  The aim of this paper is to provide a mathematical and numerical framework
for the analysis and design of bubble meta-screens. An acoustic meta-screen is
a thin sheet with patterned subwavelength structures, which nevertheless has a
macroscopic effect on the acoustic wave propagation. In this paper, periodic
subwavelength bubbles mounted on a reflective surface (with Dirichlet boundary
condition) is considered. It is shown that the structure behaves as an
equivalent surface with Neumann boundary condition at the Minnaert resonant
frequency which corresponds to a wavelength much greater than the size of the
bubbles. Analytical formula for this resonance is derived. Numerical
simulations confirm its accuracy and show how it depends on the ratio between
the periodicity of the lattice, the size of the bubble, and the distance from
the reflective surface. The results of this paper formally explain the
super-absorption behavior observed in [V. Leroy et al., Phys. Rev. B, 2015].
