Light waves can wiggle in different ways as they travel. This wiggling is called polarization. There are three main types: linear, circular, and elliptical. Each type has unique properties that affect how light interacts with materials.
We use special math tools to describe polarization. Jones vectors and Stokes parameters help us represent polarization states precisely. The Poincaré sphere gives us a visual way to understand how polarization changes as light moves through different materials.
Polarization States
Linear vs circular vs elliptical polarization
Top images from around the web for Linear vs circular vs elliptical polarization
Linear polarization occurs when the electric field oscillates in a single plane, which can be horizontal, vertical, or at any angle between
Circular polarization happens when the electric field rotates in a circular path, either right-handed (RHCP) or left-handed (LHCP), with equal amplitudes in two orthogonal components and a 90° phase difference
Elliptical polarization is characterized by the electric field tracing an elliptical path due to unequal amplitudes in two orthogonal components with a phase difference other than 0° or 90°
Linear and circular polarizations are special cases of elliptical polarization (phase difference of 0° or 90° and equal or unequal amplitudes)
Jones vectors and Stokes parameters
Jones vectors are complex 2D vectors representing the amplitude and phase of the electric field, expressed as E=(ExEy)=(axeiδxayeiδy)
Horizontal linear polarization: (10), vertical linear polarization: (01), RHCP: 21(1−i), LHCP: 21(1i)
Stokes parameters are real-valued 4D vectors representing the polarization state, given by S=S0S1S2S3=IQUV
S0 represents the total intensity, while S1, S2, and S3 represent the polarization state
Horizontal linear polarization: 1100, vertical linear polarization: 1−100, RHCP: 1001, LHCP: 100−1
Poincaré sphere for polarization
The Poincaré sphere is a 3D representation of polarization states where Stokes parameters S1, S2, and S3 form the Cartesian coordinates
Linear polarization states lie on the equator, circular polarization states are at the poles, and elliptical polarization states are on the surface of the sphere
Polarization state changes are represented by rotations on the Poincaré sphere
Birefringent elements cause rotations about an axis in the S1-S2 plane, while polarization rotators cause rotations about the S3 axis
Optical elements and polarization effects
Linear polarizers transmit light with electric field parallel to the polarizer's axis, following Malus' law: I=I0cos2θ, where θ is the angle between the polarizer and the incident polarization
Wave plates (retarders) introduce a phase difference between orthogonal components
Quarter-wave plate (QWP) introduces a 90° phase difference, converting linear polarization to circular polarization and vice versa
Half-wave plate (HWP) introduces a 180° phase difference, rotating linear polarization by twice the angle between the fast axis and the incident polarization
Polarization rotators change the polarization state
Faraday rotator uses the Faraday effect to rotate the polarization state, with the rotation angle depending on the magnetic field strength and the material's Verdet constant
Optical activity in chiral materials rotates the polarization state, with the rotation angle depending on the material's specific rotation and the path length