Suppose polarization axes x and y parallel with the slow and fast axis of the waveplate: The output depends on the polarization of the input. If the angle is in between 0° and 45° the resulting wave has an elliptical polarization.Ī circulating polarization can be visualized as the sum of two linear polarizations with a phase difference of 90°. If the axis of polarization of the incident wave is chosen so that it makes a 0° with the fast or slow axes of the waveplate, then the polarization will not change, so remains linear. The waveplate is characterized by the amount of relative phase, Γ, that it imparts on the two components, which is related to the birefringence Δ n and the thickness L of the crystal by the formula When n e n o the situation is reversed.ĭepending on the thickness of the crystal, light with polarization components along both axes will emerge in a different polarization state. This leads to a phase difference between the two components as they exit the crystal. For a light wave normally incident upon the plate, the 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. The extraordinary axis is parallel to the optic axis. The ordinary axis is perpendicular to the optic axis. ![]() 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 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. A typical waveplate is simply a birefringent crystal with a carefully chosen orientation and thickness. ![]() ![]() This alignment can allow discrimination between minerals which otherwise appear very similar in plane polarized and cross polarized light.Ī waveplate works by shifting the phase between two perpendicular polarization components of the light wave. Addition of plates between the polarizers of a petrographic microscope makes the optical identification of minerals in thin sections of rocks easier, in particular by allowing deduction of the shape and orientation of the optical indicatrices within the visible crystal sections. Ī common use of waveplates-particularly the sensitive-tint (full-wave) and quarter-wave plates-is in optical mineralogy. 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. 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. Waveplates are constructed out of a birefringent material (such as quartz or mica, or even plastic), for which the index of refraction is different for light linearly polarized along one or the other of two certain perpendicular crystal axes. ![]() A quarter-wave plate can be used to produce elliptical polarization as well. 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. 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 is a mirror-image of the entry polarization state (relative to the optic axis).Ī waveplate or retarder is an optical device that alters the polarization state of a light wave travelling through it. In the plate, the parallel wave propagates slightly slower than the perpendicular one. The combined field Linearly polarized light entering a half-wave plate can be resolved into two waves, parallel and perpendicular to the optic axis of the waveplate.
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