STUDY OF TIME-DELAY FOUR-WAVE MIXING WITH INCOHERENT LIGHT IN ABSORPTION BANDS I: Theory

A multilevel model, including homogeneous and inhomogeneous broadening, is proposed for the study of time-delay four-wave mixing with incoherent light (TDFWM-IL) in absorption bands consisting of a series of vibrational transitions. A theory of TDFWM-IL is developed for this model, and a general formula for the delay-time dependence of the signal intensity Is(τ), considering both the homogeneous and inhomogeneous broadening of the transitions, is deduced. Special analyses are given to the homogeneous and inhomogeneous limits. The differences between Is(τ) derived from multilevel theory and from two-level theory, are pointed out. When the homogeneous broadening of individual transitions is much smaller than the frequency interval of adjacent transitions, Is(τ) in the multilevel theory is modulated periodically and the envelope is close to that in the two-level theory for both the homogeneous and inhomogeneous limits. When the individual transitions are homogeneously broadened enough so that an unresolved continuous band is formed, an effective two-level model can still be used approximately for the studies of TDFWM-IL in this continuous band, with both homogeneous and inhomogeneous broadening. However, the dephasing time in the formula of Is(τ) in this effective two-level model is not the real dephasing time of an individual transition of the band, but the effective one which reflects the behavior of the whole band.