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(a) For the slab waveguide of thickness 2.2um (see Figure 1), what range of wavelengths can it support exactly 5 TE modes. [10 marks] n3=1.0 n=3.5 2.2um Figure 1 n2=1.5 (b) Calculate the normalized frequency of the lateral slab waveguide with thickness h2 =180nm (shown in Figure 2 below) at 1.55um wavelength. Use the effective index method to find the effective index for the TE guided mode in the channel waveguide at 1.55um wavelength assuming hi=250nm. [11 marks] 0.48um n3=1.0 ni=3.5 Figure 2 Silicon h=250nm h=180nm SiO2 n2=1.5 (c) Under what circumstances would the effective index method give less accurate approximations for the estimate of the propagation constant of the channel waveguide? [4 marks]