 Normalized frequency (fiber optics)

In an optical fiber, the normalized frequency, V (also called the V number), is given by
where a is the core radius, λ is the wavelength in vacuum, n_{1} is the maximum refractive index of the core, n_{2} 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 powerlaw refractive index profile, the approximate number of bound modes (the mode volume), is given by
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 4V^{2}/π^{2}. For singlemode operation is required that V < 2.405, which is the first root of the Bessel function J_{0}.
References
 This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C" (in support of MILSTD188).
Categories: Fiber optics
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