Unformatted text preview: ECE604 Homework 9
Out: Tuesday, March 23, 2004 (Session 19)
Due: Tuesday, March 30, 2004 (Session 21)
[Students with tape delays: due according to session number] Problem numbers are from the text by Ramo, Whinnery and Van Duzer (3rd edition, 1994). 1. Write a computer program (cg, in Matlab, or equivalent) to calculate the frequency— dependent reﬂectivity R in terms of power (R 2 lplz) for a multi-layer mirror composed of the following layer sequence: (air)(I—lL I-lL HL) (H) (substrate) W Fv—"
M pairs one extra NH" layer This means that the wave is incident from air, through a series of 2M+1 dielectric layers,
then onto the substrate. Take the substrate to be silica glass (index of refraction n = 1.45 ).
The high-index (H) and low index (L) layers have refractive indices 11H = 2.2 and nL = 1.4,
respectively. The thicknesses of H and L layers are each chosen to be quarter—wave at a free—space wavelength of 15th (frequency = 2 x1014 Hz). That is, the thicknesses ti}; and dL are chosen such that anH =2: and nLdL = A 4 4,for7t=1.5ttm. Using your program, plot the power reflectivity lp]2 as a function of frequency over the
range 1.3.1014 Hz to 3-1014 Hz, for M = 3, M = 5, M = 7, and M = 9. What is the impact of increasing the number of layers? 2) 6.3b
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