Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals

We present a macroscopic theory for anisotropic second- and third-harmonic generation obtained in reflection from the surface and bulk of cubic centrosymmetric single crystals. The theory is based on possible electric dipole, electric quadrupole, and magnetic dipole sources. Completely general expressions for the harmonic fields are obtained for (100), (111), and (110) faces independent of the details of the surface response but consistent with crystal symmetry. The results obtained agree with all existing experimental data obtained by various groups during the past few years. The possibility of separating out surface and bulk responses is considered using symmetry, polarization, or geometry arguments and it is concluded that for second-harmonic generation this cannot be done in general without additional information. Third-harmonic generation, barring any strong resonantly enhanced surface electric dipole effects, is essentially a bulk probe.