# Normalized frequency (fiber optics)

In an optical fiber, the normalized frequency, V (also called the V number), is given by

${\displaystyle V={2\pi a \over \lambda }{\sqrt {{n_{1}}^{2}-{n_{2}}^{2}}}\quad ={2\pi a \over \lambda }\mathrm {NA} ,}$

where a is the core radius, λ is the wavelength in vacuum, n1 is the maximum refractive index of the core, n2 is the refractive index of the homogeneous cladding, and applying the usual definition of the numerical aperture NA.

In multimode operation of an optical fiber having a power-law refractive index profile, the approximate number of bound modes (the mode volume), is given by

${\displaystyle {V^{2} \over 2}\left({g \over g+2}\right)\quad ,}$

where g is the profile parameter, and V is the normalized frequency, which must be greater than 5 for the approximation to be valid.

For a step index fiber, the mode volume is given by 4V2/π2. For single-mode operation is required that V < 2.4048, which is the first root of the Bessel function J0.