  We consider a wide class of static spherically symmetric black holes of
arbitrary dimension with a photon sphere (a hypersurface on which a massless
particle can orbit the black hole on unstable circular null geodesics). This
class includes various spacetimes of physical interest such as Schwarzschild,
Schwarzschild-Tangherlini and Reissner-Nordstr\"om black holes, the canonical
acoustic black hole or the Schwarzschild-de Sitter black hole. For this class
of black holes, we provide general analytical expressions for the Regge poles
of the $S$-matrix associated with a massless scalar field theory. This is
achieved by using third-order WKB approximations to solve the associated radial
wave equation. These results permit us to obtain analytically the nonlinear
dispersion relation and the damping of the "surface waves" lying close to the
photon sphere as well as, from Bohr-Sommerfeld-type resonance conditions,
formulas beyond the leading order terms for the complex frequencies
corresponding to the weakly damped quasinormal modes
