A graded index fiber with a core axis refractive index of 1.5 has a characteristic index profile (α) of
1.90, a relative refractive index difference of 1.3% and a core diameter of 40 μm. Estimate the number
of guided modes propagating in the fiber when the transmitted light has a wavelength of 1.55 μm,
and determine the cutoff value of the normalized frequency for single-mode transmission in the fiber.
V-Number and No. of Modes in Fibre
Fractional Index Difference: It is the ratio of the difference in the refractive index of core and cladding with respect to refractive index of core.
and
Therefore
V-Number or Normalized Frequency
V – number determines how many modes a fiber can support,  It is given by
,where d is the diameter of the core, l is the wavelength of light used and NA is the numerical aperture of the fibre.
 Â
No. of guided modes =
V=26
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