Changing the State of Polarization Using Retarders

Retarders tend to change the state of polarization and resolve an incident beam of light into two orthogonally polarized components. They retard the phase of a single component relative to the other. The emergent beam typically exhibits a varied polarization state from the incident beam.

Birefringent Material

A slice of birefringent material is the most common type of retarder, wherein the e-ray and o-ray travel at different velocities. Two rays which begin in phase form a phase difference with regard to each other. For light of wavelength λ, the phase difference, Φ, is given as:

and the optical path difference by:

Where d is the thickness of the plate, n0 represents the refractive index for the ordinary ray, and ne denotes the refractive index for the extraordinary ray.

k helps in expressing the path variation in terms of the wavelength, λ.

When k = m/4 where m is any odd integer, the path variation is a quarter wave, and therefore the plate is dubbed as a quarter wave plate. When the path variation is a half wave, the retarder is known as a half wave plate.

Rotation of polarization by a Half Wave Retarder

Figure 1. Rotation of polarization by a Half Wave Retarder

The operation of a half wave plate on a linearly polarized beam is shown in Figure 1. To this end, the Ê vector of the input beam is at θ to the optic axis. The input beam is successfully resolved into two orthogonally polarized component beams, one with the Ê vector perpendicular to the optic axis, and the other with the Ê vector parallel to the optic axis.

One of these beams is delayed by the retarder with respect to the other. After travelling via the retarder, the phase of a single vector component is delayed by π (180°) with regard to the other; a path variation of one half wavelength.

The sum of the two emergent beams is a beam with linear polarization, but rotated by 2 θ from the actual input beam. The action of this half wave plate is to rotate the Ê vector of the light through 2 x θ, twice the angle between the optic axis and the Ê vector of the incident beam.


Ideally, retarders do not polarize, nor do they induce an intensity change in the light beam - they simply change its polarization form. They are used in applications where control or analysis of polarization states is required.

About Oriel Instruments


About Oriel Instruments

Oriel Instruments, a Newport Corporation brand, was founded in 1969 and quickly gained a reputation as an innovative supplier of products for the making and measuring of light. Today, the Oriel brand represents industry-leading instruments, such as continuous light sources covering a broad range from UV to IR, and from low to high power.

Oriel also offers monochromators and spectrographs, as well as flexible FT-IR spectroscopy solutions, making it easy for users across industries to build instrumentation for specific applications. Oriel is also a leader in the area of Photovoltaics, with its offering of solar simulators allowing users to simulate hours of solar radiation within a matter of minutes. Oriel continues to bring innovative products and solutions to Newport customers around the world.

This information has been sourced, reviewed and adapted from materials provided by Oriel Instruments.

For more information on this source, please visit Oriel Instruments.


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