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# math formulation of phase difference between two linear polarization

#### yefj

Hello , I Have two linear polarizations wave propagates at z direction. one in 90 degree Y direction an the other in 180 degrees -X.
So there is a phase of 90 degrees between my polarization.
Why its not considered to be circular polarizar then?
Thanks.

If you can write your superposition like this:

then it can be written as:

so if you pick a fixed position as an observer like z=0, then you have:

And above expression shows that the direction of the electric field is rotating with time, therefore it is a circularly polarized plane wave.

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Hello , I Have two linear polarizations wave propagates at z direction. one in 90 degree Y direction an the other in 180 degrees -X.
So there is a phase of 90 degrees between my polarization.
Why do you say "so"? Phase shift between waves is an additional property and has nothing to do with oscillation plane. If both wave have additionally a phase difference, you get circular polarization, otherwise it's still linear, e.g. 135 degree if both waves wave equal magnitude.