Normalized frequency

From Wikipedia, the free encyclopedia

Normalized frequency is a dimensionless quantity, obtained by taking the ratio between an actual frequency and a reference value, or a nominal value.

[edit] Fiber optics

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

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

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

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

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 is required that V < 2.405, which is the first root of the Bessel function J₀.