The Feynman diagram shown previously (see Introduction) represents Rayleigh Scattering, a mechanism involving an incoming and an outgoing photon; this is known as a linear optical process.
This mechanism is a two light-molecule interaction, as a result the matrix element, M, equates to an alpha tensor. The measureable rate (or speed) of the process is proportional to alpha squared.
The most commonly known nonlinear optical process is second harmonic generation. This mechanism, also called frequency doubling, involves an effective "combination" of two photons into one.
Looking at the Feynman diagram of this process, starting from the bottom:
- Region I (before interaction i) - the molecule is unexcited (blue) and two photons of light are incoming
- Region II (between i and j) - a photon is absorbed by the molecule and it moves into an excited state (red)
- Region III (between j and k) - a second photon is absorbed by the molecule and it moves into a higher-energy excited state (green)
- Region IV (after k) - a single photon (of double energy and frequency) is re-emitted by the molecule and it returns to the unexcited state (blue)
This is a three light-molecule interaction, which means that M relates to the beta tensor. The rate of the process is therefore proportional to beta squared.