Discussion Overview
The discussion revolves around the calculation of the second hyperpolarizability tensor "\beta" for a compound with D(3) symmetry, specifically focusing on how this tensor transforms under coordinate rotations about the z-axis. The conversation includes theoretical considerations related to tensor transformations in the context of nonlinear optics (NLO).
Discussion Character
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant seeks clarification on the transformation rule for the second hyperpolarizability tensor "\beta" when the coordinate system is rotated, drawing a parallel to the transformation of the polarizability tensor "\alpha".
- Another participant proposes a transformation rule for the rank-3 tensor "\beta", suggesting that it can be expressed as \(\beta'_{ijk}=\sum_{mnp}\beta_{mnp}T_{mi}T_{nj}T_{pk}\), and notes that this can be generalized to tensors with different numbers of indices.
- A participant expresses uncertainty regarding the classification of the indices of the tensor "\beta" as contravariant or covariant, indicating difficulty in finding resources that clarify this aspect.
- There is a request for a specific equation involving the electric field \(E\) and polarization \(P\) to better understand how the indices transform, suggesting a relationship involving both the polarizability and hyperpolarizability tensors.
Areas of Agreement / Disagreement
Participants generally agree on the transformation approach for the hyperpolarizability tensor, but there is uncertainty regarding the classification of the indices as contravariant or covariant, indicating that this aspect remains unresolved.
Contextual Notes
The discussion highlights a lack of consensus on the classification of tensor indices, with participants noting the absence of clear resources on this topic in the literature.