Polarization dependence of 2-photon absorption in solids

Thesis (Ph.D.)--University of Rochester. College of Engineering and Applied Science. Institute of Optics, 1970.The dependence of two-photon absorption in solids on the polarization of the exciting photons has recently been studied, both experimently and theoretically, as a means of identifying electron state symmetries. Theoretically, polarization dependence has been calculated for allowed two-photon transitions at the Γ-point from a totally symmetric ground state to a final state of arbitrary symmetry for each of the thirty-two point groups and at other symmetry points for several crystal structures. More recently, polarization dependence has been studied for forbidden transitions in cubic structures in a two spherical band model with the inclusion of exciton effects in the intermediate and final states. In this model the polarization dependence was found to be independent of one-electron state symmetries or the orientation of photon polarizations with respect to the crystal axes. This work extends the previous investigations in several respects. Mathematical expressions and tables are obtained for allowed Γ-point transitions between states of arbitrary symmetry for the thirty-two point groups and for transitions at other symmetry points in hexagonal close-packed and wurtzite structures. For forbidden transitions a simpler band model is used neglecting exciton effects. This predicts a polarization dependence similar to, but more easily evaluated than, the earlier result; the ratio of maximum to minimum absorption predicted by the earlier calculation is a complicated function of the band gap and exciton binding energies, which usually are not precisely known, while in the simpler model this ratio is a simple function of the photon energies. The effects of k•p splitting of p-like valence bands is considered in this model, and it is found that only the ratio of maximum to minimum is altered. In addition the polarization dependence is calculated for forbidden X-point transitions in the two band model, but in which the ellipsoidal character of energy surfaces near this point are taken into account. The two-photon absorption is found to depend both on the symmetries of the initial and final states and on the orientation of the polarization vectors with respect to the crystal axes