Second-harmonic generation in the bulk of a chiral liquid by a focused laser beam

Second-harmonic generation (SHG) was recently detected in the bulk of a non-centrosymmetric liquid suspension of bacteriorhodopsin-bearing fragments of Halobacterium Halobium purple membranes. This effect long thought to be forbidden was attributed to the partially coherent hyper-Rayleigh scattering. More recently, a purely coherent second-harmonic (SH) signal was observed whose properties could not be interpreted using the this theory. Unlike the dc-induced near-resonance SHG in atomic gases that is due to the gas ionization by focused laser pulses with consequent diffusion-assisted charge separation, the SHG experiments in bacteriorhodopsin-containing liquids were not associated with any kind of medium´s damage, and the dependence of the SH intensity on the fundamental-beam intensity was not parabolic, but could be only approximated with a fourth-order polynomial. In this paper we will show that the coherent SH signal can be attributed to usual three-wave (due to the non-local quadratic optical nonlinearity) and five-wave (due to the local-type susceptibility χˆ⁽⁴⁾) mixing in the bulk of a homogeneous isotropic non-centrosymmetric liquid if focusing of the beam of the fundamental frequency ω is taken into account