350lect32 - 32 TM modes in dielectric waveguides Last...

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32 TM modes in dielectric waveguides Last lecture we examined the characteristic equation and the cutof Frequencies of TE mode of propagation in dielectric slab waveguides. z x d n 2 n 2 n 1 >n 2 θ i Guidance requires θ i c =s in - 1 n 2 n 1 Guided TE m mode Felds consisting of the superposition of transverse polarized electric Felds ˜ E i yE o e - jk 1 ( - cos θ i x +sin θ i z ) and ˜ E r yE o Γ TE e - jk 1 (cos θ i x +sin θ i z ) , where Γ TE = n 1 cos θ i + j ± n 2 1 s in 2 θ i - n 2 2 n 1 cos θ i - j ± n 2 1 s in 2 θ i - n 2 2 , have 1. propagation angles θ i > θ c =s in - 1 n 2 n 1 , (critical angle) 2. satisfying a characteristic equation d v 1 /f cos θ i - m 2 = 1 π ta n - 1 ± s in 2 θ i - n 2 2 / n 2 1 cos θ i ,m =0 , 1 , 2 , 3 , ··· 3. for frequencies f exceeding the cuto± frequency f c = mc 2 d ± n 2 1 - n 2 2 ,m =0 , 1 , 2 , 3 ···
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For a given f = 2 π ω ,thecharcter ist
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350lect32 - 32 TM modes in dielectric waveguides Last...

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