Simultaneously transmit LHCP and RHCP waves using two closely spaced patch antennas?
Having two patch antennas fed from single oscillator through Wilkinson power divider. First patch is LHCP, second patch is RHCP.
Distance between patch antennas is around free-space wavelength or greater.
What will happen to radiation pattern and power? Will LHCP/RHCP waves oexist or some disturbance occur?
[OSC] -> [power divider] -> [port1] [port2]
[port1] -> [LHCP patch]
[port2] -> [RHCP patch]
I think this is a pretty common thing to do. Lots of point to point wifi links use dual polarisation antennas. In fact it can actually be the same antenna so long as it has good isolation between the ports.
The question isn't clear. Do you assume both waves to be coherent?
In this case, both circular polarized waves are not orthogonal and will interfer, at least at the receiver. Ideally, the resulting wave is linear polarized.
Be careful, port to port isolation is not the same as polarization isolation. Polarization isolation is a useful technique when you want to transit two simultaneous signals and both can exist. It is like transmitting on vertical and horizontally polarized antennas.
If you are transmitting through a Wilkinson to two antennas (one RHCP and the other LHCP) you could be in for some interesting effects. The resulting polarization will depend on the rotational orientation of each antenna and any additional phase difference in the feed lines. You will end up with some elliptical polarization with the axial ratio and major axis probably in an unexpected direction. Sorting out what you have will be fun.
Ignore my previous reply. FvM and Azulykit are correct that the polorisations will combine to create something different.