Magnetic fields that are relic of epochs right after the Big Bang can still reside in the low density regions of the Large Scale Structure, between galaxies and galaxy clusters. Detection of these fields and measurement of their properties might provide a valuable “window” on physical processes that have operated in the Early Universe a fraction of a second after the Big Bang. Such measurement is possible with the methods of gamma-ray and radio astronomies, using new observational facilities: gamma-ray Cherenkov Telescope Array (CTA) and radio Square Kilometer Array (SKA). The gamma-ray measurement technique is based on the observation of extended glow around distant extragalactic sources produced by electromagnetic cascade developing along the gamma-ray beam during its propagation through the intergalactic medium. Radio technique is based on the observation of Faraday rotation of the polarised radio signal through the intergalactic medium. The goal of the internship and thesis is to develop realistic numerical models of the extended gamma-ray glow and radio Faraday rotation measure for extragalactic sources that will be observed by CTA and SKA and to apply these models to the data of the prototypes and precursors of the CTA and SKA that are starting data taking.