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Unformatted text preview: 1 School of Electrical and Computer Engineering, Cornell University ECE 303: Electromagnetic Fields and Waves Fall 2005 Homework 11 Due on Nov. 11, 2005 by 5:00 PM Reading Assignments: i) Review the lecture notes. ii) Review sections 7.1, 7.2, 7.4, and the entire chapter 2 of the paperback book Electromagnetic Waves . Problem 11.1: (Dielectric optical waveguides) Consider the following integrated dielectric optical waveguide on a Silicon chip: The dielectric waveguide is designed to carry light whose free-space wavelength is 1.55 µ m (you can find the corresponding frequency ω from this information). A side note: 1.55 µ m is the also wavelength which is used for fiber-optic communications. Propagation vectors: a) Assuming that h = 1.0 µ m, find the values of k z for the first three TE modes of the waveguide for the frequency ω indicated above. Hint: You will need to solve a transcendental equation graphically to find the value of k x for each TE mode, and then using the value of k x find the corresponding value of k z . Those of you who are thinking of using routines in Matlab or Mathamatica to solve transcendental equations need to be careful of the fact that many such routines may not give all the solutions to an equation if multiple solutions exist. Effective indices: b) Usually the value k z is not specified directly (because it can be a long cumbersome number). Instead the effective index n eff defined by the relation, c k n z eff ω = Silicon Dioxide ( n 2 = 1.5) Silicon Dioxide ( n 2 = 1.5) h Silicon ( n 1 = 3.5) z x 2 is used to specify k z . The effective index is the index of a hypothetical medium in which a plane wave of frequency ω would have the same wavevector k z as that of the waveguide mode. Using your results from part(a), find the effective indices of the first three TE modes. You need to give numerical values as answers. answers....
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This homework help was uploaded on 09/20/2007 for the course ECE 3030 taught by Professor Rana during the Fall '06 term at Cornell University (Engineering School).
- Fall '06
- Electromagnet, Total internal reflection, Waveguide