Introduction to Nonlinear Spectroscopy

All spectroscopies are based on the polarization induced by light’s oscillating electric field. While the light field is on, the polarization is forced to oscillate at the frequency of the light. The oscillating polarization in turn emits light at the same frequency as the excitation light. This process is the driven emission. When the excitation field is first turned on, the polarization builds up over the quantum state’s lifetime until it reaches a steady state equilibrium polarization that provides a continuous driven emission. When the light field is off, the polarization can continue to oscillate at the frequency defined by the molecular states. The oscillating polarization will emit light (any oscillating charge distribution will emit light as long as it has a dipole moment) over a time period determined by the quantum states’ lifetime. This emission is called free induction decay (FID). The relative amount of driven and FID emission depends on the exciting field’s pulse-width, the relaxation rate of the excited molecular states, and how close the exciting field is to resonance with the molecular states. Nonlinear spectroscopy involves multiple interactions with the excitation fields and each interaction creates a driven emission and a FID. The nonlinear interactions are described either by a phenomenological relationship between a molecular polarization and the exciting electric field or a more detailed time dependent quantum mechanical model that describes the evolution of the states that are entangled during the nonlinear process.