  We examine in a semiclassical framework the deflection function of strong
gravitational lensing, for static and spherically symmetric black holes,
endowed with a photon sphere. From a first-order WKB analysis near the maximum
of the Regge-Wheeler potential, we extract the real phase shifts from the
S-matrix elements and then we derive the associated semiclassical deflection
function, characterized by a logarithmic divergent behavior. More precisely,
using the complex angular momentum techniques, we show that the Regge poles and
the associated greybody factor residues, for a massless scalar field theory,
from which one can recover the black hole quasinormal complex frequencies as
well as the fluctuations of the high energy absorption cross section, play
naturally the role of critical parameters in the divergent behavior of the
semiclassical deflection function. For very high frequencies, we finally
recover the logarithmic part of the classical strong deflection limit, which
clarifies analytically the fundamental link between quasinormal modes and
strong gravitational lensing, suggested in recent works.
