Quantum dots (QDs) have a potential for application in semiconductor optical amplifiers (SOAs), due to their high saturation power related to the low differential gain, fast gain recovery and wide gain spectrum compared to quantum wells. Besides all advantages, QDs realized by Stranski-Krastanov growth mode have a flat shape which leads to a gain anisotropy and a related transverse magnetic (TM) and -electric (TE) polarization dependence as compared to bulk material. This has so far prevented their applications in SOAs. It has been suggested that control of optical polarization anisotropy of the QD can be obtained through QD shape engineering, in closely stacked or columnar QDs (CQDs). To this aim, we have fabricated and tested SOA structures based on closely-stacked and columnar QDs. Closely-stacked InAs QDs with 4, 6 and 10 nm GaAs spacer showed a minor improvement in the ratio of TM and TE integrated electroluminescence (EL) over standard QDs along with a strong reduction in efficiency. In contrast, a large improvement was obtained in CQDs, depending on the number of stacked submonolayers which can be attributed to the more symmetric shape of columnar QDs. A relatively small spectral separation (Delta E similar to 21 meV) between TE- and TM-EL peaks has been observed showing that heavy- and light hole-like states, respectively are energetically close in these QDs. These results indicate that columnar QDs have a significant potential for polarization-independent QD SOA.