Microstrip antennas resemble dielectric loaded cavity [two PEC walls (top and bottom) and four PMC sidewalls] and they exhibit higher order resonances. Through cavity model analysis, we can get field distribution and cutoff frequency of different mode.
For all patch antennas, we have h«L and h«W,
If L>W>h, the dominant mode is TM 010 mode
If L>W>L/2>h, the second order mode is TM 001 mode
If L>L/2>W>h, the second order mode is TM 020 mode
Use the Field Equivalent Principle (Huygens' Principle), microstrip patch is represented by an equivalent electric current density Jt at the top(there is also current density Jb at the bottom of the patch which is not need). The four side slots are represented by the equivalent electric density Js and magnetic current density Ms:
Js=n x Ha and Ms=n x Ea
where n is the unity vector normal to each side wall, Ha and Ea represent magnetic field and electric field at the sidewalls.
Because microstrip antenna has very small height-to-width ratio, the current density Jt at the top is much smaller than the current density Jb at the bottom, it is assumed it is negligible here and it will be set to zero. Also it was argued that the tangential magnetic fields along the edge of the patch are very small, ideally zero. Therefore the corresponding equivalent electric current density Js will be very small (ideally zero), and it was set to zero here.
Thus the only nonzero current density is the equivalent magnetic current density Ms of four sidewalls. Through my attached figure of field distribution, you can get the magnetic current density at each sidewall, and you will understand why only L contribute to radiating, that is why we call these two radiating slots. while other two will contribute to the imaginary part of the imput impedance.
Best Regards,