Depending on the side of the trap on which the laser is focused, the charge is going to be positive or negative, as demonstrated in Fig. 3. The phase distribution [Fig. 3, (a)-(b)] and the phase profile along the red circle [Fig. 3, (c)-(d)] are displayed when the mesa is positioned on the left side [Fig. 3 (a)-(c)] or right side [Fig. 3 (b)-(d)] of the excitation spot. It is interesting to note that this selective excitation scheme is compatible with the picture of the injection of a polariton fluid in the trap. The treatment of the polariton field as a propagating fluid has been recently highlighted in Ref. $^{18}$. It is also possible to select the value of the vortex charge, by tuning the excitation energy to be resonant with a state carrying another quantum number m . Figure 4 displays the interferogram [Fig. 4 (a)] and corresponding phase mapping [Fig. 4 (b)] of a ( n = 1 , m = +2) state [indicated with a dotted arrow in Fig. 1 (a)]. A trident-like dislocation is visible in the interferogram, resulting in a 4 π -phase shift around the core. All the measurement presented in this paper were performed in the low excitation den- sity regime. Increasing the pump power by three orders of magnitude (up to 3 . 2 kW/cm $^{2}$) allowed us to observe the effect of polariton-polariton interactions in the form of a blue-shift of the vortex state of the order of 120 µeV . A recent publication 19 investigated the effect of interactions on the size of a polariton vortex imprinted using an optical parametric oscillator (OPO) process, and reported a reduction of the vortex core diameter down to 3 µm when in- creasing the excitation density. On the range of excitation power used in our experiment, we never observed any change in the vortex core size. This result is consistent with Reference $^{19}$, as in our case, the size of the core is already limited to 3 µm by the confining potential, even in the low polariton density regime. Experiments are in progress to track this effect with mesas of different sizes and detunings. In conclusion, we have demonstrated the selective excitation of trapped polariton states in a patterned semiconductor microcavity. Thanks to the homodyne detection setup, the phase and the amplitude of the coherent polariton gas were directly visualized, and trapped polariton vortices were identified as a superposition of eigenstates of the quasi-circular traps. We have experimentally shown the selection of the vortex charge by tuning the excitation conditions. This work shows the essential role of engineered lateral confinement to tailor the wavefunction and the subsequent emission pattern of a resonantly excited exciton-polariton gas. This will possibly provide new exploitation schemes for polariton lasers which also have a cylindrical symmetry $^{20}$. 5