Selection Rules and Symmetry Relations for Four-Wave Mixing Measurements of Uniaxial Assemblies

Abstract

Uniaxial systems represent the next lowest symmetry below isotropic and are ubiquitous. The objective of the present work is to present a systematic foundation for interpreting polarization-dependent four-wave mixing measurements of oriented and aligned assemblies. Orientational averages connecting the molecular frame to the macroscopic frame in uniaxial assemblies were derived for several common molecular symmetry groups for coherent anti-Stokes Raman spectroscopy (CARS) measurements, coherent anti-Stokes two-photon spectroscopy (CATS) probing electronic transitions, resonant two-photon absorption (2PA), and traditional Raman measurements. First, the complete set of orientational averages connecting the molecular and macroscopic frames was compiled for the most general case of C1 molecular symmetry. Then, the orientational averages of a select few commonly occurring molecular symmetry groups (Cs, C2, C2v, and C3v) were explored in greater detail to illustrate the approach and to facilitate the interpretation of routine experimental measurements. One outcome of this analysis is the prediction of efficient electric dipole-allowed chiral-specific four-wave mixing in uniaxially oriented media.

Modeling Coherent Anti-Stokes Raman Scattering with Time-Dependent Density Functional Theory: Vacuum and Surface Enhancement.

“…The formula above incorporates some simplifications emerging from spherical averaging 16 explained in the supporting information. Here ε is a phenomenological linewidth (inverse lifetime), {i jkl} are Cartesian indices, and Q n are nuclear displacements along mode n.…”

Large and anisotropic third-order nonlinear optical response from anisotropy-controlled metallic nanocomposites

“…In such a direction, studying the physical contribution of the separate components of the third-order susceptibility tensor will give more information about the physics behind the optical response of metallic nanocomposites. In particular, for anisotropic Ag-and Au nanocomposites obtained by controlled deformation with Si irradiation [3], this tensor has only three linear independent components when probing with a fully-degenerate wave mixing [27,28]. Therefore, in this communication, we obtained, by a self-diffraction method, nonlinear optical measurements related to, at least, two of these three linear independent components of v (3) for the anisotropic nanocomposites, obtaining, as a first instance, a clear relationship between them.…”

High-speed polarization-resolved coherent Raman scattering imaging

“…Note that hyperspectral analyses require disentangling the content of complex molecular bond mixtures. In this context, the modulation signals measured in this work can be interpreted into orientation distribution of vibrational bonds provided their symmetry is known, using microscopic to macroscopic frame transformations as detailed in [15,39].…”