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Recent detection of sub-TeV emission from gamma-ray bursts (GRBs) representsa breakthrough in the GRB study. The multi-wavelength data of the afterglows ofGRB 190114C support the synchrotron self-Compton (SSC) origin for its sub-TeVemission. We present a comparative analysis on the SSC emission of GRBafterglows in the homogeneous and wind environment in the framework of theforward shock model. The $\gamma\gamma$ absorption of very high-energy photonsdue to pair production within the source and the Klein-Nishina effect on theinverse-Compton scattering are considered. Generally a higher SSC flux isexpected for a larger circum-burst density due to a larger Compton parameter,but meanwhile the internal $\gamma\gamma$ absorption is more severer forsub-TeV emission. The flux ratio between the SSC component and the synchrotroncomponent decreases more quickly with time in the wind medium case than that inthe homogenous-density medium case. The light curves of the SSC emission arealso different for the two types of media. We also calculate the cascadeemission resulted from the absorbed high-energy photons. In the ISM environmentwith $n> 1\,\rm cm^{-3}$, the cascade synchrotron emission could be comparableto the synchrotron emission of the primary electrons in the optical band, whichmay flatten the optical afterglow light curve at early time ($t<1$ h). In thewind medium with $A_{\ast}> 0.1$, the cascade emission in the eV-GeV band iscomparable or even larger than the emission of the primary electrons at earlytime.

Very High Energy Emission and Cascade Radiation of Gamma-Ray Burst Afterglows: Homogeneous Versus Wind External Media