Hello! Denis is saying correctly about modes which you want. As you know, your patch antenna is just like rectangular cavity due to short circuit and field lines. For circular ring patch antenna, you'll have to give more concern to your feeding techniques or transmission line. from the starting of design of antenna, first you've to modified your field equations and dispersion diagram for higher harmonics in case of circular ring antenna and the value of outer wall radius as well as eigen values for all modes, you'll have to set or fixed. Then you'll have use window to remove extra modes to get desired modes.

A circular patch antenna can be treated as a circular cavity and it supports modes which are perpendicular to the patch, as with a rectangular microstrip antenna. The first mode (TM11) produces a broadside radiation pattern. At higher frequencies, the second mode (TM21) get excited and this mode produce conical radiation pattern with lower gain.

Guys thanks for the replies. I know about patch antennas and the cavity model. I have been designing antennas for years see my profile. I am looking for specific help to enable me to set up a simple MathCad sheet that will enable me to plot the modes Ibrahim has eluded to. Am I right in thinking its a straight forward 1st kind Bessel function? TIA

Yes Bas it can be straightforward, you can consider only the electric field in the Z direction and the magnetic field in the X and Y direction and ignore the other components.  But it can also be very complicated.

yes you can generate higher order modes with modified feed as well as circular polarization