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Unformatted text preview: many TE modes for λ = 1.0μm will there be under the following conditions: a. Covered by air (nc = 1). b. Covered by water (nc = 1.33). c. Covered by another substance (nc = 1.45). You will be much familiar with mode calculations after this problem set. Solving the modes for symmetric waveguide (needed for 4, 5 and 6) is covered on page 55 of the book. The concept used is essentially the same as what we have done in the lecture. 1. Consider a planar slab waveguide on infinite extent in the y and z directions. The guiding film index is 1.5, the substrate index is 1.48, and the cover index is 1.0. The thickness is h = 2 μm. The waveguide is excited with a 1.33 μm source. For TE modes: a. What is the numerical aperture for this waveguide? b. What is the range of allowed β values for this waveguide? c. How many modes will this waveguide carry? d. Numerically or graphically, determine the allowed values of β and κ. 2. For an asymmetric planar waveguide with nf = 1.5, ns = 1.48, and a thickness of 8 μm, how ECE 437 – Fiber and Integrated Optics Homework Assignment #3; Due 25th February, 2010 Thursday 5PM many even TE modes and odd TE modes will there be under the following conditions: a. Wavelength is 1.0μm. b. Wavelength is 1.6μm. c. Wavelength is 5.0μm. d. Explain in words why the number of modes increases when the wavelength decreased or the thickness is increased. 5. For a symmetric planar waveguide with h = 8μm, ns = 1.48, and a wavelength of 1.0μm, how many TM modes will there be under the following conditions (Hint: Make sure truncating the range of the graph doesn’t cause you to miss the first even crossing point.): a. nf is 1.50. c. nf is 1.53. b. nf is 1.51. to ten? 3. Repeat problem 2 for TM modes. 4. For a symmetric planar waveguide with nf = 1.5, ns = 1.48, and a thickness of 8 μm, how d. Explain in words why the number of modes did or did not change in these three cases. e. If nc = 1.45, what thickness waveguide is needed to increase the number of modes d. Explain in words why the number of modes did or did not change in these three cases. 6. Derive the characteristic eigenvalue equation for TE modes in a symmetric waveguide (equation 3.28) ...
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This note was uploaded on 08/10/2010 for the course ECE 4370 at Cornell University (Engineering School).