A simple method to extract nonlinear signals in time-resolved spectroscopy

Abstract Time-resolved spectroscopy such as pump–probe and related techniques is the method of choice to observe molecular processes at the femtosecond timescale. The interpretation in terms of excited particles relies on the perturbative expansion of light–matter interaction. The control of contributing nonlinear orders is, however, difficult: at low excitation intensities the contribution of undesired higher orders of nonlinearity is small but so is the overall signal-to-noise ratio (SNR). At high pump intensities the SNR is improved but higher orders of nonlinearity contribute strongly to the overall signal. In this tutorial, we discuss the recently introduced technique of intensity cycling that solves this long-standing problem. Intensity cycling is a simple procedure in pump–probe type spectroscopy that relies on systematic variation of the pump intensity allowing one to separate the nonlinear orders. The nonlinear signals of different order are constructed from linear combinations of measurements at specific pump intensities. We discuss the new fundamental processes that are now accessible through separated higher-order signals such as multi-particle dynamics and interaction. The method is useful especially in extended excitonic systems such as polymers, where it can extract clean single-excitation dynamics and probe exciton diffusion via exciton–exciton annihilation. We review the fundamental and technical challenges of intensity cycling and introduce the language of double-sided Feynman diagrams providing a systematic theoretical framework to describe the various nonlinear signal contributions. We also discuss the recent developments regarding extension and generalization of intensity cycling to other techniques such as two-dimensional spectroscopy. Since intensity cycling can separate nonlinear orders independent of the sample, the method is applicable to a wide range of scientific questions and provides an exciting new perspective of time-resolved spectroscopy.