When PMMA is exposed to plasma, a stochastic surface morphology forms under certain conditions. The surface shows a notable transmittance increase in the visible spectral region. Moreover, the technology is an inexpensive alternative to the deposition of interference coatings to increase the light transmission of polymeric optical elements. The principle of antireflective subwavelength structures is also known from the "moth's eye". This work is driven by the need to fabricate such broadband antireflective morphologies on arbitrary shaped surfaces of different kinds of polymers. Beside PMMA, three transparent thermoplasts were chosen to analyze the physical processes in order to understand the structure formation. The plasma-polymer interaction was supported by Monte Carlo method to investigate the energy transfer of the ions on the substrate. The optical effect of the structured surfaces has been optimized by the use of spectrophotometry. The structure formation has been analyzed by AFM and SEM. The revealed effective pin shape was correlated with the results from spectral reverse engineering. The structure formation has been established on the surface of the polymers and shows a self-organized nature, since the topography was not prescribed from outside before or during the process. The differences in size, shape, and antireflective effect are specific for the particular polymer. The structure formation results from a combination of physical sputter-erosion and chemical etching. Aspect ratios of the pin structure above 1 can only be explained by anisotropic etching due to impact of high energetic plasma-ions. The structure has been modeled as effective medium, which allows for the subsequent description by means of graded-index layers. The occurrence of scatter losses can be kept low and might be negligible for many applications. Particular PET surfaces show an industrially appropriate transmittance increase in the visible spectral region after plasma treatment.