Retardance

Retardance is the phase difference between orthogonal polarization components of light as it passes through a birefringent material. In a birefringent crystal, the ordinary and extraordinary rays travel at different speeds, characterized by refractive indices n_o and n_e. If a light beam of thickness t and wavelength λ in vacuum traverses the material, the phase retardation is δ = 2π Δn t / λ, where Δn = n_e − n_o. The corresponding optical path difference is Δ = t Δn, and retardance can be expressed in cycles as R = δ / (2π).

A device designed to impose a specific retardance is called a retarder or waveplate. Common examples include quarter-wave plates with δ = π/2 (R = 1/4) and half-wave plates with δ = π (R = 1/2). The effect of a retarder depends on the orientation of its fast axis relative to the input polarization: components aligned with the fast and slow axes acquire a relative phase shift, altering the polarization state, often converting linear polarization to elliptical or circular polarization depending on δ and the input angle.

Retardance generally varies with wavelength, since Δn and the phase velocity depend on frequency. Achromatic retarders use multiple layers of materials to keep retardance nearly constant over a range of wavelengths, a principle important in polarimetry, ellipsometry, and optical instrumentation. Applications span liquid-crystal displays, optical communication, and stress analysis in photoelasticity, where induced birefringence from mechanical stress alters retardance.