We report the complex dielectric function of high-quality AFe2As2, (A=Ca, Sr, Ba) single crystals with TN ≈ 150 K, 200 K, and 138 K, respectively, determined by broadband spectroscopic ellipsometry at temperatures 10 ≤ T ≤ 300 K and wavenumbers from 100 cm −1 to 52000 cm −1 . In CaFe2As2 we identify the optical spin-density-wave gap 2∆SDW ≈ 1250 cm −1 . The 2∆SDW/(kBTN) ratio, characterizing the strength of the electron-electron coupling in the spin-density-wave state, amounts to ≈ 12 in CaFe2As2, significantly larger than the corresponding values for the SrFe2As2 and BaFe2As2 compounds: 8.7 and 5.3, respectively. We further show that, similarly to the Ba-based compound, two characteristic SDW energy gaps can be identified in the infrared-conductivity spectra of both SrFe2As2 and CaFe2As2 and investigate their detailed temperature dependence in all three materials. This analysis reveals the existence of an anomaly in CaFe2As2 at a temperature T * ≈ 80 K, well below the Néel temperature of this compound, which implies weak coupling between the two SDW subsystems. The coupling between the two subsystems evolves to intermediate in the Sr-based and strong in the Ba-based material. The temperature dependence of the infrared phonons reveals clear anomalies at the corresponding Néel temperatures of the investigated compounds. In CaFe2As2, the phonons exhibit signatures of SDW fluctuations above TN and some evidence for anomalies at T * . Investigation of all three materials in the visible spectral range reveals a spin-density-wave-induced suppression of two absorption bands systematically enhanced with decreasing atomic number of the intercalant. A dispersion analysis of the data in the entire spectral range clearly shows that CaFe2As2 is significantly more metallic than the other two compounds. Our results single out CaFe2As2 in the class of ThCr2Si2-type iron-based materials by demonstrating the existence of two weakly coupled and extremely metallic electronic subsystems.