Quarter Wave Plate vs. Half Wave Plate: Key Differences Explained

This article explains the differences between quarter wave plates and half wave plates, both crucial components used for phase retardation in fiber optic systems. We’ll explore how they work, their applications, and provide the formulas for calculating their respective thicknesses.

Introduction to Wave Plates

Quarter wave and half wave plates are essential in manipulating the polarization of light within fiber optic systems. These plates are typically made from uniaxial crystals like calcite or KDP. When light passes through these specially cut crystal plates, a phase difference (Δφ) is introduced between the ordinary ray (o-ray) and the extraordinary ray (e-ray).

Understanding Ordinary and Extraordinary Rays

Light entering a calcite crystal splits into two rays, a phenomenon discovered by Erasmus Bartholinus in 1669, known as double refraction.

Optical path difference

When light is incident at a normal angle (0°), Snell’s Law predicts a refraction angle of 0°. However, in double refraction, at least one of the rays violates Snell’s Law. In calcite, the ordinary ray (o-ray) obeys Snell’s Law, while the extraordinary ray (e-ray) does not.

Key Difference: Phase Difference

The crucial difference between quarter wave plates and half wave plates lies in the phase difference (Δφ) they introduce between the o-ray and e-ray. This phase difference is determined by the thickness (‘d’) of the crystal plate. By carefully selecting the value of ‘d’, we can achieve a phase difference of π/2 for a quarter wave plate and π for a half wave plate.

Half Wave Plate

Half wave plate thickness formula

• Functionality: Converts linearly polarized light into another linearly polarized light, mirrored by the fast or slow axis. As shown in figure-2 above.

Quarter Wave Plate

Quarter wave plate thickness formula

• Functionality: Converts linearly polarized light into circularly polarized light when the input polarization is at 45° to the fast and slow axes. At other azimuth angles, it transforms linearly polarized light into elliptically polarized light oriented along the fast and slow axes. See figure-2 above.