States of Polarization
The polarization state of light specifies how its electric-field vector is oriented and rotates, classified as linear, circular, or elliptical.
Definition
A specification of the orientation, ellipticity, and handedness traced by the electric-field vector of a light wave, together with the formalisms used to represent and transform these states.
Scope
This topic covers the classification and mathematical representation of polarization states. It includes linear, circular, and elliptical polarization as special cases of the general elliptical state, the decomposition of any state into orthogonal components, the Jones-vector and Jones-matrix calculus for fully polarized light, the Stokes parameters and Mueller matrices for partially polarized light, the degree of polarization, and the geometric picture provided by the Poincaré sphere. It establishes the descriptive language used throughout polarization optics.
Core questions
- How are linear, circular, and elliptical polarization related?
- How is a polarization state represented by a Jones vector or by Stokes parameters?
- What is the degree of polarization and how is partial polarization described?
- How does the Poincaré sphere visualize polarization states?
Key concepts
- linear polarization
- circular polarization
- elliptical polarization
- Jones vector
- Stokes parameters
- degree of polarization
- Poincaré sphere
- orthogonal polarization components
Key theories
- Jones calculus for polarized light
- A fully polarized field is represented by a two-component complex Jones vector and each element by a Jones matrix, so the output state is found by matrix multiplication, giving a complete algebra for coherent polarization optics.
- Stokes parameters and the Poincaré sphere
- Four real, measurable Stokes parameters describe any state including partial polarization; normalized, they map onto the surface and interior of the Poincaré sphere, providing an intuitive geometric representation.
Clinical relevance
Characterizing polarization states underlies polarization-sensitive imaging of birefringent tissues such as collagen, muscle, and the retinal nerve fibre layer, where changes in state reveal structural and pathological information.
History
Stokes introduced his four parameters in 1852 to handle partially polarized light, and Poincaré later gave them a geometric interpretation on the sphere named after him. Jones developed his matrix calculus for fully polarized light in a series of papers from 1941, completing the standard formalisms.
Key figures
- George Gabriel Stokes
- Henri Poincaré
- R. Clark Jones
Related topics
Seminal works
- hecht2017
- bornwolf1999
Frequently asked questions
- What is the difference between circular and linear polarization?
- In linear polarization the electric field oscillates along a fixed line, while in circular polarization the field has constant magnitude but rotates steadily, tracing a circle as the wave advances; elliptical polarization is the general case in between.
- Why use Stokes parameters instead of Jones vectors?
- Jones vectors describe only fully polarized, coherent light, whereas the Stokes parameters are defined in terms of measurable intensities and can represent unpolarized and partially polarized light as well.