TeV photons from extragalactic sources are absorbed in the intergalactic medium and initiate electromagnetic cascades. These cascades offer a unique tool to probe the properties of the universe at cosmological scales. We present a new Monte Carlo code dedicated to the physics of such cascades. This code has been tested against both published results and analytical approximations, and is made publicly available. Using this numerical tool, we investigate the main cascade properties (spectrum, halo extension, time delays), and study in detail their dependence on the physical parameters (extra-galactic magnetic field, extra-galactic background light, source redshift, source spectrum and beaming emission). The limitations of analytical solutions are emphasised. In particular, analytical approximations account only for the first generation of photons and higher branches of the cascade tree are neglected.
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