Pulse-shape effects in fifth-order multidimensional optical spectroscopy

We study how the effects of finite pulse durations modify the fifth-order two-quantum two-dimensional (2Q-2D) and three-dimensional (3D) optical spectra. Instead of directly calculating the time domain polarization, the equivalent approach in frequency domain significantly simplifies the calculations and delivers exact expressions for the 2Q-2D and 3D spectra. Our results minimize the number of numerical integrations needed. We also derive simple analytical formulas for practically important situations when the laser pulses are short on the timescale of nuclear motion as well as short (or long) on the timescale of electronic dephasing. These formulas evaluate the measured spectra by multiplying the spectral response function by a factor depending on the spectral pulse envelopes.