Retardation Plates and Polarizers Applet

march 2024, Jeroen Korterik - University of Twente

This applet simulates the polarization of a laser bundle as it travels trough some retardation plates (wave plates) and/or polarizers.
The bundle will first pass element1, next element2, element3 and element4. You can choose if these elements are either retardation plates or polarizers. After each element, the resulting polarization is shown.

Retardation plates

Retardation plates can be used to alter the ellipticity and angle of the polarization. show/hide more info
In vacuum (or air), light travels at about 3 * 108 m/s. In a medium like water or glass, light travels at a lower speed. For instance, in most types of glass light travels at approx. 2 * 108 m/s so it is roughly a factor 1.5 slower compared to the speed of light in vacuum. This factor is called the refractive index. In ordinary types of glass like borosilicate glass, the refractive index does not depend on the polarization of the light.
A retardation plate has slightly different refractive indeces for different angles at which the electro-magnetic (EM) wave oscillates.

This figure shows a retardation plate in which the fast and slow axis are indicated.
If the EM wave oscillates in the direction of the fast axis, the refractive index is a bit lower compared to the situation where the EM wave oscillates in the direction of the slow axis.
The incoming polarization can be linear, elliptic or circular and can have any orientation angle with respect to this slow and fast axis of the retardation plate.
However, this incoming polarization can be decomposed into a vector in the fast axis and a vector in the slow axis so it can be regarded as 2 independent EM waves, one wave oscillating in the direction of the fast axis and one wave oscillating in the direction of the slow axis.
These 2 EM waves undergo different delays inside the retardation plate and therefore, the timing between those 2 EM waves is altered after the waves have exited the retardation plate. This delta delay is called the retardation.
The polarization at the output can be determined by combining these 2 EM waves in a Lissajous figure. In this way it can be seen that in this example, the incoming polarization was linear and after the retardation plate it has become elliptical, almost circular.
The most commonly used waveplates are quarter wave plates and half wave plates.
In a quarter wave plate, the retardation is a quarter wave (90 out of 360 degrees). These can be used to change a ellipticity of the polarization.
In a half wave plate, the retardation is half a wave (180 degrees). These plates can rotate the angle of polarization without affecting the ellipticity.
In practice, these retardation plates most likely will not have exactly 90 or 180 degrees of retardation. It's also depending on the wavelength of light that is applied.
In this applet, you can see the effect of this as well as the effect of changing the angle of the retardation plate with respect to the incoming polarization angle.
More information on retardation plates can be found elsewhere, for instance Wikipedia EN Waveplate.

Polarizers

An ideal polarizer will have 100% transmission in 1 polarization angle (the allowed angle) and 0% transmission in the orthogonal polarization angle (the forbidden angle). show/hide more info
In practice the transmission in the allowed direction is between 90 and 100% and the transmission in the forbidden direction is almost 0%.
The light in the forbidden angle might be absorbed in the polarizer. In the case of a polarizing beam splitter (PBS), the incident beam will be split into two beams of orthogonal, linear polarization.
The extinction ratio of a polarizer indicates the ratio between transmissivity in the allowed angle and the transmissivity in the forbidden angle. Typical values are ranging from 1/100 to 1/10000. Note that these extinction ratios are normally specified as intensity ratios where the intensity is the square of the amplitude of the EM wave. The guaranteed extinction ratio is only valid in a certain wavelength range.

Incoming polarization




element1

Element Type: Retardation Plate  Polarizer

Angle: 

Retardation 
90=lambda/4, 180=lambda/2 

Resulting polarization after element1:


element2

Element Type: Retardation Plate  Polarizer

Angle: 

Retardation 
90=lambda/4, 180=lambda/2 

Resulting polarization after element2:


element3

Element Type: Retardation Plate  Polarizer

Angle: 

Retardation 
90=lambda/4, 180=lambda/2 

Resulting polarization after element3:


element4

Element Type: Retardation Plate  Polarizer

Angle: 

Retardation 
90=lambda/4, 180=lambda/2 

Resulting polarization after element4: