Photon-ALP beam propagation from Mrk 501

The very high energy (VHE, E $>$ $100 \mathrm~{GeV}$) $\gamma$-ray observations offer a possibility of indirectly detecting the presence of axion-like particles (ALPs). The paper focuses on detecting photon-ALP oscillations on $\gamma$-ray spectra from distant sources in astrophysical magnetic fields. Strong evidence indicates that: (1) the photon-ALP oscillations can effectively decrease the photon absorption at energies of several tens of TeV -- caused by the extragalactic background light (EBL) -- to a level able to explain better the observational data; (2) the impact of magnetic-field models in photon-ALP beams crossing several magnetized media is significant. We revisit the expected signature for the photon-ALP oscillation effects on $\gamma-\gamma$ absorption in the TeV spectra of Mrk 501. The result issues that the photon-ALP beam propagation with mass $\mathrm{m_a}\sim10^{-10} eV$ and two-photon coupling constant $\begin{aligned}g_{a\gamma}\sim0.417\times10^{-11}GeV^{-1}\end{aligned}$ crossing reasonable magnetic field scenarios considered here can roughly reproduce the observed TeV $\gamma$-ray spectra for Mrk 501.