Einstein coefficients for many nonlinear medium [2] . In three-level configuration the dye solution can be excited by light fields with two different frequencies, one group of light can involve nonlinear processes, and other light fields act in second channel to control the nonlinear processes in first channel [3] .
Saturation of complex molecules affects the nonlinear processes occurring in the medium. The medium can be described by two-, three-, and four-level configurations. The principal singlet-singlet and excited triplet-triplet channels of a four-level, N-type, configuration were used to study a nonlinear medium, which was excited by radiation with two frequencies. Under weak population of energy levels in the triplet-triplet channel (a small ratio of the total probability of spontaneous and irradiate transitions for both channels p23/p31), the principal (singlet-singlet) channel is similar to a two-level configuration. At the same time, the effective population of the energy levels in the triplet-triplet channel (the ratio p23/p31 is large and the radiation intensity in the principal channel is high) makes the excited (triplet-triplet) channel coincide with the two-level configuration. The saturation intensity of radiation in principal (excited) channel, as effective two-level configuration, and nonlinear processes in this channel can be controlled by external radiation acting on excited (principal) channel. Finally, the average excitation of molecules into the energy levels in the triplet-triplet channel (ratio p23/p31 ≈ 1) makes the four-level configuration similar to the three-level configuration with effective level as a result of combination between second singlet level S2 and first triplet level T1.
The four-level model is used to study the nonlinear media with coincident absorption and emission bands in both principal (S0S1) and excited (T1T2) channels.The excitation of molecules occurred by two light elds: radiations with intensity I12 at frequency ω0 tuned at the centre of absorption band of principal singletsinglet channel and radiations with intensity I34 at frequency ω tuned at the centre of absorption band of excited triplettriplet channel.The monotonic dependence of phase response of media in both principal and excited channels and the saturation processes are studied theoretically and numerically for four-level model.