ArticleThe Journal of chemical physics2022
Neumann's principle based eigenvector approach for deriving non-vanishing tensor elements for nonlinear optics.
Article in The Journal of chemical physics, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed, 7 citations in OpenAlex.
- Cross-polarized and stable second harmonic generation from monocrystalline copper.Nanophotonics (Berlin, Germany) · 2025Article
- Quantifying the photocurrent fluctuation in quantum materials by shot noise.Nature communications · 2024Article
- Multimodal Nonlinear Hyperspectral Chemical Imaging Using Line-Scanning Vibrational Sum-Frequency Generation Microscopy.Journal of visualized experiments : JoVE · 2023Article
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2 authors at 1 institution in 1 country.
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Abstract
Physical properties are commonly represented by tensors, such as optical susceptibilities. The conventional approach of deriving non-vanishing tensor elements of symmetric systems relies on the intuitive consideration of positive/negative sign flipping after symmetry operations, which could be tedious and prone to miscalculation. Here, we present a matrix-based approach that gives a physical picture centered on Neumann's principle. The principle states that symmetries in geometric systems are adopted by their physical properties. We mathematically apply the principle to the tensor expressions and show a procedure with clear physical intuition to derive non-vanishing tensor elements based on eigensystems. The validity of the approach is demonstrated by examples of commonly known second and third-order nonlinear susceptibilities of chiral/achiral surfaces, together with complicated scenarios involving symmetries such as D
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