Axial ratio
Encyclopedia
Axial ratio, for any structure or shape with two or more axes, is the ratio of the length (or magnitude) of those axes to each other - the longer axis divided by the shorter.
In chemistry or materials science, the axial ratio (symbol P) is used to describe rigid rod-like molecule
s. It is defined as the length of the rod divided by the rod diameter.
In physics, the axial ratio describes electromagnetic radiation
with elliptical, or circular, polarization. The axial ratio is the ratio of the magnitudes of the major and minor axis defined by the electric field vector.
. The axial ratio is the ratio of the lengths of the major and minor axes of the ellipse, and is always greater than or equal to 1.
Alternatively, polarization can be represented as a point on the surface of the Poincaré sphere
, with
as the longitude
and
, where 
, as the latitude
. The sign used in the argument of the
depends on the handedness of the polarization. + indicate left hand polarization, - right hand polarization, as defined by IEEE.
For the special case of circular polarization, the axial ratio equals 1 and the tilt angle is undefined. For the special case of linear polarization, the axial ratio is infinite.
In chemistry or materials science, the axial ratio (symbol P) is used to describe rigid rod-like molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
s. It is defined as the length of the rod divided by the rod diameter.
In physics, the axial ratio describes electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
with elliptical, or circular, polarization. The axial ratio is the ratio of the magnitudes of the major and minor axis defined by the electric field vector.
Polarization and the Polarization Ellipse
Any (fixed) polarization can be described in terms of the shape of the polarization ellipse, which is defined by two parameters: axial ratio AR and tilt angle. The axial ratio is the ratio of the lengths of the major and minor axes of the ellipse, and is always greater than or equal to 1.Alternatively, polarization can be represented as a point on the surface of the Poincaré sphere
Poincaré sphere
Poincaré sphere, often spelled Poincare sphere may refer to:* Poincaré sphere, in optics, is a graphical tool for visualizing different types of polarized light...
, with
as the longitudeLongitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
and
, where , as the latitudeLatitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...
. The sign used in the argument of the
depends on the handedness of the polarization. + indicate left hand polarization, - right hand polarization, as defined by IEEE.For the special case of circular polarization, the axial ratio equals 1 and the tilt angle is undefined. For the special case of linear polarization, the axial ratio is infinite.