Non-resonant background response in nonlinear spectroscopy

The non-resonant background is a well-known source of interference in nonlinear spectroscopy. Usually, the non-resonant response is described by a simple amplitude and phase relationship, an often employed approximation that is subject to breakdown in particular limits. To identify the legitimacy of commonly used expressions for the non-resonant response, we investigate the origins and properties of non-resonant and resonant background responses in nonlinear spectroscopy by solving the Liouville-von Neumann equation. By solving the Liouville-von Neumann equation under the electric dipole approximation, commonly found expressions used for the non-resonant response in weak-field limits, primarily arising from detuned electronic states, are justified. The importance of Liouville pathways that do not survive the rotating wave approximation and frequency-dependent expressions for the background response is discussed. By identifying the usual form of the non-resonant response, elimination strategies in ultrafast frequency domain spectroscopy are identified and justified. Discussion on quantifying the background response and its comparison with spontaneous scattering spectroscopies, is identified, along with common pitfalls that may occur when attempting to quantify the origin of the non-resonant response.