Normalized frequency (fiber optics)

In an optical fiber, the normalized frequency,, is given by
where is the core radius, is the wavelength in vacuum, is the maximum refractive index of the core, is the refractive index of the homogeneous cladding, and applying the usual definition of the numerical aperture.
In multimode operation of an optical fiber having a power-law [refractive index profile], the approximate number of bound modes, is given by
where is the profile parameter, and 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. For single-mode operation, it is required that, the first root of the Bessel function.