Kramers-Rronig relations

For polarized measurements the relationship between refractive index and absorbance is critical. Directional absorbance changes lead to birefringence, which in turn will affect strongly the nature of polarized light. The Kramers-Rronig relations come into play for cases like this one (15). They relate the complete electromagnetic absorption spectrum of a material to its refractive index at all frequencies and vice versa. A form of the relation is... 

An is the contribution to the refractive index due to the solute whose concentration is C (mol/L), c is the speed of light, and e(vO is the molar extinction coefficient. An is the difference between the refractive indexes of the solution and the solvent. An is essentially the isotropic contribution to the refractive index by the solute whose absorption spectrum determines e(vO. It should not be confused with birefringence, which uses the same symbol (see under Birefringence). A common application of the Kramers-Rronig relation appears in light scattering, especially when one is interested in the effects of scattering on absorbance measurements. 

Sixth, the functional forms and experimental material-dependent parameters were shown in Subsection 13.5.3 to he consistent with the Rronig-Kramers relations. 

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