explain the significance of v numberansv number

Question

Explain the significance of V number.

Ans:

V number or V parameter or normalized cutoff frequency is one of the parameter which is used to calculate the maximum number of modes passing through the fiber.

The V number is defined as:

V= Πd (n₁²- n₂²)^½  / λ

= 2Πa NA / λ

From this equation it is clear that the V number depends upon

• core diameter
• wavelength of the pump signal
• refractive index variations

From the calculation of V number we can easily calculate the number of modes passing through the fiber.

            For a step index fiber, the number modes is given by

Number modes = V²/2

Where V >20

For a graded index fiber

Number modes = [y/(y+2)] V²/2

Where y is the index profile

The value of    y =1 (for a triangular profile)

  y=2 (for parabolic profile)

in commonly used case number of modes = V²/4