We have previously shown that doping silicon with sulfur via femtosecond- laser irradiation leads to near-unity absorption of radiation from ultraviolet wavelengths to below band gap short-wave infrared wavelengths. Here, we demonstrate that doping silicon with two other group VI elements (chalcogens), selenium and tellurium, also leads to near-unity broadband absorption. A powder of the chalcogen dopant is spread on the silicon substrate and irradiated with femtosecond-laser pulses. We examine and compare the resulting morphology, optical properties, and chemical composition for each chalcogen-doped substrate before and after thermal annealing. Thermal annealing reduces the absorption of below-band gap radiation by an amount that correlates with the diffusivity of the chalcogen dopant used to make the sample. We propose a mechanism for the absorption of below band gap radiation based on defects in the lattice brought about by the femtosecond laser irradiation and the presence of a supersaturated concentration of chalcogen dopant atoms. The selenium and tellurium doped samples show particular promise for use in infrared photodetectors as they retain most of their infrared absorptance even after thermal annealinga necessary step in many semiconductor device manufacturing processes.