An antenna (3) of an electromagnetic probe used in investigation of geological formations GF surrounding a borehole WBH comprises a conductive base (31) and an antenna element (32). The conductive base (31) comprises an opened non-resonant cavity (33). The antenna element (32) is embedded in the cavity (33) and goes right through the cavity. The antenna element (32) is isolated from the conductive base (31). The antenna element (32) is coupled to at least one electronic module via a first 34A and a second 34B port, respectively. The electronic module operates the antenna so as to define a simultaneously superposed pure magnetic dipole and pure electric dipole.