This paper investigates, through the field enhancement factor, the increase of hydrogen adsorption around the interface between a layer of hydrogen and a periodic layered structure under different incidence angles of an applied transverse magnetic polarized electromagnetic field. This periodic layered structure is composed of n-binary unit cells based on alternating a thin layer of gold with a thin layer of a metamaterial with equal negative relative permittivity while the relative permeability of the first and the second material's unit cell is considered equal to 1 and -1, respectively. We apply the effective medium theory to replace this layered structure with a single slab of a homogeneous material with an effective permittivity tensor and an effective permeability tensor. We use the Transfer Matrix Method to analyze the reflectivity spectra at the hydrogen/slab interface for adjustable layers’ thicknesses and then we derive the field enhancement factor. We obtain a significant increase of the field enhancement factor of the structure in comparison with the field enhancement factor around the interface between a layer of hydrogen and a structure composed of one gold layer.