Normalized frequency (fiber optics)

{{short description|Property of an optical fiber}}

In an optical fiber, the normalized frequency, {{mvar|V}} (also called the V number), is given by

$$$$

V = {2 \pi a \over \lambda} \sqrt{{n_1}^2 - {n_2}^2} = {2 \pi a \over \lambda} \times NA,

where {{mvar|a}} is the core radius, {{mvar|λ}} is the wavelength in vacuum, {{math|n₁}} is the maximum refractive index of the core, {{math|n₂}} is the refractive index of the homogeneous cladding, and applying the usual definition of the numerical aperture {{mvar|NA}}.

In multimode operation of an optical fiber having a power-law refractive index profile, the approximate number of bound modes (the mode volume), is given by

$$$$

{V^2 \over 2} \left( {g \over g + 2} \right)\ ,

where {{mvar|g}} is the profile parameter, and {{mvar|V}} is the normalized frequency, which must be greater than 5 for the approximation to be valid.

For a step-index fiber, the mode volume is given by {{math|V²/2}}. For single-mode operation, it is required that {{math|V < 2.4048}}, the first root of the Bessel function {{math|J₀}}.