A straight step-index fibre has a uniform core of index and a uniform cladding of index

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Beams, resonators and guided-wave photonics · Beams, resonators and guided-wave photonics

Optics and Photonics, Ch Optical fibres in communication and endoscopy

Problem

A straight step-index fibre has a uniform core of index n1=1.46n_1 = 1.46 and a uniform cladding of index n2=1.45n_2 = 1.45. Its end faces are flat, polished and in air (index 1.001.00). Treat the light as rays in the core, consider meridional rays only (rays that cross the axis), and take the speed in the core to be c/n1c/n_1 with c=3.00×108c = 3.00\times10^{8} m s−1^{-1}. ((a)) Find the numerical aperture of the fibre and the acceptance angle θa\theta_a in air, in degrees. ((b)) Find the modal pulse spread per kilometre, in ns km−1^{-1}, taking the extreme guided ray to be the one that meets the core-cladding wall at the critical angle. ((c)) The fibre attenuates at 2.02.0 dB km−1^{-1} at the wavelength used. What fraction of the launched power survives 6.06.0 km of it?

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