The modelling of intermediate-age stellar populations: I- near-infrared properties

In this paper, we discuss how the integrated properties of intermediate-age single burst population, especially in the near-infrared, behave as a function of age and metallicity. Our models take into account all stellar evolutionary phases that affect the evolution of the integrated optical and near-infrared spectrum of such a population. Particular care was dedicated to the Asymptotic Giant Brach stars, which can be dominant at near-infrared wavelengths. First we present new synthetic model that takes into account the relevant physical processes that control the evolution through the thermally pulsing AGB. In the isochrone presented in this paper the lifetime and the nature of the AGB stars are established as consequences of the interplay between the physical processes that control the AGB star evolution. The contribution of these stars to the integrated light of the population is thus obtained in a consistent way. We optimize our models by using a new stellar library that explicitly takes into account the spectral features thar characterize only AGB stars in comparison to other cool and luminous stars (abriged)