Theory and phase-cycling scheme selection principles of collinear phase coherent multi-dimensional optical spectroscopy.

We present the theory and the selection procedure of phase-cycling schemes for phase coherent multidimension optical spectroscopy. We apply our selection procedure to determine the phase-cycling schemes with the least number of steps needed to measure the two-dimensional spectra of various time resolved four wave mixing optical processes. The phase-cycling scheme selection procedure presented in this paper can be applied to higher order nonlinear optical experiments involving more optical pulses that measure higher dimensional optical spectra.