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1. Optical second harmonic generation in anisotropic multilayers with complete multireflection of linear and nonlinear waves using ♯SHAARP.ml package

   https://doi.org/10.1038/s41524-024-01229-2  

   Zu, Rui; Wang, Bo; He, Jingyang; Weber, Lincoln; Saha, Akash; Chen, Long-Qing; Gopalan, Venkatraman (March 2024, npj Computational Materials)

   Abstract Optical second harmonic generation (SHG) is a nonlinear optical effect widely used for nonlinear optical microscopy and laser frequency conversion. Closed-form analytical solution of the nonlinear optical responses is essential for evaluating materials whose optical properties are unknown a priori. A recent open-source code, ♯SHAARP.si, can provide such closed form solutions for crystals with arbitrary symmetries, orientations, and anisotropic properties at asingleinterface. However, optical components are often in the form of slabs, thin films on substrates, and multilayer heterostructures with multiple reflections of both the fundamental and up to ten different SHG waves at each interface, adding significant complexity. 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 in Multilayers (♯SHAARP.ml). The reliability and accuracy are established by experimentally benchmarking with both the SHG polarimetry and Maker fringes using standard and commonly used nonlinear optical materials as well as twisted 2-dimensional heterostructures. 

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2. Prediction of Large Second Harmonic Generation in the Metal-Oxide/Organic Hybrid Compound CuMoO3(p2c)

   https://doi.org/10.3390/sym14040824  

   Yang, Tingting; Huang, Xueli; Cheng, Xiyue; Maggard, Paul A.; Whangbo, Myung-Hwan; Luan, Chengkai; Deng, Shuiquan (April 2022, Symmetry)

   Noncentrosymmetric hybrid framework (HF) materials are an important system in discovering new practical second-order nonlinear optical materials. We calculated the second harmonic generation (SHG) response of a noncentrosymmetric (NCS) organic–inorganic HF compound, CuMoO3(p2c) (p2c = pyrazine-2-carboxylate) to find that it exhibits the largest SHG response among all known NCS HF materials with one-dimensional helical chains. Further atom response theory analysis revealed that the metal atoms Cu and Mo contribute much more strongly than do nonmetal atoms in determining the strength of the SHG response, which is a novel example in nonlinear optical materials known to date. 

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3. Generalized analytical and numerical modeling of optical second harmonic generation in anisotropic crystals and complex heterostructures using ♯SHAARP package

   https://doi.org/10.1117/12.2676223  

   Zu, Rui; Wang, Bo; He, Jingyang; Weber, Lincoln; Wang, Jianjun; Chen, Long-Qing; Gopalan, Venkatraman (October 2023, SPIE)

   Liu, Zhiwen; Psaltis, Demetri; Shi, Kebin (Ed.)

   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. 

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4. Second-harmonic optical vortex conversion from WS2 monolayer

   https://doi.org/10.1038/s41598-019-45424-4  

   Dasgupta, Arindam; Gao, Jie; Yang, Xiaodong (June 2019, Scientific Reports)

   Abstract Wavelength, polarization and orbital angular momentum of light are important degrees of freedom for processing and encoding information in optical communication. Over the years, the generation and conversion of orbital angular momentum in nonlinear optical media has found many novel applications in the context of optical communication and quantum information processing. With that hindsight, here orbital angular momentum conversion of optical vortices through second-harmonic generation from only one atomically thin WS₂monolayer is demonstrated at room temperature. Moreover, it is shown that the valley-contrasting physics associated with the nonlinear optical selection rule in WS₂monolayer precisely determines the output circular polarization state of the generated second-harmonic vortex. These results pave the way for building future miniaturized valleytronic devices with atomic-scale thickness for many applications such as chiral photon emission, nonlinear beam generation, optoelectronics, and quantum computing. 

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5. Large exchange-driven intrinsic circular dichroism of a chiral 2D hybrid perovskite

   https://doi.org/10.1038/s41467-024-46851-2  

   Li, Shunran; Xu, Xian; Kocoj, Conrad A.; Zhou, Chenyu; Li, Yanyan; Chen, Du; Bennett, Joseph A.; Liu, Sunhao; Quan, Lina; Sarker, Suchismita; et al (March 2024, Nature Communications)

   Abstract In two-dimensional chiral metal-halide perovskites, chiral organic spacers endow structural and optical chirality to the metal-halide sublattice, enabling exquisite control of light, charge, and electron spin. The chiroptical properties of metal-halide perovskites have been measured by transmissive circular dichroism spectroscopy, which necessitates thin-film samples. Here, by developing a reflection-based approach, we characterize the intrinsic, circular polarization-dependent complex refractive index for a prototypical two-dimensional chiral lead-bromide perovskite and report large circular dichroism for single crystals. Comparison with ab initio theory reveals the large circular dichroism arises from the inorganic sublattice rather than the chiral ligand and is an excitonic phenomenon driven by electron-hole exchange interactions, which breaks the degeneracy of transitions between Rashba-Dresselhaus-split bands, resulting in a Cotton effect. Our study suggests that previous data for spin-coated films largely underestimate the optical chirality and provides quantitative insights into the intrinsic optical properties of chiral perovskites for chiroptical and spintronic applications. 

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