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</math>
where <math>k</math> is the [[wavenumber]], <math>\mathbf{I}</math> is the [[identity matrix]], and <math>\mathbf{r}</math> is the vector from the source dipole to the observation point. Evaluating the derivatives leads to the explicit form:
:<math>
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</math>
where <math>\hat{\mathbf{r}} = \mathbf{r} / |\mathbf{r}|</math> is the [[unit vector]] pointing from the source to the observation point.
This Green’s tensor describes the electric field generated by a dipole in a homogeneous medium. It is used to compute the off-diagonal blocks of the interaction matrix in DDA, that is, the interaction between distinct dipoles <math>j \ne k</math>. The singular self-term <math>\mathbf{G}(\mathbf{r} = 0)</math> is excluded and replaced by a prescribed local term involving the inverse polarizability tensor <math>\boldsymbol{\alpha}_j^{-1}</math>.
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