Minuscule 181

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

$V=\frac{2\pi a}{\lambda }\sqrt{{n_1}^2-{n_2}^2}=\frac{2\pi a}{\lambda }\mathrm{N}\mathrm{A},$

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

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

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 4V²/π². For single-mode operation is required that V < 2.4048, which is the first root of the Bessel function J₀.

References

• Template:FS1037C MS188