Rotation¶

Type:: Rotation
Range:: [SO(3)]
Default:: -/-
Appearance:: optional

The Rotation parameter defines a coordinate transformation applied to the NonLinearSusceptibility tensor. We define the rotation matrix $\TField{R}$ which transforms the laboratory frame (the internal coordinate system of the linear JCM-fieldbag) to the crystal’s principal axis system (crystalline coordinates). For example of second-order nonlinear process, the NonLinearPolarization in laboratory frame is defined as:

$\begin{alignat*}{1} \TField{p}^{(2)} & = \TField{R}^{-1} \TField{p}^{(2)'}, \end{alignat*}$

where

$\begin{alignat*}{1} \TField{p}^{(2)'}_i & = \epsilon_0 \sum_{j,k} \chi_{ijk}(\TField{R}\TField{E}^{1})_{j}(\TField{R}\TField{E}^{2})_{k} \end{alignat*}$

is the NonLinearPolarization in crystalline coordinates, and $\TField{E}^{1}$ and $\TField{E}^{2}$ are the computed linear fields.