Second- and third-harmonic generation from cubic centrosymmetric crystals with vicinal faces: phenomenological theory and experiment

TLDR: In this article, a general phenomenological theory for optical second-and third-harmonic generation obtained in reflection from all cubic centrosymmetric single crystals whose faces have macroscopic C 1υ symmetry, including vicinal faces with such symmetry.

Abstract: We present a general phenomenological theory for optical second- and third-harmonic generation obtained in reflection from all cubic centrosymmetric single crystals whose faces have macroscopic C1υ symmetry, including vicinal faces with such symmetry. This extends earlier research [ Phys. Rev. B35, 1129 ( 1987)] for crystals with low-index faces. As a test of the theory we offer experimental results for anisotropic harmonic generation from vicinal, single crystals of Si, with and without an oxide layer, for which we use 130-fs, λ = 765 nm pulses. Overall there is good agreement between the phenomenological theory and experimental results. It is demonstrated that third-harmonic generation, which is dominated by bulk electric dipole contributions, can be used as a diagnostic of crystal orientation and crystal miscut angle. The intensity and the anisotropy of second-harmonic generation (SHG), which arise from surface electric dipole and bulk electric quadrupole effects, are seen to be sensitive to surface steps, an effect that also varies with surface oxidation. Finally, the use of vicinal surfaces allows us to identify bulk and surface contributions to SHG separately.