Quarter-wave plate

A waveplate or retarder is an optical device that alters the polarization state of a light wave travelling through it. Two common types of waveplates are the half-wave plate, which shifts the polarization direction of linearly polarized light, and the quarter-wave plate, which converts linearly polarized light into circularly polarized light and vice versa. A quarter-wave plate can be used to produce elliptical polarization as well.

Waveplates are constructed out of a birefringent material (such as quartz or mica), for which the index of refraction is different for different orientations of light passing through it. The behavior of a waveplate (that is, whether it is a half-wave plate, a quarter-wave plate, etc.) depends on the thickness of the crystal, the wavelength of light, and the variation of the index of refraction. By appropriate choice of the relationship between these parameters, it is possible to introduce a controlled phase shift between the two polarization components of a light wave, thereby altering its polarization.

A common use of waveplates—particularly the sensitive-tint (full-wave) and quarter-wave plates—is in optical mineralogy. Addition of plates between the polarizers of a petrographic microscope makes easier the optical identification of minerals in thin sections of rocks, in particular by allowing deduction of the shape and orientation of the optical indicatrices within the visible crystal sections. This alignment can allow discrimination between minerals which otherwise appear very similar in plane polarized and cross polarized light.

A waveplate works by shifting the phase between two perpendicular polarization components of the light wave. A typical waveplate is simply a birefringent crystal with a carefully chosen orientation and thickness. The crystal is cut into a plate, with the orientation of the cut chosen so that the optic axis of the crystal is parallel to the surfaces of the plate. This results in two axes in the plane of the cut: the ordinary axis, with index of refraction n_o, and the extraordinary axis, with index of refraction n_e. The ordinary axis is perpendicular to the optic axis. The extraordinary axis is parallel to the optic axis. For a light wave normally incident upon the plate, polarization component along the ordinary axis travels through the crystal with a speed v_o = c/n_o, while the polarization component along the extraordinary axis travels with a speed v_e = c/n_e. This leads to a phase difference between the two components as they exit the crystal. When n_e < n_o, as in calcite, the extraordinary axis is called the fast axis and the ordinary axis is called the slow axis. For n_e > n_o the situation is reversed.

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