title: Normalized frequency (fiber optics)
text: # Normalized frequency (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, $n_1$ 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 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 $V^2/2.$ For single-mode operation, it is required that V < 2.4048, the first root of the Bessel function $J_0.$
  
  