Longitudinal Gauge Theory of Second Harmonic Generation at Semiconductor Surfaces

A theoretical review of surface second harmonic generation from semiconductor surfaces based on the longitudinal gauge is presented. The nonlinear susceptibility tensor χ is split into two terms, one that is related to inter-band one-electron transitions, and the other is related to intra-band one-electron transitions. The equivalence of this formulation to the transverse gauge approach is shown and the possibility of confirming its numerical accuracy is discussed. Also, the calculation of the surface second harmonic radiated intensity R within the three-layer-model is derived. With χ and R one has a complete description of this fascinating optical phenomena.