Forward degenerate four-wave-mixing spectra of NO in the strong-field regime including polarization, line coupling, and multipole effects.: I.: Theory -: art. no. 012716

In the present paper, we investigate the saturation mechanism of FDFWM (forward degenerate four-wave-mixing) spectra, observed with different polarizations of the input beams, line coupling, and Doppler effect. Our theoretical approach uses a nonperturbative resolution of the density matrix equations, decomposed on the irreducible tensor basis. This formalism greatly simplifies analytical expressions and allows for a correct treatment of magnetic sublevels structure in a three-J level system. Systematic calculations of the FDFWM signal for specific NO lines are performed to characterize intensities and line shapes as a function of saturation. Relative intensities exhibit strong changes in the intermediate regime of saturation further supporting the necessity for using such a complete model. Under saturating conditions, line coupling is shown to distort the spectra, according to the type of transition and the polarization configuration. This effect is observed in the following paper [V. Kruger et al., paper II, Phys. Rev. A 64, 012717 (2001)], where saturated experimental spectra of NO are presented and interpreted for two polarization configurations of interest for diagnostic purposes.