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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. 

Mid-infrared photothermal imaging is a novel chemical imaging modality that combines high sensitivity with enhanced spatial resolution. Subcellular features in fibroblast cells and tissues are imaged and analyzed with regards to their molecular structures without the need of exogenous fluorophores at a resolution that overcomes the diffraction limited spot size of the mid-infrared excitation beam. With a phase-sensitive lock-in detection scheme, changes in the thermal diffusion properties can be detected and can provide a complementary sample characterization.