Nonlinear processes occur when the effects of a perturbation become large and the response to the perturbation no longer follows the perturbation’s magnitude. A common nonlinear phenomena occurs when the volume on a sound system is raised to levels where the capacity of the system’s audio speakers is exceeded and sound distortions are created. Here, the response of the speakers no longer follows the driving voltage. The distortions create new frequencies at the sum and differences of the sound frequencies as well as changing their amplitudes. Nonlinear optical processes are analogous. They occur when the electric field strength of light becomes comparable or larger than the electric fields in a sample so the polarization induced in the matter by the electric field of the light is distorted. It acquires new frequencies and the amplitude of the previous frequencies is modified. Rather than hearing new frequencies, one sees new colors at frequencies that correspond to the sum and differences of the exciting light’s frequencies.

Molecular spectroscopy of vibrational and electronic states is largely based on the interaction of the electric field component of electromagnetic radiation fields with molecules through the induced molecular electric dipole moments. In contrast, nuclear magnetic resonance (NMR) is based on the interaction of the magnetic field component with the magnetic dipole moment of nuclear spins. There are many commonalities and differences between NMR and molecular spectroscopies. An important difference is the amount of interaction that occurs between the quantum states of matter and the thermal fluctuations of the environment. Nuclei are well-shielded from the thermal environment and have very sharply defined transitions between quantum states; electronic states interact strongly with the environment and have much broader transitions; vibrational states have interactions that are intermediate between the two cases.