Kramers-Kronig Relation Between N2 And Two-Photon Absorption

Nonlinear refractive index and two-photon absorption measurements on semiconductors show that the bound electronic nonlinearity can be calculated from two-photon absorption dispersion via a simple Kramers-Kronig analysis. This analysis shows n2 changing from positive to negative as the photon energy approaches the band-gap energy, consistent with observations. Additionally, this simple calculation, which assumes two parabolic bands, gives good agreement with measured values of n2 in wide-gap dielectrics that are 2 to 3 orders of magnitude smaller than in semiconductors