Waveplate - Quarter-wave Plate

Quarter-wave Plate

For a quarter-wave plate, the relationship between L, Δn, and λ₀ is chosen so that the phase shift between polarization components is Γ = π/2. Now suppose a linearly polarized wave is incident on the crystal. This wave can be written as

where the f and s axes are the quarter-wave plate's fast and slow axes, respectively, the wave propagates along the z axis, and E_f and E_s are real. The effect of the quarter-wave plate is to introduce a phase shift term eiΓ =eiπ/2 = i between the f and s components of the wave, so that upon exiting the crystal the wave is now given by

The wave is now elliptically polarized.

If the axis of polarization of the incident wave is chosen so that it makes a 45° with the fast and slow axes of the waveplate, then E_f = E_s ≡ E, and the resulting wave upon exiting the waveplate is

and the wave is circularly polarized.