All spectroscopies are based on the polarization induced by light’s oscillating electric field. The electric field of an exciting beam induces a polarization in the illuminated material; in turn, the oscillating polarization will produce an output electric field (or, simply, emit light).
The illumination conditions affect the nature of the electric field-polarization interaction. When the excitation field is first turned on, the polarization is forced to follow the driving frequency of the electric field, so the light emitted by the polarization is of the same frequency as the excitation light. As light is continuously absorbed, the polarization and emitted light build up until they reach a steady-state. This steady-state process is called driven emission, because the frequency of the output light is the same as that of the incident light.
When the light field is off, the polarization can continue to oscillate at the frequency defined by the material's 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. Ultrafast pulses on slow-relaxing analytes will produce FID-like behavior, whereas longer pulses, or continuous light waves, will favor driven emission conditions.
How does this relate to nonlinear spectrosopy? As will be seen in the next section, one of the two major models for understanding nonlinear interactions describes them by a phenomenological relationship between a molecular/material polarization and the exciting electric field. The second model, which we will discuss directly afterwards, is a more detailed time dependent quantum mechanical model that describes the evolution of the states that are entangled during the nonlinear process.