Circular Polarization Condition of 2 Linearly Polarized Waves

[Problem]

Show the condition such that the total field of two linearly polarized waves with crossing angle becomes a circularly polarized wave, where A and B are complex numbers.

Figure

[Solution]

[Animation]

Example 1 (Circularly polarized wave)

An animation of the total field of A=ra exp(j a) and B=rb exp(j b) in the case that =30,ra=rb=1,a=0,b=+180

Circularly Polarization

Red : x'A (linear polarization along x' axis)
Green : y'B (linear polarization along y' axis)
Black : x'A+y'B (total field, circularly polarization)

Example 2 (Circularly polarized wave)

An animation of the total field of A=ra exp(j a) and B=rb exp(j b) in the case that =90,ra=rb=1,a=0,b=+180

Circularly polarized wave Circularly polarized wave

Example 3 (Elliptically polarized wave)

An animation of the total field of A=ra exp(j a) and B=rb exp(j b) in the case that =90,ra=1,rb=1/2,a=0,b=+180

Elliptically polarized wave
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