Figure 1shows the WMEL and Mukamel diagrams for DOVE-FWM. There are three pathways that differ in the time ordering of the pulses and the resonances. There are two DOVE-IR pathways that involve excitation of two infrared transitions from the ground state followed by a normal nonresonant Raman transition (although the latter could be made resonant to achieve higher sensitivities) and one DOVE-Raman pathway that involves a vibrationally enhanced Raman transition followed by a normal nonresonant Raman transition. The nonlinear polarization from all pathways add and interfere to create the output signal. Two tunable infrared excitation pulses (frequencies labeled as ω₁ and ω₂) excite the vibrational coherences and then a third excitation (labeled ω₃ and typically in the uv/visible) excites the Raman transition between the two vibrational states. The three beams are crossed at angles that provide phase matching, $\vec{k}_4 = \vec{k}_1 - \vec{k}_2 + \vec{k}_3$. Scanning ω₁ and ω₂ while monitoring the output at $\omega_4 = \omega_1 - \omega_2 + \omega_3$ with a monochromator creates a two-dimensional spectrum.

Figure 2a shows an example two-dimensional spectrum for a mixture of CH₃CN and CD₃CN in C₆D₆. The two major features correspond to DOVE-IR resonances where ω₁ is tuned to the (C≡N stretch + C-C stretch) combination band and ω₂ is tuned to the C≡N stretch mode. There are also diagonal features that arise from DOVE-Raman resonances where ω₁ is tuned to the (C≡N stretch + C-C stretch) combination band and ω₁- ω₂ is tuned to the C-C stretch mode. There is also a diagonal CARS feature where ω₁ is nonresonant and ω₁- ω₂ is tuned to the C₆D₆ ring breathing mode. More discussion of this spectrum appears elsewhere.

The cross-peaks between vibrational transitions occur only when the modes are coupled by intra- or inter-molecular interactions. This coupling requirement is the major strength of multidimensional spectroscopy because it isolates the spectral features that are associated with interactions. The coupling requirement is manifested in DOVE-FWM by the requirement that at least one of the transitions (2 infrared and 1 Raman) must involve a combination band that gets its transition strength from coupling. In the harmonic approximation, vibrational transitions require a change of quantum number $\Delta \nu = \pm 1$ and with only three transitions, this requirement must be violated so a combination band can appear.

The different pathways for generating the output coherence in nonlinear spectroscopy result in interference effects between each pathway’s polarization and these appear as changes in the peak intensity and shape. These effects are best seen in figure 10 as the vanishing of the DOVE-Raman features as they merge with the strong DOVE-IR feature on the high energy side and the enhancement of the features as they re-emerge on the low energy side. These effects can be rigorously modeled with simulations that allow one to extract the transition moments, coupling information, and dephasing rates for the different coherences. Figure 2b shows the simulation for the experimental data in figure 2a.