# Normalized frequency (fiber optics)

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

where *a* is the core radius, λ is the wavelength in vacuum, *n*_{1} is the maximum refractive index of the core, *n*_{2} 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

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 4*V*^{2}/*π*^{2}. For single-mode operation is required that *V* < 2.4048, which is the first root of the Bessel function *J*_{0}.