= Electromagnetic aperture angular spectrum
{title2=$\mathbf q=(\kappa,\nu,\eta),\quad\kappa=\sqrt{k^2-\nu^2-\eta^2}$}
For an aperture normal to $\mathbf e_x$, let $F_y,F_z$ be its tangential <electric field> traces extended by zero outside the aperture. With the outgoing branch of $\kappa$, the <Weyl plane-wave representation> and the curl aperture integral give a spectrum proportional to $(-(\nu\widehat F_y+\eta\widehat F_z)/\kappa,\widehat F_y,\widehat F_z)$. Each wave is transverse to $\mathbf q$. The longitudinal electric component is regenerated by oblique diffraction even when it vanishes at the input. For $G=e^{ikr}/(4\pi r)$ and a unit prefactor on the stated curl integral, the spectrum has an overall factor $1/2$; a doubled half-space Green kernel gives factor one. The normalization must follow the chosen Green kernel and equivalent-current convention.
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