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EE 164 Problem Set 4 Solution

# EE 164 Problem Set 4 Solution - EE 164 Problem 1 Problem...

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EE 164 Problem Set 4 Spring 2005 Problem 1: How many TE modes can propagate in the symmetrical slab in Section 4.2 (AlGaAs) if 5 d λ = ? Repeat the problem for 10 d = and 100. Solution 22 12 1 2 2 1 , 3.6 , 3.55 d Nn n n n =+ = = d N Number of modes ( ) dm µ 5 6.98 6 4.1 10 12.96 12 8.2 100 120.6 120 82 Problem 2: For a certain symmetrical dielectric slab, 1 1.48 n = and 2 1.46 n = . The slab is surrounded by air. Draw the ray path of a cladding mode if θ (the angle in the film) is75 D . At what values of do the cladding modes no longer appear? Solution () ( ) 1 112 21 , sin 80.6 C nn n n == D ( ) 1 220 02 , sin 43.23 C D Therefore, the ray is totally reflected. There are no cladding modes for , 80.6 C θθ >= D and for ( ) , tC < , 1 2 sin sin 42.5 C <=   D 75 = D 0 1 n = 2 1.46 n = 1 1.48 n = 78.3 t = D 2 n 0 n Problem 3: Use this equation ( ) 11 2 2 nn n L cn τ ∆= to show that the modal pulse spread per unit length can be approximated by the following expressions: ( ) 1 L nc =∆ 2 1 2 NA L cn Solution: From ( ) 2 L cn 2 L cn (0.1)

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If 1 n nearly equals 2 n () 1 n L c τ ∆= (0.2) Also, using the approximation 1 2 NA n =∆ (0.3) we find 22 1 2 NA n (0.4) 1 2 NA n (0.5) Then putting this into (0.2) 2 1 2 1 2 nNA L cn    2 1 2 NA L cn
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EE 164 Problem Set 4 Solution - EE 164 Problem 1 Problem...

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