Question

A typical relative refractive index difference for an optical fiber designed for long-
distance transmission is 1%. Estimate the NA and the solid acceptance angle in air
for the fiber when the core index is 1.46. Further, calculate the critical angle at the
core-cladding interface within the fiber. It may be assumed that the concepts of geo-
metric optics hold for the fiber.

Answer 1

Answer:

NA is also given by = n1(2Δ)^1/2

Where Δ is the index difference = 0.01 then NA = 1.46(0.02)^1/2 = 0.21

For small angles, the solid acceptance angle in air ζ is given by:   ζ≈ πa^2= π sin2^a

Hence ζ ≈ π (NA)² = π × 0.04= 0.13 rad19

Fort the relative refractive index difference Δ gives Δ ≈ = 1-

Hence n1/n2 = 1- Δ = 1-0.01 = 0.99

From Eq. (2) the critical angle at the core–cladding interface is:

c= sin^-1= sin^-1 0.99 = 81.9

Modes of Fibres

A mode is described by the indices l and m characterizing its azimuth and radial distribution respectively.

The stable interference patterns (the modes of the cavity) occur only when the phase shift for a complete round trip is equal to an integral number of 2 radians.

We can denote the round trip phase shift by Δ

then the cavity resonance condition can be written as ΔФ= m2Ф..(1) where m is an integer.

I HOPE THIS WILL HELP YOU OUT :)

Answer 2

NA can alternatively be represented as = n1(2)1/2.

Explanation:

NA = 1.46(0.02)1/2 = 0.21 when the index difference is equal to 0.01.

For small angles, a2= sin2a is the solid acceptance angle in air.

(NA)2 = 0.04= 0.13 rad19 as a consequence.

The result of multiplying the relative refractive index difference by one is = 1-

n1/n2 = 1- = 1-0.01 = 0.99 as a consequence.

According to Eq. (2), the critical angle at the core–cladding interface is:

c= sin-1= sin-1 0.99 = 81.9 c= sin-1= sin-1 0.99 = 81.9 c= sin-1= sin-1 0.99 = 81.9 c= sin-1= sin-1 0.99 = 81.9 c= sin-1= sin-1 0.99 = 81.9

Modes of Fibres

The indices l and m are used to characterise a mode's azimuth and radial distribution, respectively.

Only when a whole round trip's phase change equals an integral quantity of 2 radians can stable interference patterns (cavity modes) appear.