Polarization and angle dependence of hyper-Rayleigh scattering (HRS) measured for liquid acetonitrile and dimethyl sulfoxide (DMSO) is analyzed in terms of contributions from randomly oriented molecules and additional contributions produced during intermolecular collisions and induced by the electric field of dissolved ions. All three contributions show the effect of long-range correlation, and the correlation functions are determined using the HRS observations combined with the results of molecular dynamics simulations. HRS from acetonitrile is polarized transverse to the scattering vector. This is due to long-range molecular orientation correlation produced by the dipole-dipole interaction, and correlation at distances r > 100 nm must be included to account for the HRS observations. Analysis of the HRS measurements for acetonitrile determines the length scale a = 0.185 nm for the long-range longitudinal and transverse orientation correlation functions B=-2B=a/r. Transverse polarized collision-induced HRS is also observed for acetonitrile, indicating long-range correlation of intermolecular modes. Strong longitudinal HRS is induced by the radial electric field of dissolved ions in acetonitrile. For DMSO, the angle between the molecular dipole and the vector part of the first hyperpolarizability tensor is about 100°. As a result, HRS from the randomly oriented molecules in DMSO is nearly unaffected by dipole correlation, and ion-induced HRS is weak. The strong longitudinal polarized HRS observed for DMSO is due to the collision-induced contribution, indicating long-range correlation of intermolecular modes. The HRS observations require correlation that has r long-range asymptotic form, for molecular orientation and for intermolecular vibration and libration, for both acetonitrile and DMSO.

A completely spectrally resolved model that incorporates an arbitrary signal spectrum and the SBS gain spectrum, was used to distinguish the resulting Stokes spectrum from the proper interaction between the two. This model was employed in the study of the behavior of the Stokes power spectrum given an input of two narrow signal tones into a fiber. The simulations show several behaviors in the Stokes spectrum that are a function of the input tone separation and reveal the process by which the Stokes spectrum is shifted and broadened before finally splitting as the separating tones couple through the SBS process.

For the first time, a completely spectrally resolved model is used to study SBS for nontrivial spectra. A deeper understanding of Brillouin gain and new physics are revealed, including Stokes tone shifting, broadening, and splitting.