Optical Second Harmonic Generation (SHG) is a nonlinear optical effect widely used for nonlinear optical microscopy and laser frequency conversion. The closed-form analytical solution of the nonlinear optical responses is essential for evaluating the optical responses of new materials whose optical properties are unknown a priori. Many approximations have therefore been employed in the existing analytical approaches, such as slowly varying approximation, weak reflection of the nonlinear polarization, transparent medium, high crystallographic symmetry, Kleinman symmetry, easy crystal orientation along a high-symmetry direction, phase matching conditions and negligible interference among nonlinear waves, which may lead to large errors in the reported material properties. To avoid these approximations, we have developed an open-source package named Second Harmonic Analysis of Anisotropic Rotational Polarimetry (♯SHAARP) for single interface (si) and in multilayers (ml) for homogeneous crystals. The reliability and accuracy are established by experimentally benchmarking with both the SHG polarimetry and Maker fringes predicted from the package using standard materials. SHAARP.si and SHAARP.ml are available through GitHub https://github.com/Rui-Zu/SHAARP and https://github.com/bzw133/SHAARP.ml, respectively.
Optical second harmonic generation (SHG) is a process that doubles the photon frequency and is widely used to detect broken inversion symmetry and local polar order. Analytical SHG modeling is essential to connect experimental results to material properties, such as point group symmetry and SHG susceptibilities. However, complexity builds up when the crystal exhibits low symmetry, absorption, and consists of multiple interfaces. Thus, the SHG model in the literature involves many approximations, leading to a scattered dataset of reported SHG properties. Here, we have developed an open-source package called ♯SHAARP which derives analytical solutions and performs numerical simulations of reflected SHG from crystals with arbitrary symmetry group, orientation, complex and anisotropic linear dielectric tensors with frequency dispersion, a general SHG tensor, and any polarization state of the incident and SHG light. ♯SHAARP enables accurate SHG analysis of a broad range of materials.
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