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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.

Questions and Comments from Users


What is the relation between V number and power flow in cladding?

Answer from the author:

Tentatively, for fibers with low V number a larger fraction of the total optical power propagates in the fiber cladding. The numerical value, however, depends on the details, not just the V number.

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[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


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