Encyclopedia … combined with a great Buyer's Guide!

Sponsoring this encyclopedia:     and others

V Number

Definition: a normalized frequency parameter, which determines the number of modes of a step-index fiber

Category: fiber optics and waveguides

Formula symbol: V

Units: (dimensionless number)

How to cite the article; suggest additional literature


The V number is a dimensionless parameter which is often used in the context of step-index fibers. It is defined as

V number

where λ is the vacuum wavelength, a is the radius of the fiber core, and NA is the numerical aperture. Of course, the V number should not be confused with some velocity v, e.g. the phase velocity of light, and also not with the Abbe number, which is also sometimes called V-number.

Calculation of the NA and V Number of a Fiber

Core index:
Cladding index:
Core radius:
Numerical aperture: calc
V number: calc

Enter input values with units, where appropriate. After you have modified some values, click a "calc" button to recalculate the field left of it.

It is assumed that the external medium is air (n = 1).

The V number can be interpreted as a kind of normalized optical frequency. (It is proportional to the optical frequency, but rescaled depending on waveguide properties.) It is relevant for various essential properties of a fiber:

number of modes versus V number

For certain types of photonic crystal fibers, an effective V number can be defined, where ncladding is replaced with an effective cladding index. The same equations as for step-index fibers can then be used for calculating quantities such as the single-mode cut-off, mode radius and splice losses.


[1]A. W. Snyder and J. D. Love, Optical Waveguide Theory, Chapman and Hall, London (1983)

(Suggest additional literature!)

See also: fibers, step-index fibers, fiber core, numerical aperture, single-mode fibers, multimode fibers, Abbe number
and other articles in the category fiber optics and waveguides


If you like this article, share it with your friends and colleagues, e.g. via social media: