Waveplate

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

)[1] 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.

depends on the thickness of the crystal, the wavelength of light, and the variation of the index of refraction.

[1] With an engineered combination of two birefringent materials, an achromatic waveplate[2] can be manufactured such that the spectral response of its phase retardance can be nearly flat.

Addition of plates between the polarizers of a petrographic microscope makes the optical identification of minerals in thin sections of rocks easier,[3] in particular by allowing deduction of the shape and orientation of the optical indicatrices within the visible crystal sections.

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.

For a light wave normally incident upon the plate, the polarization component along the ordinary axis travels through the crystal with a speed vo = c/no, while the polarization component along the extraordinary axis travels with a speed ve = c/ne.

Although the birefringence Δn may vary slightly due to dispersion, this is negligible compared to the variation in phase difference according to the wavelength of the light due to the fixed path difference (λ0 in the denominator in the above equation).

For a single waveplate changing the wavelength of the light introduces a linear error in the phase.

For the extraordinary polarization the tilt also changes the refractive index to the ordinary via a factor of cos θ, so combined with the path length, the phase shift for the extraordinary light due to tilt is zero.

For calcite the refractive index changes in the first decimal place, so that a true zero order plate is ten times as thick as one wavelength.

For quartz and magnesium fluoride the refractive index changes in the second decimal place and true zero order plates are common for wavelengths above 1 μm.

For a half-wave plate, the relationship between L, Δn, and λ0 is chosen so that the phase shift between polarization components is Γ = π.

denotes the polarization vector of the wave exiting the waveplate, then this expression shows that the angle between

[1] For a quarter-wave plate, the relationship between L, Δn, and λ0 is chosen so that the phase shift between polarization components is Γ = π/2.

Suppose polarization axes x and y parallel with the slow and fast axis of the waveplate:

If not the amplitude but both sine values are displayed, then x and y combined will describe a circle.

With other angles than 0° or 45° the values in fast and slow axis will differ and their resultant output will describe an ellipse.

In optical mineralogy, it is common to use a full-wave plate designed for green light (a wavelength near 540 nm).

This means that under these conditions the plate will appear an intense shade of red-violet, sometimes known as "sensitive tint".

These plates are widely used in mineralogy to aid in identification of minerals in thin sections of rocks.

Zero-order waveplates are less sensitive to temperature and wavelength shifts, but are more expensive than multiple-order ones.

Either the filters can be rotated, or the waveplates can be replaced with liquid crystal layers, to obtain a widely tunable pass band in optical transmission spectrum.

The sensitive-tint (full-wave) and quarter-wave plates are widely used in the field of optical mineralogy.

Addition of plates between the polarizers of a petrographic microscope makes easier the optical identification of minerals in thin sections of rocks,[3] in particular by allowing deduction of the shape and orientation of the optical indicatrices within the visible crystal sections.

In practical terms, the plate is inserted between the perpendicular polarizers at an angle of 45 degrees.

This allows two different procedures to be carried out to investigate the mineral under the crosshairs of the microscope.

Firstly, in ordinary cross polarized light, the plate can be used to distinguish the orientation of the optical indicatrix relative to crystal elongation – that is, whether the mineral is "length slow" or "length fast" – based on whether the visible interference colors increase or decrease by one order when the plate is added.