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Extra info for Nonlinear Optics Material Research
61) Two major limitations of the MG approximation are that the interaction between the nanospheres and the scattering of light are neglected. Furthermore, the MG model does not take into account either the size nor the the distance between the nanospheres, thus neglecting agglomeration and polydispersion effects. In the literature, some extended versions of MG approximation, which take into account the size of the nanospheres, have been discussed [57, 58]. However, in the frame of the conventional MG approximation, the volume fraction of the nanospheres must be relatively low (fi 1).
The first significant experimental applications of the normal reflectivity measurements for the determination of the optical constants of semiconductors have been carried out in 1962 by Ehren- 40 4 Kramers-Kronig relations and sum rules in linear optics reich and Philipp [89, 90]. Since then, the method has become a standard spectroscopic technique [10, 91]. 28) r(ω) = η(ω) − 1 + iκ(ω) N (ω) − 1 = . 29) There is an analytic continuation of function r(ω) from the real axis into the upper half of the complex angular frequency ω-plane .
Causality implies that the general S-matrix has an 28 4 Kramers-Kronig relations and sum rules in linear optics analytic (also referred to as holomorphic) continuation in the upper complex energy plane while and complex poles (= singular points) are located in the lower half of a complex energy plane. In optical physics, with the aid of analytic continuation of the refractive index to the upper half of a complex angular frequency plane, Kramers  proved that the principle of relativistic causality allows the calculation of the real refractive index of a medium from the absorption spectrum.