I want to know the modes propagated given an antenna (espacilly the PIFA). I know it depends also on how you designed the source and the matching and others parameters. I want to know what a simulator can give concerning the modes.
Dear Zakka, that you gave concerns the simple case of rectangular patch filled up by air because this formula is used originally for rectangular waveguide and it's obtained by analytical method. But for modt of antennas like PIFA, you can't even theoretically forecast the propagated modes.For that I exposed the problem. also, it's so fifficult to estimate the modes regarding the fields layout.
With all my respect but I don't agree with all what you said. You were right about the theoretical formula but there is no need to forecast the propagated modes !! However the formula works for any resonant cavity (i.e. patch antenna) therefore u can use as you said a patch filled up with air with a PEC background and short circuit boundary conditions or you can design a PIFA implemented on the desired substrate with special boundary conditions where you will be able to calculate your resonant frequencies modes!!!
Thank you for the interest you give to my question. I think we can't apply the cavity model to a PIFA and therefore we can't use the formula because ther are no clear magnetic or electric walls in PIFA and the cavity interior is not homogenious.
I believe that you can use HFSS to know what propagating modes exist in your antenna. There is a tutorial on rectangular waveguide (I think) wher ANSOFT shows the settings to see the propagating modes.
HFSS can give you all you need about modes, like radiation pattern, scattering parameters and spatial distribution, in open (IE HFSS) and closed model.