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In lecture we introduced the Goos-Hänchen effect and presented equations for the phase shifts for TE and TM modes. (10 marks) a) Show with brief explanation how the phase shift is derived for TE modes. (hint: look it uponline) (5 marks) b) Calculate the phase shift vs. ray angle for silicon-on-insulator and silicon nitride planar waveguides for TE and TM modes. Compare the two wave guide systems and polarizations and comment. (5 marks)

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