Theory and experiments of angle-dependent second-order nonlinear optical scattering
Phys. Rev. B 113, 195427 – Published 18 May, 2026
DOI: https://doi.org/10.1103/tgqd-h2pp
Abstract
Second harmonic scattering (SHS) has emerged as a powerful tool for probing molecular organization and interfacial structures in aqueous systems. Owing to its intrinsic surface sensitivity and ability to operate under in situ conditions, SHS provides valuable insights into molecular adsorption, orientation, and dynamics at interfaces that are inaccessible to linear optical methods. However, the development of SHS research faces several fundamental and technical challenges owing greatly to the discrepancy between experimental results and the approximations which interpret them stemming from unintuitive coordinate system transformations. Here, we present a reformulation of the Rayleigh-Gans-Debye approximation which defines the scattered light volume in the in-plane and out-of-plane directions to improve experiment and theory cohesion and overcome experimental challenges. These definitions are then applied to slit- and pinhole-based SHS patterns with 1° resolution and allow the complete interpretation of data from both systems. By using a slit-based collection arm nonlinear scattering experiments can integrate more of the scattered volume and increase detection sensitivity. Thorough analysis of SHS patterns from aqueous suspensions of 200 and 509 nm diameter spheres shows robust alignment with the reformulated approximation, allowing accurate prediction of polarization-resolved scattering patterns as well as geometric and polarization intensity ratios. By collecting the scattered signal over a greater collection angle, researchers will be able to retain angular resolution for the determination of scatterer geometry and molecular orientation, while improved signal-to-noise ratios will allow for enhanced simultaneous probing of interfacial identification, kinetics, and thermodynamics. Last, this work provides an approachable definition for the complete scattered light volume, which will inspire the integration of variable collection angle resolution to increase the available information in nonlinear scattering experiments into three-dimensional scattering pattern extraction.
