This work reports on the optical properties of self-assembled InAs/GaAs quantum dots (QDs) grown by molecular beam epitaxy. A sigmoidal temperature-dependent variation of the bandgap energy of the dots is detected from the photoluminescence (PL) investigations of the studied sample. This sigmoidal dependence of the bandgap energy was accompanied by an anomalous increase in the integrated PL intensity (IPLI) over the temperature range of 10 K to 110 K. Such optical observations are related to the existence of deep localized states (LS) within the QD structure. To illustrate the presence of the LS, pump power-dependent PL measurements at different temperatures were performed. It is found that the sigmoidal dependence of the PL peak energy (PLPE) gradually converts into a monotonous variation with the gradual increase in the excitation density. These observations show a saturation behavior of a limited number of states within the bandgap of the QDs. Such optical results provide clear evidence for the existence of deep levels within the InAs dots.