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A step index multi mode fibre along with numerical aperture of 0.2 supports approximately 1000 modes at an 850µm wavelength. Calculate
a) What is the diameter of the core? b) How many modes this fibre supports at 1320nm? c) How many modes this fibre supports at 1550nm?
Given, numerical aperture Sinψ = (n12- n22)½=0.2 No. of modes, m=1000 Λ=850nm
For a multi mode fibre m= V2 /4 V= (4 x No. of modes) ½ = (4 x 1000) ½ =63.24Take V=63
a) We know that V= Πd (n12- n22)½ / λ where d is the diameter. Substituting the values of V, n1, n2, d and solving for Λ, we get d= 85.227µm
b) At Λ=1320nm,
From V= Πd (n12- n22)½ / λ Substituting Λ=1320nm, we get V=40.5679 Take V=40 No. of modes= V2/2 =402/2 = 400
c) At Λ=1550nm,
From V= Πd (n12- n22)½ / λ Substituting Λ=1550nm, we get V=34.548 Take V=35 No. of modes= V2/4 =352/4 = 298
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