Theory of Quadrupole Contributions from Interface and Bulk in Second-Order Optical Processes

Abstract

A unified treatment of the dipole and quadrupole contributions to the second-order optical response is developed. The concept of the effective susceptibility is expanded to incorporate both the surface and bulk contributions. This treatment allows us to quantitatively evaluate both surface and bulk contributions in experimental SFG/SHG spectra. The present theory clarifies a number of qualitative features in the quadrupole contribution, and is thereby utilized to settle recent confusions about the quadrupole and/or bulk effects on the surface nonlinear spectroscopy.

Observation and Identification of a New OH Stretch Vibrational Band at the Surface of Ice

“…It has been theoretically shown that a bulk quadrupolar contribution can be distinguished from an interfacial contribution by varying the optical geometry of the experiment. 39 This will be the subject of future study.…”

First-Principles Framework to Compute Sum-Frequency Generation Vibrational Spectra of Semiconductors and Insulators

“…Recently, Shiratori and Morita [12] proposed a computational framework for the evaluation of SFG spectra, using mixed quantum and molecular mechanics methods to compute dipole and quadrupole contributions from molecular non-linear polarizabilities. However their method was applied only to a non-polar molecular liquid [13], using empirical atomic potentials.…”

“…The latter are of key importance to account for the variation of the electric field across the interface. [9,12], where χ IQB eff is fully determined by bulk properties and can be computed using a bulk sample (with x,y,z periodicity); χ IQI eff is instead computed using a slab geometry [25]. The χ BQ term [27] can be experimentally identified by comparing signals from transmission or reflectance optical geometries [9].…”

“…[25] for expressions of A X q (z)). We note that A X q (z) coefficients may be recast into TCFs and computed using molecular dynamics for disordered or liquid systems [12].…”

“…The total quadrupole moment tensor Q νµ = 1 2 ρ(r)r ν r µ dr (ρ(r) is the total charge density of the system) and the terms χ Q1 , χ Q2 and χ Qs are well defined and origin independent only for a system with zero dipole and zero χ D , respectively. Hence to properly compute quadruple contributions from isotropic bulk regions, we used the total charge density of the supercell; we avoided summations over quadrupole contributions associated to single polar molecular units, at variance from several formulations presented in the literature [12,14]. We emphasize that it is key to use properties of the entire system, such as the total charge density, to evaluate χ Q1 , χ Q2 and χ Qs , thus insuring that, as long as the entire sample under consideration is centrosymmetric (χ D = 0), the results are origin independent.…”