# Axial ratio

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 molecules. 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.

## Polarization and the polarization ellipse

Any fixed polarization can be described in terms of the shape and orientation of the polarization ellipse, which is defined by two parameters: axial ratio AR and tilt angle ${\displaystyle \tau }$. 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 one.

Alternatively, polarization can be represented as a point on the surface of the Poincaré sphere, with ${\displaystyle 2\times \tau }$ as the longitude and ${\displaystyle 2\times \epsilon }$ as the latitude, where ${\displaystyle \epsilon =\operatorname {arccot} (\pm AR)}$. The sign used in the argument of the ${\displaystyle \operatorname {arccot} }$ depends on the handedness of the polarization. Positive indicates left hand polarization, while negative indicates right hand polarization, as defined by IEEE.

For the special case of circular polarization, the axial ratio equals 1 (or 0 dB) and the tilt angle is undefined. For the special case of linear polarization, the axial ratio is infinite.