# PM fiber beat length calculator

## About this calculator

This calculator computes the polarization beat length of a polarization maintaining (PM) optical fiber. Beat length is the distance after which the polarization state has made one rotation, i.e. the phase shift between the two polarization modes is $2 \pi$. Beat length is one way to define a PM fiber's birefringence, the other two being the index difference $\Delta n$ or the propagation constant difference $\Delta \beta$ between the polarization modes.

Either $\Delta n$ or $\Delta \beta$ (in $m^{-1}$) can be given as input to the calculator along with the wavelength of the signal. $\Delta \beta$ is related to the index difference as follows

$\Delta \beta = \dfrac{2 \pi}{\lambda} \Delta n$

so the calculator first calculates $\Delta n$ (if necessary)

$\Delta n = \dfrac{\lambda}{2 \pi} \Delta \beta$

and then the beat length as$L_b = \dfrac{\lambda}{\Delta n}$