[Problem]

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

[Solution]

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[Animation]

Example 1 (Circularly polarized wave)

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

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 θa) and B=rb exp(j θb) in the case that θ=90°,ra=rb=1,θa=0°,θb=θ+180°

• How to make the animation with Mathematica

Example 3 (Elliptically polarized wave)

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