SHAARP: An Open-Source Package for Analytical and Numerical Modeling of Optical Second Harmonic Generation in Anisotropic Crystals

Optical second harmonic generation is a second-order nonlinear process that combines two photons of a given frequency into a third photon at twice the frequency. Due to the symmetry constraints, it is widely used as a sensitive probe to detect broken inversion symmetry and local polar order. Analytical modeling of the electric-dipole SHG response is essential to extract fundamental properties of materials from experiments. However, complexity builds up dramatically in the analytical model when the probed crystal is of a low bulk crystal symmetry, with a low-symmetry surface orientation, exhibits absorption and dispersion, and consists of multiple interfaces. As a result, there is a largely uneven landscape in the literature on the SHG modeling of new materials, involving numerous approximations and a wide range of (in)accuracies, leading to a rather scattered dataset of reported SHG nonlinear susceptibility. Towards streamlining the reliability and accuracy of this process, we have developed an open-source package called the Second Harmonic Analysis of Anisotropic Rotational Polarimetry (SHAARP) which derives analytical solutions and performs numerical simulations of reflection SHG from a single interface for homogeneous crystals. Five key generalizations in SHG modeling are implemented, including all crystal symmetries down to triclinic, any crystal orientation, complex dielectric tensor (refractive indices) with frequency dispersion, and general polarization states of the light. SHAARP enables accurate anisotropic modeling of SHG response for a broad range of materials systems. The method is extendible to multiple interfaces. The code is free to download from https://github.com/Rui-Zu/SHAARP