Although we determine the size of the microstrip antenna for a single frequency, why it seems to have a resonance frequency on more than one frequency? Is there an antenna function at each oscillating frequency?
Microstrip antennas are usually designed to operate at their lowest resonant frequency. For simple shapes this is the half-wave resonance. It will resonante for 1/2, 3/2, 5/2 etc. wavelengths, so there are an infinite number of resonant frequencies, which will all have different patterns. Look in a book for the behaviour of a wire dipole antenna. It is similar.
Due to harmonic frequency property, it resonant also on 2f_o, 3f_o. 4f_o .....but radiation pattern for the harmonic resonants will be completly different than your desired ones. And TE/TM mood will be different also.