 Polynomial-source photon transport solution

For $\dot{\Delta }+ik\mu \Delta =2{\mu }^2\dot{h}$ with $\stackrel{...}{h}=0$ and $k\ne 0$, a particular solution is $B=-2i\mu \dot{h}/k+2\ddot{h}/k^2$. Differentiating it cancels its $\ddot{h}$ terms and gives the prescribed source. The homogeneous solution transports the initial condition with a direction-dependent Fourier phase. The inverse powers of $k$ need not signal a physical singularity: use the original source integral to take a long-wavelength limit consistently.