Kramers-Kronig relations in Optical Materials Research

The purpose of this book is to highlight the relevance of the general integral properties of susceptibility functions for the inspection of the linear and nonlinear optical properties of materials. The conceptual foundation of the general integral properties set forth is the principle of causality in light–matter interaction. The bridge between the causality of the physical system and the holomorphic properties of the susceptibilities analyzed, which determine the possibility of writing the integral relations, is Titchmarsch’s theorem in the case of linear optics and Scandolo’s theorem in the nonlinear case. We have shown that, in all generality, such general properties only depend on the expectation value of suitable operators in the ground state of the electronic density matrix densities, with appropriate modifications to account for local field effects and for inhomogeneous media. Moreover, since we have adopted a rather general quantum mechanical framework, these results are derived for any physical system. MATLAB codes are included in the text