What is the polarization ?

Light is a wave traveling in space. Its polarization is the property that defines the way it oscillates. The most usual polarization states are the following :

• linear polarization : the light oscillates in a single direction (figure A - blue and green waves).

• circular polarization : the light rotates in a plane as it oscillates (figure A - red wave). The light can either rotate to the right or the left with respect to the direction of travel.

• elliptical polarization : similar to the circular polarization but the light rotates around an ellipse instead of a circle.

Even though the eye does not perceive polarization directly, we cannot ignore the polarization to compute a physical render. Indeed, at a scale we do not perceive, light-matter interactions depend on the polarization : it can affect the intensity of the light reflected or transmitted by materials.

Some examples of situations where polarization has an influence on the appearance of materials could be :

• an outdoor scene with a clear sky (the light from the sky is polarized),

• scenes with dielectric materials (polarization is induced when reflected by such materials),

• a scene with polarizers such as sunglasses for instance : in the example 1, the glasses have linearly polarized lenses with different polarization directions.

• a scene with a polarized display (phone, computer,...) : in the example 1, the display is linearly polarized.

How is the polarization induced ?

The light can be polarized by transmission, reflection, refraction or scattering :

• Polarization by transmission : some transmissive materials are capable of filtering the light depending on their polarization (Figure B). These materials are called Polarizers or Polarization Filters : see the materials section for more details on optical filters. A good example of where to find such a material is the glass of polarized sunglasses.

• Polarization by reflection : the reflected light by an interface is partially polarized in a linear direction parallel to the surface (Figure C). This effect occurs on every material but it is mostly visible on specular materials (dielectrics and conductors). A good example of how to observe this effect is by looking at the reflections on a window, on snow, on a pool, on the sea, through linearly polarized sunglasses.

• Polarization by refraction : when light hits a surface, part of the light is reflected by the surface and the rest is transmitted inside the material. Just like the light reflected by the surface, the light transmitted inside the material is also partially polarized in a direction perpendicular to the surface (Figure C). A good example of how to observe this effect is by looking at a light source through a window, through linearly polarized sunglasses.

• Polarization by scattering : polarization also occurs when light is scattered while traveling through a medium. This means that if light travels for a very long distance in the air, or in any other medium, it will become partially polarized : the sunlight in space is unpolarized but it gets polarized in the direction perpendicular to the sun direction when scattered by the atmosphere.

Characterizing the polarization

The polarization of the light can be represented in different ways :

• Stokes vector : the polarization is fully described with a vector of four components. The first component of the vector is the light intensity, the remaining 3 components relates to the state of polarization. The Stokes vector can describe either unpolarized light, partially polarized light or fully polarized light.

• Reduced Stokes vector : the reduced Stokes vector is equivalent to the Stokes vector but its components are divided by the intensity of the light : the reduced Stokes vector is independent of the intensity of the light and the first component, being equal to 1, is usually omitted.

• Degree, ellipticity and orientation : a practical way of representing polarization is by using the Poincaré sphere. The reduced 3D Stokes vector can be plotted directly in three-dimensional Cartesian coordinates and mapped to points on the surface of the so-called Poincaré sphere (figure D).

• The degree of polarization is the radius of the sphere. A degree of 0 means the light is unpolarized. A degree of 1 means the light is fully polarized.

• The ellipticity χ represents the shape of the polarization (figure E). An ellipticity of 0° represents a linear polarization (horizontal plane of the sphere). An ellipticity of -45° represents a right-circular polarization (south pole of the sphere). An ellipticity of +45° represents a left-circular polarization (north pole of the sphere).

• The orientation ψ represents the direction of polarization (figure E). It is defined between 0° and 180°.

Polarization in the Predict Suite

Materials can also induce polarization. Most of the materials in Predict Matter do not have polarization specific settings : the polarization induced by specular materials is directly defined by their reflectivity and their transmittance. An exception is made for optical filters : see the materials section for more details on optical filters.