Normalized frequency (fiber optics)

In an optical fiber, the normalized frequency, Template:Mvar (also called the V number), is given by $$V=\frac{2\pi a}{\lambda }\sqrt{{n_1}^2-{n_2}^2}=\frac{2\pi a}{\lambda }\times NA,$$ where Template:Mvar is the core radius, Template:Mvar is the wavelength in vacuum, Template:Math is the maximum refractive index of the core, Template:Math is the refractive index of the homogeneous cladding, and applying the usual definition of the numerical aperture Template:Mvar.

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 Template:Mvar is the profile parameter, and Template:Mvar 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 Template:Math. For single-mode operation, it is required that Template:Math, the first root of the Bessel function Template:Math.

See also

• Abbe number

References

• Template:FS1037C MS188