# Optical fiber V parameter and cutoff calculator

## About this calculator

This calculator computes the V parameter/number (also known as normalized frequency) of a step-index optical fiber. The V parameter is defined as

$V = \dfrac{2\pi}{\lambda} a \mathrm{NA}$

where $\lambda$ is the wavelength of the signal, $a$ is the core radius of the fiber and $\mathrm{NA}$ is the numerical aperture of its core.

This calculator also computes the cutoff wavelength, which determines when the fiber becomes single-mode. At shorter wavelengths, at least two LP modes can propagate; at longer wavelengths the fiber guides only a single transverse mode. V parameter value at the cutoff wavelength is $V_{cutoff}=2.405$ so the cutoff wavelength can be calculated from the V parameter as follows:

$\lambda_{cutoff} = \dfrac{2\pi a \mathrm{NA}}{V_{cutoff}} = \dfrac{V}{V_{cutoff}} \lambda$