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

Marks: 05

Years: MAY 2014

• Numerical Aperture is the ability of fiber to collect the light from the source and save the light inside it by maintaining the condition of total internal reflection.

• Consider a light ray entering from a medium air of refractive index $n_o$ into the fiber with a core of refractive index $n_1$ which is slightly greater than that of the cladding $n_2.$

Applying Snell’s law of reflection at point A,

$\dfrac {\sin⁡ Ө_1 }{\sin⁡ Ө_2 } = \dfrac {n_1}{n_o} =n_1\space\space as\space\space n_0= 1 $

In right angled Δabc,

$θ_2 = \dfrac π2 - ∅_c \\ \sinθ_1 = n_1\sin (\dfrac π2 - ∅_c) =n_1\cos ∅_c \\ \cos∅_c = (1-\sin ∅_c^2)^{1/2} $

From the above equation

$\sin θ_1 = n_1 (1-\sin ∅_c^2)^{1/2} $

When the TIR takes place, $∅_c=θ_c$ & $θ_1= θ_a.$

Where $\theta_c =$ critical angle & $\theta_a =$ acceptance angle

Therefore ,

$\sin \theta_a=n_1 (1-\sin \theta_c^2)^{1/2}$

we know

$\sin \theta_c=\dfrac {n_2}{n_1} \\ \sin \theta_a=n_1 [1-(\dfrac {n_2}{n_1})^2]^{1/2} \\ N.A =\sin \theta_a$

• $\sin θ_a$ represents all the light rays within cone of θ_a , which maintain the condition of TIR inside the fiber.

• The NA is always chosen so as to accept maximum incident light, satisfying other requirements.

$NA = \sin θ_a= \sqrt{n_1^2-n_2^2 } $

• The core transmits the optical signal while the cladding guides the light within the core and if the cladding is removed then there is a loss of signal.

• For a step index fiber with a constant refractive index core, the wave equation is Bessel differential equation and solutions are cylindrical functions, therefore if cladding is removed the step index fiber behaves like a cylindrical circular optical fiber with $n_2=1$ of air.

• Thus, NA increases if the cladding is removed.