  High energy gamma-ray emission from two nearby bright starburst galaxies, M82 and NGC 253, have recently been detected by Fermi, H.E.S.S., and VERITAS. Since starburst galaxies have a high star formation rate and plenty of dust in the central starburst region, infrared emissions are strong there. Gamma-ray photons are absorbed by the interstellar radiation field photons via electron and positron pair creation. The generated electron and positron pairs up scatter the interstellar photons to very high energy gamma-ray photons via cascade emission through inverse Compton scattering. In this paper, we evaluate the contribution of this cascade emission to the gamma-ray spectra of M82 and NGC 253. Although it would be difficult to see direct gamma- ray evidence of cosmic-rays with an energy > 10 TeV due to the gamma-ray attenuation, the resulting cascade emission would be indirect evidence. By including the cascade component, we find that the total flux above 1 TeV increases ~18% and ~45% compared with the absorbed flux assuming the maximum kinetic proton energy as 45.3 TeV and 512 TeV, respectively. Future gamma-ray observatories such as CTA would be able to see the indirect evidence of cosmic-ray with an energy > 10 TeV by comparing with theoretical emission models including this cascade effect. 
High Energy Gamma-ray Absorption and Cascade Emission in Nearby   Starburst Galaxies