Waveplate

A half-wave plate. Linearly polarized light entering a wave plate can be resolved into two waves, parallel (shown as green) and perpendicular (blue) to the optical axis of the wave plate. In the plate, the parallel wave propagates slightly slower than the perpendicular one. At the far side of the plate, the parallel wave is exactly half of a wavelength delayed relative to the perpendicular wave, and the resulting combination (red) is orthogonally polarized compared to its entrance state.

A wave plate or retarder is an optical device that alters the polarization state of a light wave travelling through it.

A wave plate works by shifting the phase of the light wave between two perpendicular polarization components. A typical wave plate is simply a birefringent crystal with a carefully chosen thickness. The crystal is cut so that the extraordinary axis (polarized parallel to the axis of anisotropy) is parallel to the surfaces of the plate. When the extraordinary index is smaller than the ordinary (polarized perpendicularly to axis of anisotropy) index, as in calcite, the extraordinary axis is called the fast axis and the ordinary axis is called the slow axis. Light polarized along the fast axis propagates faster than light polarized along the slow axis. Thus, depending on the thickness of the crystal, light with polarization components along both axes will emerge in a different polarization state. The wave plate is characterized by the amount of relative phase Γ that it imparts on the two components, which is related to the birefringence Δn and the thickness L of the crystal by the formula

$\Gamma =2\pi \,\Delta n\,L/\lambda .$

For instance a quarter wave plate creates a quarter wavelength phase shift and can change linearly polarized light to circular and vice versa. This is done by adjusting the plane of the incident light so that it makes 45° angle with the fast axis. This gives equal amplitude ordinary and extraordinary waves.

The other common type of wave plate is a half wave plate, which retards one polarization by a half wavelength, or 180 degrees. This type of wave plate rotates the polarization direction of linear polarized light.

Because of dispersion, a simple wave plate will impart a phase difference that depends on the wavelength of the light. Waveplates are thus manufactured to work for a particular range of wavelengths. The dispersion can be minimized by stacking two waveplates that differ by a tiny amount in thickness back-to-back, with the slow axis of one along the fast axis of the other. With this configuration, the relative phase imparted can be, for the case of a half wave plate, half a wavelength rather than half plus an integer. This is called a zero order wave plate. Like lenses, wave plates can also be made achromatic by combining materials with different dispersion.

See also

• Crystal optics