Vertically stacked InAs/InP columnar quantum dots (CQDs) for polarization insensitive semiconductor amplifier in telecommunications applications are studied theoretically. An axial model is used to predict mechanical, electronic, and optical properties of these CQDs. A crossover from a dominant transverse electric (TE) optical ground state absorption to a dominant transverse magnetic (TM) absorption is predicted for a number of layers equal to about 9 in good agreement with the experiment. The weight of the light hole component of the valence band ground state increases as a function of the number of layers. The change of the TE/TM polarization ratio is also associated to a symmetry change of the heavy hole component. A modification of the aspect ratio of the CQD seems to be the most important factor to explain the change of the electronic states configuration as a function of the strain distribution.