Answer to Question #272815 in Optics for Sahil

Question

a multimode, optimum near parabolic profile graded index fiber has a material dispersion parameter of 30 ps nm km when used with a good led source of rms spectral width 25nm. the fiber has a numerical aperture of 0.4 and a core axis refractive index of 1.48. estimate the total rms pulse broadening per kilometer within the fiber assuming waveguide dispersion to be negligible. hence, estimate the bandwidth length product for the fiber.

Answer 1

Given - Multi mode, optimum near parabolic profile graded index fiber has a material dispersion parameter 

$\frac{\Delta ty}{\Delta \lambda }=30$ ps/km.nm

$\eta_1=1.48$ ,

N_{A = 0.4 ,}

$C=3\times10^8$

so,

$\sigma s=\frac{N_A}{4(\sqrt{3})\eta_1C}$

$\sigma s=\frac{N_A}{4(\sqrt{3})1.48\times3\times10^8}$

$\sigma s=5.20\times10^{-11}$

and the pulse broadening =$\frac{\Delta ty}{\Delta \lambda }\times\sigma s$

$=5.20\times10^{-11}\times30$

$=1.56\times10^{-9}$ ps/km.nm

= 1.56 ps/km