ABSTRACT
As emphasized throughout this book and found in innumerable experiments, the two-level approximation is valid and useful for describing resonant electronic transition of a chromophore in solution when the incident radiation frequency is close to the transition frequency between the ground state and one particular excited state. Therefore, discussions on the 2D spectroscopy of a model 2LS will be presented first. Among a variety of 2D optical spectroscopic techniques, we will focus on the 2D peak shape of pump-probe spectrum.1-4
General results of pump-probe and photon echo spectroscopy for multi-level systems were presented previously. The pump-probe polarization, which is the expectation value of the electric dipole operator over the appropriate third-order perturbation-expanded density operator, was given as a triple convolution of the third-order response function with three interacting external fields.5, 6 Therefore, any quantitative calculations of pump-probe signal require numerical integrations, and pump and probe pulses should be treated realistically. This is achievable, but the numerical calculation results cannot provide a conceptually clear picture on the 2D pump-probe spectroscopy in general. Consequently, in the present chapter, we will use a few approximations to perform the triple convolution integrations mathematically and present the resultant expressions for the frequency-scanning 2D pump-probe spectra of a model 2LS.
