Mumbai University > Electronics and telecommunication > Sem 7 > optical communication and networks

Marks: 10

Years: MAY 2014

It is a dimensionless parameter that determines the number of modes a fiber can support. It is given by:

$ V= \dfrac{2π}{λ} a\sqrt{n_1^2-n_2^2}\\ V = \dfrac {2πa}{λ}(N.A) \\ V = \dfrac {2πan_1}{λ}(\sqrt{2∆})$

Where, a = radius of the core

λ = wavelength of ray

N.A = numerical aperture

$n_1$ and $n_2$ are the refractive indices of the core and cladding.

$\Rightarrow$ Fiber with a V-parameter of less than 1.1505 only supports the fundamental mode, and is therefore a single mode fiber whereas fiber with a higher V-parameter has multiple modes.

$\Rightarrow$ In single mode fiber, V is less than or equal to 1.1505, single mode fibers propagate the fundamental mode down the fiber core, while high order modes are lost in the cladding.

$\Rightarrow$ For low V values, most of the power is propagated in the cladding material. Power transmitted by the cladding is easily lost at fiber bends.

$\Rightarrow$ The value of the normalized frequency parameter (V) relates core size with mode propagation.

$\Rightarrow$ The number of modes in an optical fiber distinguishes multimode optical fiber from single mode optical fiber.

$\Rightarrow$ Graded Index fiber(Derivation):

1. Graded Index Fiber does not have a constant refractive index in the core. Due to this property they are also called inhomogeneous core fibers.

2. For guided modes we know the V number given as:

$V= \dfrac {2π}{λ} a\sqrt{n_1^2- n_2^2} \\ V = \dfrac {2πa}{λ}(N.A) \\ V = \dfrac {2πan_1}{λ}(\sqrt{2∆}) $

Where, ∆ = relative refractive index

Where, $Δ= \dfrac {n_1-n_2}{n_1 }$

N.A = numerical aperture

Total number of guided modes is:

$M_g = \dfrac α{α+2}.(n_1 . \dfrac {2π}λ. a)^2. Δ$

$\alpha$ = profile parameter which gives the characteristics refractive index profile of the fiber core.

but $,n_1. \dfrac {2π}{λ} .a. \sqrt{2.∆} =V \\ (n_1. \dfrac { 2π}{λ}.a)^2 . Δ = \dfrac {V^2}2 \\ ∴M_g= \dfrac α{α+2}.\dfrac { V^2}2 $

For a parabolic refractive index profile core fiber (????=2),

$M_g= \dfrac {V^2}4$