# Wave plate

A wave plate 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 is parallel to the surfaces of the plate. When the extraordinary index is smaller than the ordinary 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

[itex]\Gamma=2 \pi\, \Delta n\, L/\lambda.[itex]

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 extra-ordinary waves.

The other common type of wave plate is a half wave plate, which retards one polarization by a half wavelength, or 90 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.

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