Nonlinear electrical susceptibilities of nonlinear crystals

Non-linear optical effects were discovered a long time ago: Kerr (1875), Pockels (1893), Raman (1928), but their real potential only became apparent with the first laser sources, first with the ruby crystal (1960) and then the Nd ³⁺ -doped YAG (Yttrium Aluminium Garnet) crystal (1964). The first paper showing harmonic generation by frequency doubling dates back to 1961 with the ruby pulse laser. Laser sources that deliver intense, monochromatic electric fields are ideal for producing these non-linear phenomena. In "classical" optics, the oscillating electric field E of a light wave propagating through a transparent dielectric medium induces a polarization field P within the collection of atomic dipoles characterized by the same frequency as that of the incident field: