Efficient method for the calculation of time- and frequency-resolved four-wave mixing signals and its application to photon-echo spectroscopy

Abstract

An efficient method has been developed for the calculation of third-order time- and frequency-resolved optical signals. To obtain the general four-wave mixing signal, seven auxiliary density matrices have to be propagated in time. For the special cases of two-pulse photon-echo and transient-grating signals, two or three density matrices, respectively, are required. The method is limited to weak laser fields (it is thus valid within the third-order perturbation theory) but allows for any pulse durations and automatically accounts for pulse-overlap effects. To illustrate the method, we present the explicit derivation of the three-pulse photon-echo signal. Any other third-order optical signal can be calculated in the same manner. As an example, two- and three-pulse photon-echo and transient-grating signals for a weakly damped displaced harmonic oscillator have been calculated.

Parametric projection operator technique for second order non-linear response

“…This applies also to the validity of non-perturbative schemes of calculations of non-linear response, such as those derived in Refs. [54] and [55]. A general solution of this problem was proposed in Ref.…”

An analytic approach to 2D electronic PE spectra of molecular systems

“…(C.1)). The auxiliary energy x e is of the order of electronic interstate bang-gap [14,15]. The semi-classical interaction for external electric field [16] with np pulses has in the RWA an explicit form (see also Appendix B for detail),…”

“…A final note deserves also the electronic dephasing P in Eq. (3) [14], which is proportional to the inverse of the corresponding electronic dephasing time between neighboring electronic bands. In order to simplify the model, we choose a single dephasing time for all neighboring sets.…”

Linear and nonlinear optical responses in bacteriochlorophyll a

“…These are the so-called the reverse transient grating signal. As theoretically investigated by Gelin et al, the signals in regions c and d cannot be explained by a simple two-level system (Gelin et al 2005). Since the excitation energy is set to resonate the Q y state of BChl a, it is natural to consider only the ground and Q y states (Mukamel 1983(Mukamel , 2000.…”