waveplate

A waveplate, also called a retarder, is an optical device that introduces a fixed phase delay between two orthogonal polarization components of light, thereby changing its polarization state. The phase delay, or retardance, δ, is given by δ = 2π Δn d / λ, where Δn is the birefringence (difference between ordinary and extraordinary refractive indices), d is the plate thickness, and λ is the wavelength in vacuum. The plate has a fast axis and a slow axis, defined by its crystal orientation.

When linearly polarized light enters the plate, if its polarization aligns with one axis, the output remains linearly polarized but rotated depending on orientation; if the plate is a half-wave plate, with the input polarization at an angle θ to the fast axis, the output polarization is rotated by 2θ. A quarter-wave plate, oriented at 45° to the input linear polarization, converts it to circular polarization (for ideal conditions).

Common materials include quartz, calcite, and other birefringent crystals; zero-order waveplates are designed to give a specific retardance with minimal thickness, reducing sensitivity to wavelength and temperature than higher-order plates. Achromatic waveplates use pairs of plates with different dispersion to flatten retardance over a band of wavelengths.

Applications include polarization control in laser systems, imaging polarimetry, ellipsometry, interferometry, optical communications, and photolithography; they are used as polarization analyzers, modulators, and in scientific instruments.

Limitations include wavelength dependence, sensitivity to temperature, and the need for precise orientation; reflections at the surfaces are often minimized with anti-reflection coatings.