Dual-polarized weather radars are gaining popularity due to their promise of accurate and faster weather prediction. This work presents the design of a dual-polarized, patch antenna element operating in the band 2.7 GHz - 3.0 GHz, with 30 dB isolation between the ports, which can be utilized for a dual-pol weather radar array. To characterize current design for weather radar, recently published parameters called W-parameters, have been evaluated for the demonstrated antenna hardware. Certain other properties of these W-parameters have also been studied. In the process of reaching a low cross-pol design, basic mechanism of cross-polar radiation in rectangular patch antennas has also been analyzed using a novel strategy of near-field analysis. This near field analysis has been further applied on slotted antennas to understand their radiation properties. New strategy of understanding the radiation properties based on the near-field provides visualization based understanding of the radiation mechanism in small antennas.