Half Waveplate
The thickness of a half waveplate is such that the phase difference is 1/2-wavelength (true-zero order) or some multiple of 1/2-wavelength [(2n+1)l/2multiple order].

A linearly polarized beam incident on a half waveplate emerges as a linearly polarized beam but rotates such that its angle to the optical axis is twice that of the incident beam. Therefore, half waveplates can be used as continuously adjustable polarization rotators. Half waveplates are used in rotating the plane of polarization, electro-optic modulation and as a variable ratio beamsplitter when used in conjunction with a polarization cube.

Quarter Waveplate
The thickness of the quarter waveplate is such that the phase difference is 1/4 wavelength (l/4,true-zero order) or some multiple of 1/4 wavelength [(2n+1)l/2,multiple order].

If the angle q (between the electric field vector of the incident linearly polarized beam and the retarder principal plane) of the quarter waveplate is 45, the emergent beam is circularly polarized. When a quarter waveplate is double passed, i.e. by mirror reflection, it acts as a half waveplate and rotates the plane of polarization to a certain angle. Quarter waveplates are used in creating circular polarization from linear or linear polarization from circular, ellipsometry, optical pumping, suppressing unwanted reflection and optical isolation.