lecture26 - Lecture 26 Dielectric Slab Waveguides In this...

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1 ECE 303 – Fall 2005 – Farhan Rana – Cornell University Lecture 26 Dielectric Slab Waveguides In this lecture you will learn: • Dielectric slab waveguides •TE and TM guided modes in dielectric slab waveguides ECE 303 – Fall 2005 – Farhan Rana – Cornell University TE Guided Modes in Parallel-Plate Metal Waveguides z o µ ε x z k x k k z x i ˆ ˆ + = r z k x k k z x r ˆ ˆ + = r i k r E r H r r k r E i H i () z k j x o x z e x k E y r E > = sin ˆ 0 r r Guided TE modes are TE-waves bouncing back and fourth between two metal plates and propagating in the z-direction ! E y i k r E i H i K K , 3 , 2 1 : where , m d m k x = = π The x-component of the wavevector can have only discrete values – its quantized
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2 ECE 303 – Fall 2005 – Farhan Rana – Cornell University Dielectric Waveguides - I z o µ ε 1 x z k x k k z x i ˆ ˆ + = r z k x k k z x r ˆ ˆ + = r i k r E r H r r k r E i H i Consider TE-wave undergoing total internal reflection : () ( ) z k x k j i z k x k j i x z x z x e E y e E y r E + + > Γ + = ˆ ˆ 0 r r 1 = Γ o 2 i θ i when c i > 2 1 > When : c i > x z k j i x x z e e E T y r E α < = ˆ 0 r r 1 2 2 2 ω o x z k k = + 2 2 2 2 o x z k = Evanescent wave x x j k = ECE 303 – Fall 2005 – Farhan Rana – Cornell University Dielectric Waveguides - II z o 1 i k r E r H r r k r E i H i o 2 i i 2 1 > Evanescent wave o 2 i k r E i H i x One can have a guided wave that is bouncing between two dielectric interfaces due to total internal reflection and moving in the z-direction core cladding cladding Evanescent wave
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3 ECE 303 – Fall 2005 – Farhan Rana – Cornell University Dielectric Slab Waveguides W 2d z x Assumption: W >> d core cladding cladding y ECE 303 – Fall 2005 – Farhan Rana – Cornell University Dielectric Vs Metal Waveguides z o µ ε m = 1 m = 2 E y E y Metal Waveguides (modes are tightly confined) (modes are loosely confined) Dielectric Slab Waveguides z o 2 o 1 o 2 E y E y core cladding cladding
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4 ECE 303 – Fall 2005 – Farhan Rana – Cornell University Dielectric Slab Waveguides – TE Modes: Formal Solution The TE solutions are of the form: () ( ) z k j x x o d x z e x k x k E y r E < = sin cos ˆ r r z k j d x d x z k j d x d x z x z x e e E y r E e e E y r E + + < > + = = α 1 1 ˆ ˆ r r r r The “sine” and “cosine” represent the symmetric and antisymmetric solutions w.r.t. the z-axis 1 2 2 2 ε µ ω o x z k k = + 2 2 2 2 o x z k = Where: Given a frequency , the values of k z , k x , and x are still not known z
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lecture26 - Lecture 26 Dielectric Slab Waveguides In this...

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