Atmospheric muons are one of the main backgrounds for current Water- and Ice-Cherenkov neutrino telescopes designed to detect astrophysical neutrinos. The inclusive fluxes of atmospheric muons and neutrinos from hadronic interactions of cosmic rays have been extensively studied with Monte Carlo and cascade equation methods, for example, CORSIKA and MCEq. However, the muons that are pair produced in electromagnetic interaction of high energy photons are quantitatively not well understood. We present new simulation results and assess the model dependencies of the high-energy atmospheric muon flux including those from electromagnetic interactions, using a new numerical electromagnetic cascade equation solver EmCa that can be easily coupled with the hadronic solver MCEq. Both codes are in active development with the particular aim to become part of the next generation CORSIKA 8 air shower simulation package. The combination of EmCa and MCEq accounts for material effects that have not been previously included in most of the available codes. Hence, the influence of these effects on the air showers will also be briefly discussed.
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