Waveplate - Half-wave Plate

Half-wave Plate

For a half-wave plate, the relationship between L, Δn, and λ₀ is chosen so that the phase shift between polarization components is Γ = π. Now suppose a linearly polarized wave with polarization vector is incident on the crystal. Let θ denote the angle between and, where is the vector along the waveplate's fast axis. Let z denote the propagation axis of the wave. The electric field of the incident wave is

where lies along the waveplate's slow axis. The effect of the half-wave plate is to introduce a phase shift term eiΓ = eiπ = −1 between the f and s components of the wave, so that upon exiting the crystal the wave is now given by

If denotes the polarization vector of the wave exiting the waveplate, then this expression shows that the angle between and is −θ. Evidently, the effect of the half-wave plate is to mirror the wave's polarization vector through the plane formed by the vectors and . For linearly polarized light, this is equivalent to saying that the effect of the half-wave plate is to rotate the polarization vector through an angle 2θ; however, for elliptically polarized light the half-wave plate also has the effect of inverting the light's handedness.