Distinct photon-ALP propagation modes

The detection of ultra high energy gamma-rays provides an opportunity to explore the existence of ALPs at the multi-hundred TeV and PeV energy scales. We discover that we can employ analytic methods to investigate the propagation of photon-ALP beams in scenarios where the energy of photons $\omega \geq 100$ TeV. Our analytical calculations uncover the presence of two distinct modes of photon propagation resulting from the interplay between ALP-photon mixing and attenuation effects. Next, we analyze observable quantities such as the degree of polarization and survival probability in these two modes. We determine the conditions under which a significant polarization effect can be observed and identify the corresponding survival probability. Finally, we extend our analytic methods to cover the energy range of $10^{-3}$ to $10^4$ GeV and analyze the influence of ALPs on the experimental signals.Comment: 19 pages, 8 figure