Cylindrical Dielectric Waveguides
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1 03/02/2017 Cylindrical Dielectric Waveguides Integrated Optics Prof. Elias N. Glytsis School of Electrical & Computer Engineering National Technical University of Athens
2 Geometry of a Single Core Layer Cylindrical Waveguide b y ^ φ b a n 2 n 2 n 1 z a core n 1 r φ ^ r x cladding Maxwell s Equations: Helmholtz s Equation: Prof. Elias N. Glytsis, School of ECE, NTUA 2
3 Single Core Layer Cylindrical Waveguide Helmholtz s Equations for Transverse and Longitudinal Components Expressions for Longitudinal Components Prof. Elias N. Glytsis, School of ECE, NTUA 3
4 Single Core Layer Cylindrical Waveguide Relations of Transverse and Longitudinal Components Maxwell s Curl Equations Prof. Elias N. Glytsis, School of ECE, NTUA 4
5 Single Core Layer Cylindrical Waveguide Transverse Field Components as Functions of Longitudinal Field Components Prof. Elias N. Glytsis, School of ECE, NTUA 5
6 Single Core Layer Cylindrical Waveguide Transverse Electric Field Component Separation of Variables Prof. Elias N. Glytsis, School of ECE, NTUA 6
7 Single Core Layer Cylindrical Waveguide Field Solutions Azimuthal and Radial Solutions Transverse Electric Field Component Solution Prof. Elias N. Glytsis, School of ECE, NTUA 7
8 Oscillatory Bessel Functions Behavior (J ν and Y ν ) Prof. Elias N. Glytsis, School of ECE, NTUA 8
9 Modified Bessel Functions Behavior (I ν and K ν ) Prof. Elias N. Glytsis, School of ECE, NTUA 9
10 Single Core Layer Cylindrical Waveguide Field Solutions Guided Modes Condition Core Region Longitudinal Field Components (r < a) Cladding Region Longitudinal Field Components (r > a) Prof. Elias N. Glytsis, School of ECE, NTUA 10
11 Single Core Layer Cylindrical Waveguide Boundary Conditions z-component of Electric field (E z ) at r = a z-component of Magnetic field (H z ) at r = a Prof. Elias N. Glytsis, School of ECE, NTUA 11
12 Single Core Layer Cylindrical Waveguide Boundary Conditions φ-component of Electric field (E φ ) at r = a Prof. Elias N. Glytsis, School of ECE, NTUA 12
13 Single Core Layer Cylindrical Waveguide Boundary Conditions φ-component of Magnetic field (H φ ) at r = a Prof. Elias N. Glytsis, School of ECE, NTUA 13
14 Single Core Layer Cylindrical Waveguide Dispersion Equation Guided Modes Condition Prof. Elias N. Glytsis, School of ECE, NTUA 14
15 Single Core Layer Cylindrical Waveguide Dispersion Equation Relations between coefficients Prof. Elias N. Glytsis, School of ECE, NTUA 15
16 Single Core Layer Cylindrical Waveguide Dispersion Equation Case of ν = 0: TE 0m and TM 0m Guided Modes Prof. Elias N. Glytsis, School of ECE, NTUA 16
17 Single Core Layer Cylindrical Waveguide Dispersion Equation Case of ν = 0: TE 0m and TM 0m Guided Modes Prof. Elias N. Glytsis, School of ECE, NTUA 17
18 Single Core Layer Cylindrical Waveguide Dispersion Equation Case of ν 0: EH νm and HE νm Guided Modes Dispersion Equation for EH νm Guided Modes Dispersion Equation for HE νm Guided Modes Prof. Elias N. Glytsis, School of ECE, NTUA 18
19 TE 0m and TM 0m Guided Modes Electric & Magnetic Fields TE 0m Guided Modes Prof. Elias N. Glytsis, School of ECE, NTUA 19
20 TE 0m and TM 0m Guided Modes Electric & Magnetic Fields TM 0m Guided Modes Prof. Elias N. Glytsis, School of ECE, NTUA 20
21 TE 0m and TM 0m Guided Modes Electric & Magnetic Fields TE 01 Guided Mode: n 1 = 1.50, n 2 = 1.47, a = 5μm, λ 0 = 1.55μm Prof. Elias N. Glytsis, School of ECE, NTUA 21
22 TE 0m and TM 0m Guided Modes Electric & Magnetic Fields TE 01 Guided Mode: n 1 = 1.50, n 2 = 1.47, a = 5μm, λ 0 = 1.55μm Prof. Elias N. Glytsis, School of ECE, NTUA 22
23 TE 0m and TM 0m Guided Modes Electric & Magnetic Fields TE 02 Guided Mode: n 1 = 1.50, n 2 = 1.47, a = 5μm, λ 0 = 1.55μm Prof. Elias N. Glytsis, School of ECE, NTUA 23
24 TE 0m and TM 0m Guided Modes Electric & Magnetic Fields TE 02 Guided Mode: n 1 = 1.50, n 2 = 1.47, a = 5μm, λ 0 = 1.55μm Prof. Elias N. Glytsis, School of ECE, NTUA 24
25 TE 0m and TM 0m Guided Modes Electric & Magnetic Fields TM 01 & TM 02 Guided Modes: n 1 = 1.50, n 2 = 1.47, a = 5μm, λ 0 = 1.55μm Prof. Elias N. Glytsis, School of ECE, NTUA 25
26 Mode Effective Index vs Normalized Frequency Small Δn = n 1 n 2 = 0.03 Prof. Elias N. Glytsis, School of ECE, NTUA 26
27 Mode Effective Index vs Normalized Frequency Large Δn = n 1 n 2 = 0.20 Prof. Elias N. Glytsis, School of ECE, NTUA 27
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