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hmwk8%20solution

# hmwk8%20solution - Homework 8 solutions 8.1 Omega beta...

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Homework 8 solutions 8.1 Omega beta diagram for the PPP n 1 3 .. := a 0.01 := c 3 10 8 := omegacutoff n π n a c := omegacutoff 2 π 0 1.5 10 10 × 3 10 10 × 4.5 10 10 × = i 1 1000 .. := f i 100 10 9 i 1000 := omega i f i 2 π := k0 i omega i c := kz i n , omega i c 1 omegacutoff n omega i 2 := kz i n , Re kz i n , ( ) i Im kz i n , ( ) := making sure that k is beta - j alpha 0 1 . 10 11 2 . 10 11 3 . 10 11 4 . 10 11 5 . 10 11 6 . 10 11 7 . 10 11 1000 500 0 500 1000 1500 2000 2500 Re kz i 1 , ( ) Re kz i 2 , ( ) Re kz i 3 , ( ) Im kz i 1 , ( ) Im kz i 2 , ( ) Im kz i 3 , ( ) k0 i 95 10 9 191 10 9 omega i I have highlighted the first two cutoff omegas where the propagation constant comes out of being -j alpha to become purely real. You also see how as frequency goes up kz approaches k0

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only plot real angles slope n kx n Re knz n ( ) 0.0000001 + := Then the ray representing the wave travels with the slope: z p p a 1000 := p 0 1000 .. :=
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hmwk8%20solution - Homework 8 solutions 8.1 Omega beta...

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