Four wave mixing spectroscopy and additional boundary conditions: A proposal

A nonlinear spectroscopic method for the direct measurement of amplitude ratios among various polariton modes in spatially dispersive media is proposed and theoretically analyzed. In this method four wave mixing among three laser beams is used. Two beams have the same frequency higher than the longitudanal exciton, but different angles of incidence, and excite various polariton modes in the crystal. The third is the probe beam whose frequency can be chosen in the transparent region of the crystal. The probe beam is elastically diffracted from the grating generated by the interference between some appropriate pair of excited modes. The phase matching condition and hence the exit angle of the diffracted beam depend sensitively on the wave-vector of the grating. Thus the contribution from each polariton branch can be measured separately, by selectively tuning the angle of incidence of the probe beam; from the measured ratio the amplitude ratio, and hence the ABC can be obtained.