Independent phasing of rephasing and non-rephasing 2D electronic spectra

Assigning absolute phase to two-dimensional (2D) third-order nonlinear optical signals generally requires acquiring both the rephasing and the non-rephasing signals and comparing the sum of the two to spectrally resolved pump-probe spectra. To date, however, Gradient Assisted Photon Echo Spectroscopy (GRAPES) has only been able to acquire rephasing spectra. Such a constraint requires a new phasing protocol. Here, we analytically prove that the rephasing and non-rephasing spectra can be phased independently using pump-probe signal. We verify this result holds even for finite duration pulses by simulation. This relationship holds for all 2D spectroscopies, not only GRAPES. In addition, we present improvements to GRAPES that enable acquisition of rephasing and non-rephasing signals in different phase-matched directions. We employ our phasing protocol to phase the data for laser dye IR-144, leading to reconstruction of purely absorptive 2D spectrum.