Kramers-Kronig-consistent optical functions of anisotropic crystals: Generalized spectroscopic ellipsometry on pentacene

The Kramers-Kronig relations between the real and imaginary parts of a response function are widely used in solid-state physics to evaluate the corresponding quantity if only one component is measured. They are among the most fundamental statements since only based on the analytical behavior and causal nature of the material response [Phys. Rev. 104, 1760-1770 (1956)]. Optical losses, for instance, can be obtained from the dispersion of the dielectric constant at all wavelengths, and vice versa [Handbook of optical constants of solids, Vol. 1, p. 35]. Although the general validity was never casted into doubt, it is a longstanding problem that Kramers-Kronig relations cannot simply be applied to anisotropic crystalline materials because contributions from different directions mix in a frequency-dependent way. Here we present a general method to identify frequency-independent principal polarizability directions for which the Kramers-Kronig relations are obeyed even in materials with lowest symmetry. Using generalized spectroscopic ellipsometry on a single crystal surface of triclinic pentacene, as an example, enables us to evaluate the complex dielectric constant and to compare it with band-structure calculations along the crystallographic directions. A general recipe is provided how to proceed from a macroscopic measurement on a low symmetry crystal plane to the microscopic dielectric properties of the unit cell, along whose axes the Kramers-Kronig relations hold.