  The intrinsic flux of very high energy (VHE, Energy > 100 GeV) gamma-rays
from extragalactic sources is attenuated due to pair production in the
interaction with photons of the extragalactic background light (EBL). Depending
on the distance of the source, the Universe should be opaque to VHE photons
above a certain energy. However, indications exist that the Universe is more
transparent than previously thought. A recent statistical analysis of a large
sample of VHE spectra shows that the correction for absorption with current EBL
models is too strong for the data points with the highest attenuation. An
explanation might be the oscillation of VHE photons into hypothetical
axion-like particles (ALPs) in ambient magnetic fields. This mechanism would
decrease the opacity as ALPs propagate unimpeded over cosmological distances.
  Here, a large sample of VHE gamma-ray spectra obtained with imaging air
Cherenkov telescopes is used to set, for the first time, lower limits on the
photon-ALP coupling constant over a large range of ALP masses. The conversion
in different magnetic field configurations, including intra-cluster and
intergalactic magnetic fields together with the magnetic field of the Milky
Way, is investigated taking into account the energy dependence of the
oscillations. For optimistic scenarios of the intervening magnetic fields, a
lower limit on the photon-ALP coupling of the order of
$10^{-12}\mathrm{GeV}^{-1}$ is obtained whereas more conservative model
assumptions result in $2\times10^{-11}\mathrm{GeV}^{-1}$. The latter value is
within reach of future dedicated ALP searches.
