V-number in Fiber Optics

What is the V-number in fiber optics?


According to ray theory of light propagation through optical fiber, every light rays that enter the fibre within acceptance cone should propagate through the fibre. However, only certain light rays or modes, which satisfy all the phase conditions, required for sustained propagation, are able to propagate along the optical fiber. Each mode has a cut-off frequency, below which it cannot propagate through optical fibre. The V-number is a very important characteristic parameter of an optical fiber, which is proportional to the frequency of the propagating light and given by:


                         w(omega) is the angular frequency of the mode,

a is the radius of the core,

c is the speed of light in vacuum,

NA is the numerical aperture of the fibre,

n1 is the refractive index of core,

n2 is the refractive index of cladding,

and                  Delta is the fractional refractive index change.

We know that, if nu is the frequency of mode and Lemda is its wavelength in vacuum then,

Since the V-number is proportional to the frequency, it is also called as the normalized frequency. If a fibre has V-number lower than 2.405, then it will support only a single mode to propagate. Such a fibre is called single mode fiber. On the other hand, if V-number is greater than 2.405, then more than one modes are allowed and such a fibre is called multimode fibre.

The maximum number of modes that may be propagate through a multimode fiber is given by


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