The probe acts as a top loaded monopole antenna, which has only a Eu component with maximum value in the u = 90° plane.
With an increase in the substrate thickness, the probe length
increases, so that the magnitude of the Eu component increases, which
vectorially gets added to the Eu component of the patch.
So, total Eu is not equal to the Ef component of the patch, thereby increasing AR. Thus, for a thick low dielectric substrate, the impedance BW increases at the expense
of degradation in the AR.