Broad aspects of the interaction in parametric devices

Parametric interaction can be interpreted classically as the scattering of waves or quantum mechanically in terms of the collision of coherent trains of particles. In this paper we would like to illustrate the significance of these classical and quantum concepts in the development of a broad class of new devices. The concept of traveling wave parametric interaction in a periodic medium will be extended to three dimensions. It will be shown that these device concepts apply not only to electromagnetic waves but also to Other types of interaction involving elastic waves, spin waves, etc. The particle view would interpret the parametric interaction as the annihilation or creation of photons, phonons, magnons, etc. The particular case of phonon-phonon interaction will be used in discussing electronically tunable parametric amplifiers. In this case the crystal structure becomes the parametric medium supporting the pump, signal and idler waves. The anharmonicity of the crystal supplies the interaction between the three waves.