The growth of InAs columnar quantum dots (CQDs) on GaAs substrates by molecular beam epitaxy was investigated. The CQDs were formed by depositing a 1.8 monolayer (ML) InAs seed dot layer and a short period GaAs/InAs superlattice (SL). It was found that the growth of the CQDs is very sensitive to growth interruption (GI) and growth temperature. Both longer GI and higher growth temperature impact the size dispersion of the CQDs, which causes the broadening of photoluminescence (PL) spectrum and the presence of the additional PL peak tails. By properly choosing the GI and the growth temperature, CQDs including GaAs (3 ML)/InAs (0.62 ML) SL with period number up to 35 without plastic relaxation were grown. The corresponding equivalent thickness of the SL is 41 nm which is two times higher than the theoretical critical thickness of the strained InGaAs layer with the same average In composition of 16%. The increase of the critical thickness is partially associated with the formation of the CQDs. Based on a five-stack CQD active region, laser diodes emitting around 1120 nm at room temperature were demonstrated, indicating a high material quality. CQDs with nearly isotropic cross section (20 nm×20 nm dimensions) were formed by depositing a 16-period GaAs (3 ML)/InAs (0.62 ML) SL on an InAs seed dot layer, indicating the feasibility of artificial shape engineering of QDs. Such a structure is expected to be very promising for polarization insensitive device applications, such as semiconductor optical amplifiers.