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In an optical fiber, the normalized frequency, $V$ (also called the V number), is given by $V={2\pi a \over \lambda }{\sqrt {{n_{1}}^{2}-{n_{2}}^{2}}}={2\pi a \over \lambda }\times NA,$ 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 ${V^{2} \over 2}\left({g \over g+2}\right)\ ,$ 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 $V 2 /2$ . For single-mode operation, it is required that $V < 2.4048$ , the first root of the Bessel function $J 0$ .