GENERALIZED STOKES-MUELLER FORMALISM FOR 2-PHOTON ABSORPTION, FREQUENCY-DOUBLING, AND HYPER-RAMAN SCATTERING

We consider processes quadratic in incident intensity, in which two id entical photons are annihilated simultaneously. We construct a formali sm for these processes that is maximally analogous to the Stokes-Muell er formalism for linear processes. The two-photon properties of the in cident beam require nine Stokes-like parameters for their description; the Mueller-like matrix which gives a complete description of frequen cy doubling or hyper-Raman scattering is of size 4 X 9. Of the 36 inde pendent observable matrix elements, 12 are activated by pure real elas tic dipole susceptibilities, four by an imaginary component in the ele ctric dipole susceptibility (absorption), nine by handedness alone, tw o by extramultipole mechanisms alone, and nine require both handedness and extramultipole mechanisms.