= Spectral acoustic flux
{title2=$I_x(\nu)$}
With the time convention $e^{-i\omega t}$, pressure amplitude $p$ and background density $\rho_0$, the <acoustic energy flux> is $I_x=(2\rho_0\omega)^{-1}\operatorname{Im}(\overline p\,\partial_xp)$. A transverse <plane wave> mode with positive axial <wavenumber> $\kappa$ carries flux $\kappa|p|^2/(2\rho_0\omega)$. For the reduced pressure $p=e^{ikx}E$, the <parabolic wave equation> gives $\kappa=k-\nu^2/(2k)$, approximated by $k$ at leading paraxial order. Stationary illumination uses the <infinite-aperture spectral normalization>: replace $|p|^2$ by the corresponding spectral power per unit transverse length. Other acoustic amplitude conventions change the dimensional prefactor.
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