**SHG: Second Harmonic Generation** Second harmonic generation (SHG; also called frequency doubling) is a nonlinear optical process, in which photons interacting with a nonlinear material are effectively "combined" to form new photons with twice the energy, and therefore twice the frequency and half the wavelength of the initial photons.

The SHG phenomenon can be arrived at from considering the dipole of a molecule in a oscillating E field:

μ(E)=μ

_{0} + ½βE

^{2} ; E=E

_{0}cos(ωt)

μ(E)=μ

_{0} + ½βE

_{0}cos

^{2}(ωt)

μ(E)=μ

_{0} + ½βE

_{0}^{2} [1+cos(2ωt)]

μ(E)=μ

_{0} + ½βE

_{0}^{2} : linear effect, oscillating at pulsation ω

+ ½βE

_{0}^{2}cos(2ωt) : non-linear effect oscillating at 2x the fundamental pulsation: 2ω

__See also:__ NLO: NonLinear optics

http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1355745251/0#0 __Source:__ http://en.wikipedia.org/wiki/Second-harmonic_generation