Question

A multimode step-index has a relative refractive index difference of 2% and a core refractive index of 1.5. The Number of modes propagating at a wavelength of 1.3um is 1000. Calculate:

a) The cladding refractive index

b) Numerical Aperture

c) The diameter of the fiber core

Answer 1

Relative index difference, Δ= 2% = 0.02

$λ = 1.3 \;\mu m = 1.3 \times 10^{-6} \;m$

Core refractive index \mu_1= 1.5

Number of modes M = 1000

a) Proportion:

1.5 – 100 %

$\mu_2$ – (100 -2) %

$\mu_2 = \frac{1.5 \times 98 }{100}=1.47$

b) Numerical Aperture

$NA = \mu_1 (2 Δ)^{\frac{1}{2}} \\ NA = 1.5 \times (2 \times 0.02)^{\frac{1}{2}} = 0.3$

c) The diameter of the fiber core

$d = \frac{λ \sqrt{2M}}{\pi NA} \\ d = \frac{1.3 \times 10^{-6} \sqrt{2 \times 1000}}{3.14 \times 0.3} \\ = 61.71 \times 10^{-6} \;m \\ = 61.72 \;\mu m$