Thermal gratings and phase in high-order, transient-grating spectroscopy

Abstract

Thermal gratings are a well known feature in one-dimensional (i.e., single excitation) transient-grating spectroscopy. This paper presents theory and experiments for thermal gratings in multiple dimensions (i.e., with many excitations). The theory of thermal gratings is extended to an arbitrary number of dimensions using an incoherent Hilbert-space formalism. Interference between Hilbert-space pathways makes it impossible for a thermal grating to propagate across multiple time intervals. The only surviving signal is a hybrid--a population grating between excitations and a thermal grating between the final excitation and the probe. This theory is tested on auramine O in methanol (1D) and in an ionic liquid (3-butyl-1-methylimidazolium hexafluorophosphate) (1D and 2D). In methanol, the ground-state recovery and thermal-grating signals are well separated in time; in the ionic liquid, they are not. Using the results of the theory, accurate subtraction of the thermal-grating signal is possible, extending the useful time range of the experiments. Both the comparison to the theory and the subtraction of the thermal-grating signal are dependent on accurate measurements of the time-dependent phase in these systems. Models are proposed to account for the time-dependent phase. Beer's law is generalized to multidimensional grating spectroscopy. This law provides conventions for consistently comparing the absolute phases and magnitudes between grating and nongrating experiments and between experiments of differing dimensionality.

Multiple population-period transient spectroscopy (MUPPETS) in excitonic systems

“…The degree sign indicates that the calculations are done without the phase factors for the excitation fields. 7 The phase convention for the complex absorbance is the same as for the complex cross-section: real parts correspond to absorption; imaginary parts correspond to index-of-refraction. The final state | f ] is obtained from the initial, equilibrium state |eq] by successive operators T n , representing optical transitions due to the nth excitation, and G(t n , t n−1 ), representing evolution between times t n−1 and t n ,…”

“…In Ref. 7, we showed how to incorporate thermal effects into pathway calculations of multidimensional experiments. Here that treatment is extended to multilevel systems.…”

“…is an adequate expression. 7 This thermal correlation function is zero when τ = 0 and reaches a maximum of two at half the acoustic period due to interference between the slowly decaying pure thermal response and the more rapidly oscillating acoustic response. The convolution in Eq.…”

“…Our group has been exploring multidimensional kinetics in which there is more than one perturbation, and thus, more than one period of time evolution. [1][2][3][4][5][6][7][8][9][10] We have called our approach, which uses weak optical perturbations, multiple population-period transient spectroscopy (MUPPETS). So far, its focus has been on nonexponential relaxation (rate dispersion) in two-level systems.…”

“…Real MUPPETS experiments detect not only the resonant signal due to the chromophore, but also see solvent heating due to chromophore relaxation. 7 These thermal effects are the multidimensional extension of thermal-grating spectroscopy. [13][14][15] They are both a complication to measuring the resonant signal and a potential route to measuring nonradiative relaxation between spectroscopically dark states.…”