Separating orders of response in transient absorption and coherent multi-dimensional spectroscopy by intensity variation

Interpretation of time-resolved spectroscopies such as transient absorption (TA) or two-dimensional (2D) spectroscopy often relies on the perturbative description of light-matter interaction. In many cases the third order of nonlinear response is the leading and desired term. When pulse amplitudes are high, higher orders of light-matter interaction can both distort lineshapes and dynamics and provide valuable information. Here, we present a general procedure to separately measure the nonlinear response orders in both TA and 2D spectroscopies, using linear combinations of intensity-dependent spectra. We analyze the residual contamination and random errors and show how to choose optimal intensities to minimize the total error in the extracted orders. For an experimental demonstration, we separate the nonlinear orders in the 2D electronic spectroscopy of squaraine polymers up to 11$^{th}$ order.