Engineering:Normalized frequency (fiber optics)

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

[math]\displaystyle{ V = {2 \pi a \over \lambda} \sqrt{{n_1}^2 - {n_2}^2}\quad = {2 \pi a \over \lambda} \mathrm{NA}, }[/math]

where a is the core radius, λ is the wavelength in vacuum, n₁ is the maximum refractive index of the core, n₂ is the refractive index of the homogeneous cladding, and applying the usual definition of the numerical aperture 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

[math]\displaystyle{ {V^2 \over 2} \left( {g \over g + 2} \right)\quad, }[/math]

where g is the profile parameter, and 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 V²/2. For single-mode operation, it is required that V < 2.4048, the first root of the Bessel function J₀.

See also

• Abbe number