I understand the shape of the dipole antenna, but how is it fed so that the current only flows through one direction during the half cycle? Even in a normal pole antenna, is there a ground at the edge of the antenna so that there is a potential difference?
A1: It doesn't flow through one direction during the half cycle, it's AC.
"Normal pole antenna" - what kind is this antenna? Perhaps you meant quarter wavelength antenna?
A2: The current flows through air due to the capacitance, from one half to the another half of the antenna - for a dipole.
For a quarter length, the ground acts as the second part of the antenna, therefore the coax is grounded at the antenna. A dipole antenna has to use BALUN transformer if fed from coax.