The V number is a dimensionless parameter which is often used in the context of step-index fibers. It is defined as
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.
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:
- For V values below ≈ 2.405, a fiber supports only one mode per polarization direction (→ single-mode fibers).
- Multimode fibers can have much higher V numbers. For large values, the number of supported modes of a step-index fiber (including polarization multiplicity) can be calculated approximately as
- The V number determines the fraction of the optical power in a certain mode which is confined to the fiber core. For single-mode fibers, that fraction is low for low V values (e.g. below 1), and reaches ≈ 90% near the single-mode cut-off at V ≈ 2.405.
- There is also the so-called Marcuse equation for estimating the mode radius of a step-index fiber from the V number; see the article on mode radius.
- A low V number makes a fiber sensitive to micro-bend losses and to absorption losses in the cladding. However, a high V number may increase scattering losses in the core or at the core–cladding interface.
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.
|||A. W. Snyder and J. D. Love, Optical Waveguide Theory, Chapman and Hall, London (1983)|