THEORETICAL ANALYSIS OF THE RESONANCE FOUR-WAVE MIXING AMPLITUDES: A FULLY NON-DEGENERATE CASE.

Degenerate (one-color) and two-color variants of the resonant four-wave mixing (RFWM) have developed into a sensitive and nonintrusive spectroscopic tool to study molecules in different gaseous environments. Yet, the fully non-degenerate (four-color, 4C) RFWM was scrutinized and implemented only for the Coherent AntiStokes Raman Scattering (CARS) excitation schemefootnote{B. Attal-Tr'{e}tout, P. Berlemont, and J. P. Taran, Mol. Phys. textbf{70}, 1 (1990).},footnote{J.P. Kuehner, S.V. Naik, W.D. Kulatilaka, N. Chai, N.M. Laurendeau, R.P. Lucht, M.O. Scully, S. Roy, A.K. Patnaik, and J.R. Gord, J. Chem. Phys. textbf{128}, 174308 (2008).} . Here, by using the line-space approachfootnote{A. Kouzov and P. Radi, J. Chem. Phys. textbf{140}, 194302 (2014).}, we analyze other 4C-RFWM schemes potentially interesting for the efficient up- and down-frequency conversion as well as for studies of molecular states. Decoupled expressions of the 4C-RFWM amplitudes are derived which allows to predict their polarization dependence