It is shown that the accuracy of fulfilling the KK's relations depends on the removal of the pole of the lower half-plane from the real axis. To determine the optical parameters of the absorbing medium from the reflection spectra, it is necessary to perform a conformal transformation. An example of the application of this approach to the reflection spectrum of silicon is shown.