Phenomenological theory of generation of second harmonic reflected from silicon surface

In this chapter, we will derive expressions for the amplitudes of the SH waves reflected from a centrosymmetric semiconductor at various combinations of polarization of the pump wave at frequency ω and a SH wave at a frequency of ω₂ = 2ω. Calculations will be carried out within the framework set out in chapter 2 of the phenomenological approach to the description of NP. When calculating the fields we will not use the formalism of Green’s functions and use instead the solution of the set of Maxwell’s equations with the boundary conditions connecting the fields in a non-linear medium and outside it. This approach was used in the pioneering works of N. Bloembergen et al on the non-linear optics of surfaces [1, 2]. In our opinion, this approach, despite its greater complexity, is more illustrative.