Third-order transient response

Equation (3.79) shows that the third-order transient response eontains both first-order and seeond-order elements whose time eonstants and equivalent time eonstants are 2 seeonds, i.e. a transient period of about 8 seeonds. The seeond-order element has a predominate negative sine term, and a damped natural frequeney of 4.97 rad/s. The time response is shown in Figure 3.23. 

Finally, we note that the time scale for the PE experiment is determined by the dephasing times, which are very short in proteins ( 300 fs) (41). Other complementary 2D techniques were proposed in Ref. 17. In particular, energy relaxation, which occurs in proteins and polypeptides on a large time scale ( 2-15 ps) (15,41), can be studied by utilizing the transient grating and the three pulse PE techniques. These can be calculated as well using the third-order response function presented here. 

When the pulse duration is much shorter than the nonlinear response time of the material (transient case), the third-order nonlinear susceptibility can be expressed in a phenomenological time-independent form similar to the one corresponding to the long-lasting pulse regime - the adiabatic case [68]. It is then a priori possible to compare the measurement results obtained in such opposite temporal regimes, provided the physical processes involved in the optical response remain exactly the same and, especially, are not intensity-dependent. This condition being fulfilled, the... 

In the event the pulse duration tp is longer than the molecular relaxation time, the expression in [14] corresponds to a third-order correlation function Gq - (t). Note also from equation [13] that the transient birefringence has both an instantan us and a slower response to the picosecond pump pulse, since n as the electronic component of the nonlinear susceptibility is expected to follow the laser pulse profile but the molecular component n > a combination of vibrational and orientational parts, carries with it a time-dependence characteristic of each molecular system It is through the latter that information on orientational correlations can be deduced (39). 

To summarize, the EOM-PMA considerably facilitates the computation of various optical signals and 2D spectra. With shght alterations, the EOM-PMA can also be applied to compute nonlinear responses in the infrared (IR). The three-pulse EOM-PMA can be extended to calculate the A-pulse-induced nonhnear polarization [51], which opens the way for the interpretation of fifth-order spectroscopies, such as heterodyned 3D IR [52], transient 2D IR [53, 54], polarizability response spectroscopy [55], resonant-pump third-order Raman-probe spectroscopy [56], femtosecond stimulated Raman scattering [57], four-six-wave-mixing interference spectroscopy [58], or (higher than fifth order) multiple quantum coherence spectroscopy [59]. 

Consider the root locus diagram in Fig. 11.27 for the third-order s5Tstem of Example 11.13. For Kc = 10, determine values of 5 and t that can be used to characterize the transient response approximately. 

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