Multidimensional photon echo spectroscopy (nD PES) is a type of nonlinear n-wave mixing (nWM) technique that reveals intramolecular coupling between states that share common electronic or vibrational ground state. 2D PES, for instance, may distinguish a series of physical systems that exhibit identical linear spectra, but are chemically and physically distinct. For instance, using linear absorption, a mixture of compounds, each with a single optical transition cannot be distinguished from a homogeneous mixture of compounds with several distinct transitions. Similarly, a system exhibiting fast chemical exchange will show transitions that are the average of the temporally distinct states. In addition to the locations of the peaks in the spectrum, which indicate the average transition energies, the line widths potentially encode additional critical information about the system. Unfortunately, linear absorption or emission cannot distinguish between inhomogenous and homogeneous line broadening. The former indicates that a distribution of molecules, each with a slightly different optical transition reside within the ensemble. On the other hand, homogeneous broadening is an inherent characteristic of the individual molecules that may be used as an additional identifying marker. Unlike linear techniques, nD PES may uniquely identify each of these physically distinct scenarios. When recorded as a function of time, the two-dimensional spectra exhibits cross-peaks that indicate coupling between transitions at specific snapshots in time, clearly identifying short-lived or transient species. Higher order (n > 2) incarnations of nd PES can further distinguish systems such as those that exhibit a high degree of degeneracy (e.g. polymers, DNA, etc…) as well as the ability to elucidate the influence of the surrounding environment (e.g. solvent) on the chromophores of interest. Essentially, this is possible because nD PES is a nonlinear technique that approximates to high-order the full optical polarization of the system, while linear methods are only first-order approximations. The full optical polarization encodes all the information available from a spectroscopic measurement.
2D PES spectra are acquired by using a pulse sequence consisting of three pulses that generate a polarization in the sample, which then acts as a source for the emitted radiation. The delay, t, between pulses 1 and 2 is scanned for each constant delay time, T, between pulses 2 and 3. The signal generated for each pair of delays is passed through a spectrometer where it interferes with a reference pulse. Using spectral interferometry, the phase and amplitude of the signal field may be retrieved. The raw data is Fourier transformed with respect to τ to generate a frequency-frequency correlation map. These 2D maps may then be generated for each delay time, T, encoding information about the dynamics of the system on the ultrafast (<1 ns) time scale.