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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