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.