Applications:

   Half Waveplate
   When applying a linearly polarized beam to a half waveplate, it emerges as a linearly polarized beam but its polarization plane is rotated with respect to the polarization plane of the input beam. The rotation of the polarization plane is such that the angle between the input polarization and the output polarization is twice the angle between the input polarization and the waveplate's axis. When applying a circularly polarized beam, a clockwise circular polarization will transform into a counter-clockwise circular polarization and vice versa. Half waveplates are often used as continuously adjustable polarization rotators and as a variable ratio beamsplitter when used in conjunction with a polarization beamsplitter cube.
 
Quarter Waveplate
   When applying a linearly polarized beam with the polarization plane aligned at 45deg to the waveplate's principal plane, the output beam will be circularly polarized. Similarly when applying a circularly polarized beam to a λ/4 waveplate the output beam will be linearly 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 widely used in creating circular polarization from linear or linear polarization from circular, ellipsometry, optical pumping, suppressing unwanted reflection, optical isolation and etc.