Chapter #10 Solutions - Optics - Ajoy Ghatak - 1st Edition

1. Using the empirical formula given by Eq.(14) calculate the phase and group velocities in silica at λ0 = 0.7μm ,0.8μm, 1.0μm, 1.2μm and 1.4μm. Compare with the (more accurate) values given in Table 10.1. Get solution

2. For pure silica we may assume the empirical formula...where λ0 is measured in μm.(a) Calculate the zero dispersion wavelength.(b) Calculate the material dispersion at 800 nm in ps/km.nm.[1.32 μm; -101 ps/km.nm] Get solution

3. Let...where λ0 is the free space wavelength. Derive expressions for phase and group velocities.[Ans: vg = c/n0] Get solution

4. Consider a LED source emitting light of wavelength 850 nm and having a spectral width of 50 nm. Using Table 10.1 calculate the broadening of a pulse propagating in pure silica.[Ans: 4.2 ns/km] Get solution

5. In 1836 Cauchy gave the following approximate formula to describe the wavelength dependence of refractive index in glass in the visible region of the spectrum...Now (see also Table 12.2)  n(λ1) = 1.50883 ; n(λ2) = 1.51690 for borosilicate glass  n(λ1) = 1.45640 ; n(λ2) = 1.46318 for vitreous quartzwhere λ1 = 0.6563 μm and λ2 = 0.4861 μm.(a) Calculate the values of A and B.(b) Using the Cauchy formula calculate the refractive index at 0.5890 μm and 0.3988 μm and compare with the corresponding experimental values:(i) (1.51124 and 1.52546) for borosilicate glass and(ii) (1.45845 and 1.47030) for vitreous quartz. Get solution

6. The refractive index variation for pure silica in the wavelength region 0.5 μm 0 ...where C0 = 1.4508554, C1 = – 0.0031268, C2 = – 0.0000381, C3 = 0.0030270, C4= –0.0000779, C5 = 0.0000018, l = 0.035 and λ0 is measured in μm. Calculate and plot n(λ0) and d2n/dλ02 in the wavelength domain 0.5 0 Get solution

7. (a) For a Gaussian pulse given by...the spectral width is approximately given by...Assume λ0 = 8000 Å. Calculate ...for τ0 =1 ns and for τ0 = 1 ps.(c) For such a Gaussian pulse, the pulse broadening is given by ... where .... Using Table 8.1, calculate Δτ and interpret the result physically. Get solution

8. As a Gaussian pulse propagates the frequency chirp is given by...(a) where p is defined in Eq. (50). Assume a 100 ps (= τ0) pulse at λ0 = 1 μm. Calculate the frequency chirp ...at t – z/vg = –100 ps, –50 ps, +50 ps and +100 ps. Assume z = 1 km and other values from Table 8.1. Get solution

9. Repeat the previous problem for λ0 = 1.5 μm ; the values of τ0 and z remain the same. Discuss the qualitative difference in the results obtained in the previous problem. Get solution

10. The frequency spectrum of E(0,t) is given by the function A(ω). Show that the frequency spectrum of E(z,t) is simply ...implying that no new frequencies are generated – different frequencies superpose with different phases at different values of z. Get solution

11. The time evolution of a Gaussian pulse in a dispersive medium is given by...where .... Calculate explicitly the frequency spectrum of E(0,t) and E(z,t) and show that the results agree with that of the Problem 10.10. Get solution


Chapter #30 Solutions - Optics - Ajoy Ghatak - 1st Edition

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