Averaged third-order susceptibility of ZnO nanocrystals from Third Harmonic Generation and Third Harmonic Scattering

Second harmonic spectroscopy of ZnO, BiFeO3 and LiNbO3 nanocrystals

“…Comparatively to LN and BFO, SH and even third harmonic properties of ZnO films and nanostructures including nanowires and nanoparticles have already been the subject of reviews and several papers [40,41]. Nanoparticle suspensions of ZnO dispersed in ethanol were prepared from commercial nanopowders (NanoAmor Inc., commercial size 90-200 nm) as recently described [42]. SHS spectroscopy is then performed with an excitation wavelength varying from 700 to 1300 nm as shown in Fig.…”

Irreducible Cartesian Tensor Analysis of Harmonic Scattering from Chiral Fluids

“…In the above expressions, the microscopic nonlinear susceptibility (or hyperpolarizability) is formulated in terms of electric dipole (E1) interaction with each optical field-indeed by far the major part of nonlinear optics is based on this often implicit assumption. This accords with the simple appearance of the electric field operator for each of the four photons involved in each distinct frequency conversion interaction, which it will be convenient to represent as E1 4 . The mathematical formulation of the tensor, which comprises four terms, is readily derivable from time-dependent perturbation theory by the use of the Feynman diagrams shown in Figure 1.…”

“…In the study of molecules the scatterers are commonly randomly oriented. Regular gases and liquids are both suitable media, but to secure a decent measurable signal the latter is experimentally more viable; randomly oriented nanocrystals are also amenable to study (see references [3,4], for example).…”

“…Notably, since the three input photons are identical, only the part of γijkl that is symmetric with respect to the interchange of the corresponding three tensor indices can be manifest in THS observations. It is expedient to denote the correspondingly index-symmetric part of γijkl as γi(jkl), the subscript brackets Feynman diagrams for the four distinct leading orders, each of which is fourth order in electric dipole (E1) coupling, i.e., E1 4 , which generate the full set of contributions to the third harmonic scattering (THS) tensor γ i( jkl) . Time progresses upwards, the scatterer progressing from the ground electronic state g through the virtual intermediate states r, s, t, before resuming the ground state.…”

“…Third harmonic scattering can occur in individual molecules or nanoparticles, often in regular liquids or suspensions. Although the prospect and character of a THS effect were established relatively early in the development of laser science [1,2], the topic has recently acquired new interest [3,4], as the requisite high intensities have now become routinely available in commercial systems. Symmetry principles of several entirely distinct kinds are involved in the mechanism and selection rules for all forms of optical nonlinearity [5,6], and they come powerfully into play in optical frequency conversion.…”