= Contracted nonlinear susceptibility notation
{title2=$jk\mapsto J\in\{xx,yy,zz,yz,zx,xy\}$}
For identical input frequencies, <intrinsic permutation symmetry of nonlinear susceptibility> makes the last two Cartesian indices symmetric. Store their six independent pairs as one index, so the quadratic response uses a three-by-six array $d_{iJ}$. In the convention $d_{ijk}=\chi^{(2)}_{ijk}/2$, the contracted input vector is $(A_x^2,A_y^2,A_z^2,2A_yA_z,2A_zA_x,2A_xA_y)^T$. The factors of two preserve the sum over both off-diagonal orderings. This bookkeeping does not assert the stronger <Kleinman symmetry> and does not change the tensor's physical order.
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