In a paper by Lu-Ming Duan and Guang-Can Guo, they develop an alternative approach to quantising the EM field in a nonlinear and inhomogeneous media. In this derivation, they use the holo-exchange symmetry of the tensor $\chi^{(2)}$ in the expansions of the $\vec{D}$ and $\vec{B}$ fields. This is done so that only the terms with the subscript $|\vec{k}|$=$k_i$ contribute to the interaction, which simplifies the expression. I have never heard of this symmetry, so I was wondering if anyone could tell what it means?

The paper is linked here: http://cds.cern.ch/record/316020/files/9612009.pdf

  • $\begingroup$ It's currently unclear what exactly this question is asking without clicking on the link you provided. To make questions more accessible and guard against link rot, please include all relevant information, such as the explanation of notation or specific terminology used, in your question. Please also mention author and title of papers you cite so the source can be reconstructed if the link rots. $\endgroup$ – ACuriousMind May 25 at 9:32
  • $\begingroup$ According to google & ddgo, the phrase "holo-exchange symmetry" is unique to that paper :-). I can only guess that they mean that given a chi-2 tensor that takes electric field $E^\alpha$ and gives the polarization $P^\alpha$: $P^\alpha=\chi^{\left(2\right)\alpha}_{\beta\gamma}E^\beta E^\gamma$, it must be that $\chi^{\left(2\right)\alpha}_{\beta\gamma}=\chi^{\left(2\right)alpha}_{\gamma\beta}$. This of course is a simplified case, more complications can arise, e.g. due to dispersion etc. $\endgroup$ – Cryo May 25 at 10:44

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