Abstract: I discuss two wave propagation problems that arise in connection with axion search experiments, which can be solved by both Green's function and wave matching methods. The first (arXiv:0611267) is a calculation of the vacuum-polarization induced ellipticity acquired by a laser beam traversing a magnetic field rotating with a small angular velocity around the beam axis. I show that there are only two sidebands, displaced by twice the magnetic field rotation frequency, and that the acquired ellipticity is independent of the magnetic field rotation. The second (arXiv:0801.4739) is a detailed analysis of "light shining through a wall experiments", retaining a nonzero axion mass. When the photon frequency is very close to the axion mass, there is a threshold cusp which significantly enhances the photon to axion conversion amplitude, relative to the corresponding axion to photon conversion process. For zero axion mass, the enhancement factor reduces to unity and the results of previous calculations are recovered.