Start from the definition of directive gain. It compares the power density an antenna produces in a given direction with the power density that would exist if the same total power were radiated equally in all directions:

\(G_d(\theta,\phi)=\dfrac{U(\theta,\phi)}{U_{av}}=\dfrac{4\pi U(\theta,\phi)}{P_{rad}}\)

The denominator, \(U_{av}=P_{rad}/4\pi\), is precisely the radiation intensity of a source that radiates uniformly over the whole sphere — an isotropic antenna. So the isotropic radiator is the reference built into the definition itself.

Why it is chosen even though it cannot exist. A truly isotropic radiator is physically impossible: any real antenna must have a null somewhere, a result of the boundary conditions on the fields (you cannot comb a sphere without a parting). But that does not matter, because the reference is only a normalising constant. Its virtues are that it is unambiguous, frequency-independent, polarisation-independent and identical for every author — which no real antenna is.

The units that follow. Gain referred to an isotropic radiator is written dBi, and it is the standard used in every antenna specification and link budget.

Why the other three fail as references.

Note that "infinitesimal dipole" and "elementary dipole" are two names for the same thing, so neither could be uniquely correct in any case — a useful elimination clue.

The conversion worth remembering.

\(G_{dBi}=G_{dBd}+2.15\)

because the half-wave dipole itself has 2.15 dBi of gain. Confusing the two references is the commonest error in practical link calculations.

Directive gain versus power gain. Directive gain uses radiated power in the denominator; power gain uses input power and therefore includes the radiation efficiency: \(G_p=\eta G_d\). Both are referred to the same isotropic standard.

Hence, the standard reference antenna is the isotropic antenna.