RP Photonics

Encyclopedia … combined with a great Buyer's Guide!


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.

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
and other articles in the category fiber optics and waveguides

How do you rate this article?

Click here to send us your feedback!

Your general impression: don't know poor satisfactory good excellent
Technical quality: don't know poor satisfactory good excellent
Usefulness: don't know poor satisfactory good excellent
Readability: don't know poor satisfactory good excellent

Found any errors? Suggestions for improvements? Do you know a better web page on this topic?

Spam protection: (enter the value of 5 + 8 in this field!)

If you want a response, you may leave your e-mail address in the comments field, or directly send an e-mail.

If you enter any personal data, this implies that you agree with storing it; we will use it only for the purpose of improving our website and possibly giving you a response; see also our declaration of data privacy.

If you like our website, you may also want to get our newsletters!

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