retardances

Retardance, also called phase retardation, is a property of birefringent materials and optical retarders that quantifies the phase difference that two orthogonal polarization components of a light wave acquire after passing through the material. It is commonly expressed as δ and is related to the material’s birefringence Δn, thickness d, and the wavelength λ by the formula δ = (2π/λ) Δn d. Retardance can be stated in radians or in units of waves (δ/2π). Depending on δ, a retarder can convert or modify polarization states in specific ways.

Common examples include quarter-wave plates, which have δ = π/2, and half-wave plates, which have δ = π. The effect of a retarder depends on the orientation of its optical axis relative to the incident polarization. In an ideal plate, the output polarization state is determined by δ and the axis angle, enabling precise control of linear, circular, or elliptical polarization.

Retardance is wavelength dependent and can be influenced by temperature and mechanical stress, making it chromatic and sensitive to environmental conditions. This dependence is important in design and calibration of optical systems that rely on stable polarization manipulation.

Applications of retardance include polarization control in imaging and spectroscopy, liquid crystal displays, optical communications, and measurement techniques such as polarimetry and photoelasticity. Characterization methods include spectroscopic ellipsometry and Mueller matrix polarimetry, which quantify how a material or device alters polarization across wavelengths.