Waveplates (retardation plates or phase shifters) are made frommaterials which exhibit birefringence. The velocities of theextraordinary and ordinary rays through the birefringent materialvaries inversely with their refractive indices. This difference invelocities gives rise to a phase difference when the two beamsrecombine. In the case of an incident linearly polarized beam thisis given by α=2πd(ne-no)/λ, where α is phase difference; d isthickness of waveplate; ne, no are refrective indices ofextraordinary and ordinary rays respectively; λ is wavelength. Atany specific wavelength the phase difference is governed by thethickness of the retarder.

λ/ 2 Waveplates
The thickness of a half waveplate is such that the phase differenceis 1/2-wavelength (λ/2, true zero order) or certain multiple of1/2-wavelength ((2n 1)λ/2, multiple order).
A linearly polarized beam incident on a half waveplate emerges as alinearly polarized beam but rotated such that its angle to theoptical axis is twice that of the incident beam. Therefore,half-waveplates can be used as continuously adjustable polarizationrotators. Half-waveplates are used to rotate the plane ofpolarization, electro-optic modulation and as a variable ratiobeamsplitter when used in conjunction with a polarization cube.

λ/ 4 Waveplates
The thickness of the quarter waveplate is such that the phasedifference is 1/4-wavelength (λ/4, true zero order) or certainmultiple of 1/4-wavelength ((2n 1)λ/4, multiple order).

If the angle θ (between the electric field vector of theincident linearly polarized beam and the retarder principal plane)of the quarter waveplate is 45 degree , the emergent beam isircularly polarized. When a quarter waveplate is double passed,i.e. by mirror reflection, it acts as a half waveplate and rotatesthe plane of polarization to certain angle. Quarter waveplate areused in creating circular, ellipsometry, optical pumping,suppressing unwanted reflcetion and optical isolation.