PERIODIC STRUCTURES: Mode- Matching Approach and Applications in Electromagnetic Engineering -- Contents -- Preface -- 1 Introduction -- 1.1 Historical Perspective on the Research in Periodic Structures -- 1.2 From 1D Periodic Stratified Medium to 3D Photonic Crystals: An Overview of this Book -- 1.2.1 Chapter 2: Wave Propagation in Multiple Dielectric Layers -- 1.2.2 Chapter 3: One-Dimensional Periodic Medium -- 1.2.3 Chapter 4: Two- and Three-Dimensional Periodic Structures -- 1.2.4 Chapter 5: Introducing Defects into Periodic Structures -- 1.2.5 Chapter 6: Periodic Impedance Surface -- 1.2.6 Chapter 7: Exotic Dielectrics Made of Periodic Structures -- References -- Further Readings -- 2 Wave Propagation in Multiple Dielectric Layers -- 2.1 Plane-Wave Solutions in a Uniform Dielectric Medium -- 2.2 Transmission-Line Network Representation of a Dielectric Layer of Finite Thickness -- 2.2.1 Wave Propagating in Regular and Exotic Mediums -- 2.3 Scattering Characteristics of Plane Wave by Multiple Dielectric Layers -- 2.3.1 Recursive-Impedance Method -- 2.3.2 Transfer-Matrix Method -- 2.3.3 Scattering-Matrix Method -- 2.4 Transverse Resonance Technique for Determining the Guiding Characteristics of Waves in Multiple Dielectric Layers -- 2.4.1 Transverse Resonance Technique -- 2.4.2 Will Surface Waves be Supported in a Single Interface Environment? -- 2.4.3 Single Dielectric Layer Backed with a PEC or PMC -- 2.4.4 Mode Dispersion Relation of a Closed Structure Consisting of Dielectric Layers -- Appendix: Dyadic Definition and Properties -- References -- Further Reading -- 3 One-Dimensional Periodic Medium -- 3.1 Bloch-Floquet Theorem -- 3.2 Eigenwave in a 1D Holographic Grating -- 3.2.1 Two Space-Harmonic Approximation -- 3.2.2 Single Interface between a Semi-infinite Uniform and a 1D Periodic Medium.

3.3 Eigenwave in 1D Dielectric Gratings: Modal Transmission-Line Approach -- 3.3.1 In-Plane Incidence: ky = 0 -- 3.3.2 Out-of-Plane Incidence: ky /=0 -- 3.3.3 Eigenwave in a Two-Tone Periodic Medium -- 3.3.4 Sturm-Liouville Differential Equation with Periodic Boundary Condition -- 3.4 Eigenwave in a 1D Metallic Periodic Medium -- 3.4.1 Generalized Scattering Matrix at the Interface between a 1D Metallic Periodic Medium and Uniform Medium -- 3.5 Hybrid-Mode Analysis of a 1D Dielectric Grating: Fourier-Modal Approach -- 3.6 Input-Output Relation of a 1D Periodic Medium of Finite Thickness -- 3.7 Scattering Characteristics of a Grating Consisting of Multiple 1D Periodic Layers -- 3.7.1 Building-Block Approach -- 3.7.2 Scattering Analysis of 1D Diffraction Gratings -- 3.8 Guiding Characteristics of Waveguides Consisting of Multiple 1D Periodic Layers -- 3.8.1 Transverse Resonance Technique -- 3.8.2 Dispersion Relation of a 1D Grating Waveguide -- References -- Further Readings -- 4 Two- and Three-Dimensional Periodic Structures -- 4.1 Modal Transmission-Line Approach for a 2D Periodic Metallic Medium: In-Plane Propagation -- 4.1.1 Generalized Scattering Matrix at the Interface between a 1D Periodic Metallic Medium and Uniform Medium -- 4.1.2 Periodic Boundary Condition on the Unit Cell along the y-axis -- 4.1.3 A Simple Graphical Method -- 4.1.4 Phase Relation: The Relationship among kx, ky, and ko -- 4.1.5 Dispersion Relation: The Relationship between ko and kx (or ky) -- 4.1.6 Brillouin Zone and Band Structure -- 4.2 Modal Transmission Line Approach for a 2D Periodic Dielectric Medium: In-Plane Propagation -- 4.2.1 Input-Output Relation at the Interface: Generalized Scattering Matrix Representation -- 4.2.2 Brillouin Diagram and Phase Relation -- 4.3 Double Fourier-Modal Approach for a 2D Dielectric Periodic Structure: Out-of-Plane Propagation.

4.3.1 Scattering Analysis of a 2D Grating: Out-of-Plane Propagation -- 4.4 Three-Dimensional Periodic Structures -- 4.4.1 Scattering Analysis of a 3D Periodic Structure -- 4.4.2 Eigenwave Analysis of a 3D Periodic Medium -- Appendix: Closed-Form Solution of εpq,mn and μpq,mn -- References -- 5 Introducing Defects into Periodic Structures -- 5.1 A Parallel-Plane Waveguide having a Pair of 1D Semi-Infinite Periodic Structures as its Side Walls -- 5.1.1 Bloch Impedance -- 5.1.2 Surface States Supported at the Interface of a Semi-Infinite 1D Periodic Structure -- 5.1.3 A Semi-Infinite 1D Periodic Structure Consisting of Symmetric Dielectric Waveguides -- 5.2 Dispersion Relation of a Parallel-Plane Waveguide with Semi-Infinite 1D Periodic Structures as Waveguide Side Walls -- 5.2.1 Numerical Example -- 5.3 A Parallel-Plane Waveguide with 2D Dielectric Periodic Structures as its Side Walls -- 5.3.1 Method of Mathematical Analysis -- 5.3.2 Dispersion Relation of a Channel with a Pair of 2D Periodic Structures as its Waveguide Side Walls -- 5.4 Scattering Characteristics of a Periodic Structure with Defects -- 5.4.1 Fabry-Perot Etalon -- 5.4.2 The Correlation between the Scattering and Guiding Characteristics -- 5.5 A Parallel-Plane Waveguide with 2D Metallic Periodic Structures as its Side Walls -- 5.6 Other Applications in Microwave Engineering -- References -- 6 Periodic Impedance Surface -- 6.1 Scattering Characteristics of Plane Wave by a 1D Periodic Structure Consisting of a Cavities Array -- 6.1.1 An AMC Surface Made of Corrugated Metal Surface with Quarter-Wavelength Depth -- 6.2 Periodic Impedance Surface Approach (PISA) -- 6.3 Scattering of Plane Wave by 1D Periodic Impedance Surface: Non-Principal Plane Propagation -- 6.3.1 Guiding Characteristics of Waves Supported by a 1D Periodic Impedance Surface.

6.4 Scattering of Plane Wave by a Dyadic 2D Periodic Impedance Surface -- References -- 7 Exotic Dielectrics Made of Periodic Structures -- 7.1 Synthetic Dielectrics Using a 2D Dielectric Columns Array -- 7.1.1 Description of the Example -- 7.1.2 Phase-Relation Diagram of a Uniform Dielectric Medium -- 7.2 Refractive Index of a 2D Periodic Medium -- 7.2.1 Conclusion -- 7.3 An Artificial Dielectric Made of 1D Periodic Dielectric Layers -- 7.3.1 Effective Refractive Index of the 1D Dielectric Periodic Medium -- 7.3.2 Effective Wave-Impedance of the 1D Dielectric Periodic Medium -- 7.4 Conclusion -- References -- Index.