Guided Modes and Resonant Transmission in Periodic Structures
نویسنده
چکیده
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Periodic Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Periodic Pillars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Summary of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . 9 Chapter 2: Wave Scattering and Guided Modes in Periodic Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1 The Wave Equation and Helmholtz Equation . . . . . . . . . . . . . 11 2.2 Periodic Structures and Pseudo-periodic Solutions . . . . . . . . . . 12 2.3 Plane-wave Scattering by Periodic Slabs . . . . . . . . . . . . . . . 14 2.3.1 Radiation Condition . . . . . . . . . . . . . . . . . . . . . . 14 2.3.2 Plane-wave Scattering Problems and Guided Modes . . . . . 15 2.3.3 Existence of Solutions of Scattering Problems . . . . . . . . 19 2.4 Guided Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.5 Existence and Nonexistence of Guided Modes . . . . . . . . . . . . 25 2.5.1 Existence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.5.2 Nonexistence . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.6 Transmission Anomalies . . . . . . . . . . . . . . . . . . . . . . . . 27 Chapter 3: Total Transmission Resonance in Periodic Slabs . . . . . . 30 3.1 Complex Extension . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2 Scattering and Guided Modes with Complex Extension . . . . . . . 33 3.3 Analyticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.4 Main Theorem: Total Resonant Transmission and Reflection for Symmetric Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.4.1 The Reduced Scattering Matrix . . . . . . . . . . . . . . . . 42 3.4.2 Resonant Transmission . . . . . . . . . . . . . . . . . . . . . 47 3.5 Nongeneric Resonant Transmission . . . . . . . . . . . . . . . . . . 51 3.5.1 Total Background Reflection and Transmission . . . . . . . . 51 3.5.2 Multiple Anomalies . . . . . . . . . . . . . . . . . . . . . . . 57 3.6 Transmission Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Chapter 4: Guided Modes in Periodic Pillars . . . . . . . . . . . . . . . . . . . . . 71 4.1 Bessel Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.2 Media Structure and Scattering Problem . . . . . . . . . . . . . . . 74
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