Lect26SlabWaveguides - ECE 3030 Electromagnetic Fields and...

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1 ECE 3030 Electromagnetic Fields and Waves Fall 2009 Lecture 26 2009/10/28 Dielectric Slab Waveguides TE and TM Guided Modes 1 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 26: Instructor: Dr. Wesley E. Swartz core cladding TE Guided Modes in Parallel-Plate Metal Waveguides z o μ ε x i k E r r k E i H i () z k j x o x z e x k E y r E > = sin ˆ 0 E y i k E i H i 2 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 26: Guided TE modes are TE-waves bouncing back and fourth between two metal plates and propagating in the z -direction ! The x-component of the wavevector can have only discrete values – its quantized: z k x k k z x i ˆ ˆ + = z k x k k z x r ˆ ˆ + = r , 3 , 2 1 : where , m d m k x = = π Dielectric Waveguides (1) Consider TE-wave undergoing total internal reflection : z o 1 x z k x k k z x i ˆ ˆ + = z k x k k z x r ˆ ˆ + = i k E r H r r k E i H i o 2 i θ i Evanescent wave 3 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 26: ( ) 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 1 = Γ 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 1 2 2 2 ω o x z k k = + 2 2 2 2 o x z k = x x j k = Dielectric Waveguides (2) z o 1 i k E r H r k E i H i i i 2 1 > o 2 i k E i H i x core cladding Evanescent wave 4 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 26: One can have a guided wave that is bouncing between two dielectric interfaces due to total internal reflection and moving in the z -direction. o 2 Evanescent wave cladding Dielectric Slab Waveguides Assumption: W >> d W 2d 5 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 26: z x core cladding cladding y Dielectric versus Metal Waveguides z o m = 1 m = 2 E y E y Metal Waveguides (modes are tightly confined) o 2 cladding 6 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 26: (modes are loosely confined) Dielectric Slab Waveguides z o 1 o 2 E y E y core cladding
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2 Dielectric Slab Waveguides TE Modes: Formal Solution The TE solutions are of the form: z d 2 o μ ε 2 o 1 o 2 E y E y core cladding cladding x symmetric antisymmetric 7 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 26: () z k j x x o d x z e x k x k E y r E < = sin cos ˆ 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 The “ sine ” and “ cosine ” represent the symmetric and antisymmetric solutions w.r.t. the x -axis.
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This note was uploaded on 11/26/2009 for the course ECE 3030 at Cornell University (Engineering School).

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Lect26SlabWaveguides - ECE 3030 Electromagnetic Fields and...

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