## Calculate critical angel and fundamental gaussian mode, Electrical Engineering

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(1) An argon ion laser, emitting light at a wavelength of 488nm with a beam divergence of 150 firad, is used to illuminate the moon.

(i) Assuming the earth-to-moon distance is 3:8_108 m, estimate the diameter of the spot on the moon.

(ii) Calculate the waist of the beam in the laser, assuming that the beam is a fundamental Gaussian mode.

(iii) Suggest a way by which the spot diameter on the moon could be reduced by a factor of 100.

(2) The bandgap of GaAs is 1.4 eV.

(i) Calculate the probability of a valence electron being in the conduction band by thermal excitation at 0°C.

(ii) The donor binding energy in GaAs is 5.8 meV. Calculate the probability of finding a donor electron in the conduction band at 0°C.

(iii) From an electronic point of view, what is the difference between undoped and n-type GaAs?

(3) An optical fibre has a core refractive index of 1.52, and a numerical aperture of 0.12.

Calculate its:

(i) Critical angle.

(iii) Maximum acceptance angle in (a) air, and in (b) water (refractive index =1.3)

(4) (i) What is the primary reason that optical fibres are used for communicating information?

(ii) How can you maximise the amount of information transmitted?

(iii)Estimate the bandwidth of a fibre of core diameter 50°m, n1 = 1:50, n2 = 1:49, and length L = 50 km.

(iv) Identify 2 other things that optical fibres are useful for.

(5) The mean power launched into an optical fibre of length 10 km is 150 _W and the average power at the output is 5°W. Calculate the overall attenuation in dB, and the attenuation per kilometre, assuming there are no interface losses.

Each question is worth ten points.

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