Dispersion theory of liquids containing optically linear and nonlinear Maxwell Garnett nanoparticles

Kramers-Kronig relations and sum rules for effective linear permittivity of the Maxwell Garnett liquid-nanosphere system were obtained using complex a nalysis and general expression of the effective permittivity. When reflecta nce from optically linear and nonlinear Maxwell Garnett nanoparticles was c alculated it was observed that the reflectance, in the case of attenuated t otal reflection, depends on the fill fraction of the nanospheres and their nonlinear susceptibility. According to simulations a good sensitivity of th e nonlinear contribution on the reflectance can be obtained by using a prob e wavelength corresponding to the resonance frequency of the nanosphere sys tem. In Kretchmann's configuration it was observed that the surface-plasmon -resonance angle depends on the fill fraction and on the intensity of the i ncident light. By using reflectance, it is possible to detect optically non linear nanospheres in liquids.