RHCP signal to a LHCP receiver

[xz4chx]

My electrical engineering teacher had us do a research project, and i decided to do my on the effects of polarized electric fields and antennas. I was reading that RHCP signals have no effect on LHCP antenna receivers. When i sent my paper to my teacher, he told me that i had to prove this theory. So i went searching around the internet but could not find a solid math theory or explanation why this is true. I was wondering if someone could either guide me on how to prove this or give me a reference that shows the math of why this is true.

Thank you for your time and help.

 

[berkeman]

Since this is your schoolwork project, you need to show us what you have done so far. What are typical configurations for antennas that use circular polarization? What are some of the equations that you use to analyze antennas? Do you have access to any antenna simulation software?

 

[xz4chx]

No antenna software. As for equations I have in polar form that one wave would be

Your RHCP wave would be

X direction would be Ae^(-jkz)
Y direction would be Ae^(-jkz-(∏/2))

And the wave it would accept would be (LHCP)

X direction would be Ae^(-jkz)
Y direction would be Ae^(-jkz+(∏/2))

I understand that an antenna will radiate a RHCP signal in the positive z direction, and LHCP in the negative z direction.

The only thing I see is if you added the two equations together you would get rid of the Y component since they are out of phase by PI.

So why would a LHCP antenna only accept LHCP but RHCP have no effect on the antenna? Does it have something to do with the Y component cancelling each other out?

I know for the antenna you are suppose to make the length of one transmission line long enough to be 90 degrees out of phase with the other line giving the RHCP or LHCP antenna.
βL1-βL2 = ∏/2