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Journal of Nonlinear Optical Physics & Materials

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

Peixian Ye, Ruihua Zhang, Xin Mi, Haitian Zhou, Qian Jiang

Published Apr 1, 1992• 3 citations
Publisher

Abstract

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 [Formula: see text] 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.

DOI
10.1142/s0218199192000121

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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 [Formula: see text] 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.
A series of experiments of time-delay four-wave mixing with incoherent light (TDFWM-IL) in absorption bands of ruby and dye molecules at 300 K-20 K are reported, which demonstrate that two-level theory fails in the interpretation of the results, and that our multilevel theory of TDFWM-IL should be applied. The following experimental results are emphasized: the normalized delay-time dependences of the signal intensity IS (τ) are not dependent on the sample temperature from 80 K to 300 K for the pump-beam wavelengths not closed to the zero-phonon line or the absorption edge as the power spectrum S0(ω) of the incoherent light source kept invariable; at low temperature of 20 K, IS(τ) is modulated periodically with a period equal to the interval of two adjacent vibrational transitions in the absorption band 4T2 of ruby, as predicted by the multilevel theory. The experiments performed at the zero-phonon line of ruby and at the absorption edge of Cresyl Violet in PMMA demonstrate that the effective two-level model is suitable to approximately analyze not only the experimental results of TDFWM-IL in the unresolved continuous absorption bands with homogeneous broadening, but also the effects of inhomogeneous broadening on the behavior of TDFWM-IL in these bands. Additionally, some data of the subpicosecond dephasing processes of these materials are also obtained for the first time.
A homogeneous broadening multilevel theory of time-delay four-wave mixing with incoherent light is developed for absorption bands that consist of a series of vibrational transitions. A formula for the delay-time dependence of the signal intensity I(τ) is obtained. The differences between I(τ) derived from multilevel theory and from two-level theory are pointed out. It has been demonstrated experimentally that the multilevel theory is more suitable than the two-level theory for this type of absorption band. It is shown, in particular, that when we apply the two-level theory to the analysis of experiments in this type of absorption band, what we determine is not the dephasing time of an individual transition but the effective dephasing time, which reflects the behavior of the total absorption spectrum of the band.
In this paper, our multi-level theory of time-delay four wave mixing with incoherent light (TDFWM-IL) developed previously for the case of homogeneous broadening system has been extended to a generally inhomogeneous broadening case. From the present theory, a general expression of signal intensity for absorption band with both homogeneous and inhomogeneous broadening is given as a function of mutual time delay τ between two pump beams. Photon echo with incoherent light under the condition of extremely inhomogeneous broadening is discussed, and the difference of results obtained scperately from multi-level and two-level theory is pointed out. It has been demonstrated that the experiment of TDFWM-IL can also be analysed approximately by using an effective two-level model when a weak effect of inhomogeneous broadening of absorption band exists. Finally, our experimental results of TDFWM-IL obtained at zero-phonon line of ruby and absorption edge of cresyl violet film in PMMA are also presented and compared with the theory mentioned above.
Signal intensity as a function of mutual delay time of three incoherent pump beams in the degenerate four-wave mixing (DFWM) process has been calculated with the second-order correlation time of the fields being much shorter than both the dephasing time T 2 and the inverse of the inhomogeneous broadening width δω. The results show that when broadening is purely homogeneous and extremely inhomogeneous, the curve of the DFWM signal intensity as a function of the delay time τ shows no peak shift, while when the inhomogeneous broadening is finite, the peak shift is related to the dephasing time T 2 and the inhomogeneous width δω, and can thus be used to estimate T 2.
The development of the incoherent light time-delay four-wave mixing theory is described the differe-nce of the two-level theory and the theory of multilevel is analysed.The photon echo signal of the Er2O3 and CeO2 doped TeO2-Nb2O5-ZnO glass is also observed by the experiment of time-delay four-wave mixing with incoherent light,with the temperatures at 7.5K and 300K respectively.The Photon echo signal indicates the interference-beat modulation.The multi-level theory in the case of non-uniform broadening the theoretical formula is used to fit the experimental results.The multi-level theory is used to explain the experimental results.The reference for the development of the incoherent light four-wave mixing theory is provided.