Fresnel propagator
= Fresnel propagator
{c}
{title2=$U_x=\exp(i x\Delta_\perp/(2k_0))$}
In two transverse dimensions, the <Fresnel propagator> has kernel $k_0(2\pi i x)^{-1}\exp(ik_0|\mathbf z-\mathbf z'|^2/(2x))$ for $x>0$. It evolves the homogeneous <parabolic wave equation>.