  The Pierre Auger Observatory is the most sensitive instrument to detect
photons with energies above $10^{17}$ eV. It measures extensive air showers
generated by ultra high energy cosmic rays using a hybrid technique that
exploits the combination of a fluorescence detector with a ground array of
particle detectors. The signatures of a photon-induced air shower are a larger
atmospheric depth of the shower maximum ($X_{max}$) and a steeper lateral
distribution function, along with a lower number of muons with respect to the
bulk of hadron-induced cascades. In this work, a new analysis technique in the
energy interval between 1 and 30 EeV (1 EeV = $10^{18}$ eV) has been developed
by combining the fluorescence detector-based measurement of $X_{max}$ with the
specific features of the surface detector signal through a parameter related to
the air shower muon content, derived from the universality of the air shower
development. No evidence of a statistically significant signal due to photon
primaries was found using data collected in about 12 years of operation. Thus,
upper bounds to the integral photon flux have been set using a detailed
calculation of the detector exposure, in combination with a data-driven
background estimation. The derived 95% confidence level upper limits are
0.0403, 0.01113, 0.0035, 0.0023, and 0.0021 km$^{-2}$ sr$^{-1}$ yr$^{-1}$ above
1, 2, 3, 5, and 10 EeV, respectively, leading to the most stringent upper
limits on the photon flux in the EeV range. Compared with past results, the
upper limits were improved by about 40% for the lowest energy threshold and by
a factor 3 above 3 EeV, where no candidates were found and the expected
background is negligible. The presented limits can be used to probe the
assumptions on chemical composition of ultra-high energy cosmic rays and allow
for the constraint of the mass and lifetime phase space of super-heavy dark
matter particles.
