Hello Raj Hakani, mode that u said TM010 is used to define the first resonance, so if u want to design/analyze your antenna, first you can design on that mode.
Ok, i got it, we all know that the EM wave has it propagation on "x" axis and "y" axis, with "z" axis as a main direction on EM Wave, so TE100 and TM010 both are represent the first resonance of EM Wave inside the antenna.
usually for simple microstrip antenna the dominant mode is excited which include first mode. but for enhancing the performance of antenna you can excite other modes with proper techniques proportion with your application. for achieving the dimensions of microstrip antenna at specified frequency we refer to antenna book by balanis chapter 14.
Only TM modes are generated between the patch and the ground. That is, transverse to the Z-axis of the antenna. Because, the magnetic fields in patch antennas are always transverse to their Z-axis. So, we consider E-field along Z-direction and MF along X and Y directions.