Plane Waves and Polarization
The simplest electromagnetic waves are transverse plane waves whose electric-field orientation defines their polarization.
Definition
A plane electromagnetic wave is a solution in which the fields depend on a single propagation direction and oscillate sinusoidally; polarization specifies how the electric-field vector is oriented and how that orientation evolves over a cycle.
Scope
This topic covers monochromatic plane-wave solutions of Maxwell's equations in vacuum, the transverse relationship and relative magnitudes of the electric and magnetic fields, the wavevector and dispersion relation, energy and momentum flux carried by the wave, and states of polarization — linear, circular, and elliptical — together with their description and manipulation.
Core questions
- What is the structure of a monochromatic plane electromagnetic wave?
- How are the electric and magnetic fields related in such a wave?
- How are the different states of polarization defined and produced?
Key concepts
- monochromatic wave
- wavevector
- transverse fields
- linear polarization
- circular polarization
- elliptical polarization
- Poynting vector
- intensity
Key theories
- Transverse plane-wave solution
- A monochromatic plane wave has electric and magnetic fields perpendicular to each other and to the propagation direction, with their magnitudes related by the wave speed and energy flux given by the Poynting vector.
- States of polarization
- Superposing perpendicular field components with definite relative phase and amplitude yields linear, circular, or elliptical polarization, which can be analyzed and transformed by polarizers and wave plates.
Clinical relevance
Polarization control is essential to liquid-crystal displays, polarized sunglasses, optical communications, polarimetry for measuring optical activity, and stress analysis, while plane-wave models underlie antenna and radar analysis.
History
Malus discovered polarization by reflection in 1808, and Fresnel and Young established the transverse nature of light waves in the 1810s-1820s, which Maxwell's theory later explained as the transverse character of electromagnetic waves.
Key figures
- Augustin-Jean Fresnel
- Étienne-Louis Malus
- James Clerk Maxwell
Related topics
Seminal works
- jackson1998
- born1999
Frequently asked questions
- What does it mean for light to be polarized?
- Polarization describes the direction in which the electric field oscillates; in linearly polarized light it stays along one axis, while in circular or elliptical polarization it rotates as the wave advances.
- Why are electromagnetic waves transverse in vacuum?
- Maxwell's equations in free space require the fields to be perpendicular to the propagation direction, so there is no component of the oscillating field along the direction of travel.