- Book
- xi, 352 p. : ill.
- Preface ixChapter 1: Transfer Matrix 11.1 A Scattering Experiment 21.2 Scattering Matrix and Transfer Matrix 31.3 Transmission and Reflection Amplitudes 101.4 Properties of the Transfer Matrix 121.5 Supplementary Notes 191.6 Problems 24Chapter 2: Rectangular Potentials 282.1 Transfer Matrix 292.2 Transmission Coefficient: E > V0 322.3 Tunneling: 0 < E < V0 382.4 Current Density 422.5 Bound States: V0 < E < 0 452.6 Inverse Problem for Rectangular Potential 472.7 Problems 49Chapter 3: Î´ -Function Potential 563.1 Single Î´-Function Potential 563.2 Two Î´-Function Repulsive Potentials 603.3 Bound States of Double Î´-Function Attractive Potentials 623.4 N Identical Î´-Function Barriers 643.5 Supplementary Notes 683.6 Problems 69Chapter 4: Kronig-Penney Model 744.1 The Periodic Model 754.2 Allowed Energy Bands 764.3 The Density of States 814.4 Wave Function 834.5 Single Impurity 844.6 N Î´-Function Barriers versus Infinite Kronig-Penney Model 874.7 Supplementary Notes 884.8 Problems 91Chapter 5: Tight Binding Model 985.1 Periodic Model 1005.2 The Transfer Matrix 1045.3 Transmission Coefficient 1065.4 Single Impurity 1075.5 Transmission through Impurities 1085.6 Coupled Pendulum Analogy of the Tight Binding Model 1115.7 Problems 114Chapter 6: Tight Binding Models of Crystals 1206.1 Periodic One-Dimensional System with Two Different Atoms 1206.2 Periodic Model with Different Distances between Neighboring Atoms 1256.3 Periodic One-dimensional System with Two Different Atoms and Spatial Period l = 4a 1266.4 Reduced Zone Scheme 1296.5 Problems 130Chapter 7: Disordered Models 1377.1 Random Tight Binding Model 1387.2 Random Kronig-Penney Model 1507.3 Supplementary Notes 1597.4 Problems 168Chapter 8: Numerical Solution of the Schrodinger Equation 1738.1 Numerical Procedure 1738.2 Accuracy of Numerical Data 1748.3 Numerical Data for Transmission 1778.4 Problems 179Chapter 9: Transmission and Reflection of Plane Electromagnetic Waves on an Interface 1819.1 Plane Wave at the Interface 1819.2 Transmission and Reflection Coefficients 1849.3 Interface between Two Dielectric Materials 1899.4 Interface between a Dielectric Material and a Metal 1909.5 Total Transmission 1959.6 Total Reflection 1989.7 Problems 200Chapter 10: Transmission and Reflection Coefficients for a Slab 20510.1 Transmission and Reflection Amplitudes: TE and TM modes 20610.2 Dielectric Slab Embedded in Vacuum 20910.3 Transmission through a Metallic Slab 22010.4 Problems 223Chapter 11: Surface Waves 22511.1 Surface Waves at the Interface between Two Media 22611.2 Surface Modes on a Slab 23311.3 Experimental Observation of Surface Waves 23711.4 Problems 241Chapter 12: Resonant Tunneling through Double-Layer Structures 24312.1 Transmission through Two Dielectric Layers 24312.2 Transmission through Two Metallic Layers 24612.3 Problems 248Chapter 13: Layered Electromagnetic Medium: Photonic Crystals 24913.1 Photonic Crystals: Infinite Periodic Layered Medium 25013.2 Periodic Arrangement of Dielectric Layers 25213.3 Band Structure of Photonic Crystals 25413.4 Coupling to a Finite Photonic Crystal 25813.5 Layered Dispersive Media 26313.6 Kronig-Penney Model of a Photonic Crystal 26913.7 Problems 271Chapter 14: Effective Parameters 27514.1 Effective Parameters of a Layered Medium 27614.2 Retrieval Procedure 27914.3 Alternating Layers with Negative Permittivity and Negative Permeability 28214.4 Problem 285Chapter 15: Wave Propagation in Nonlinear Structures 28615.1 Single Î´-Function Layer of a Nonlinear Dielectric 28615.2 Nonlinear Kronig-Penney Î´-Function Model 29015.3 Problems 296Chapter 16: Left-Handed Materials 29816.1 Electromagnetic Properties of Left-Handed Materials 29916.2 Transmission through a Slab of Left-Handed Material 30316.3 Structure of Left-Handed Materials 30916.4 Problems 317Appendix A: Matrix Operations 321A.1 The Determinant and the Trace of the Matrix 321A.2 Inverse, Transpose, and Unitary Matrices 322A.3 Eigenvalues and Eigenvectors 324A.4 Similarity Transformations 324A.5 Degeneracy 325Appendix B: Summary of Electrodynamics Formulas 327B.1 Maxwell's Equations 327B.2 Wave Equation 330B.3 Group Velocity and Phase Velocity 331B.4 Poynting Vector 333B.5 Boundary Condition at an Interface 334B.6 Permitivity and Permeability 335B.7 Metals 337Bibliography 341Index 349.
- (source: Nielsen Book Data)9780691130033 20170814
(source: Nielsen Book Data)9780691130033 20170814
- Preface ixChapter 1: Transfer Matrix 11.1 A Scattering Experiment 21.2 Scattering Matrix and Transfer Matrix 31.3 Transmission and Reflection Amplitudes 101.4 Properties of the Transfer Matrix 121.5 Supplementary Notes 191.6 Problems 24Chapter 2: Rectangular Potentials 282.1 Transfer Matrix 292.2 Transmission Coefficient: E > V0 322.3 Tunneling: 0 < E < V0 382.4 Current Density 422.5 Bound States: V0 < E < 0 452.6 Inverse Problem for Rectangular Potential 472.7 Problems 49Chapter 3: Î´ -Function Potential 563.1 Single Î´-Function Potential 563.2 Two Î´-Function Repulsive Potentials 603.3 Bound States of Double Î´-Function Attractive Potentials 623.4 N Identical Î´-Function Barriers 643.5 Supplementary Notes 683.6 Problems 69Chapter 4: Kronig-Penney Model 744.1 The Periodic Model 754.2 Allowed Energy Bands 764.3 The Density of States 814.4 Wave Function 834.5 Single Impurity 844.6 N Î´-Function Barriers versus Infinite Kronig-Penney Model 874.7 Supplementary Notes 884.8 Problems 91Chapter 5: Tight Binding Model 985.1 Periodic Model 1005.2 The Transfer Matrix 1045.3 Transmission Coefficient 1065.4 Single Impurity 1075.5 Transmission through Impurities 1085.6 Coupled Pendulum Analogy of the Tight Binding Model 1115.7 Problems 114Chapter 6: Tight Binding Models of Crystals 1206.1 Periodic One-Dimensional System with Two Different Atoms 1206.2 Periodic Model with Different Distances between Neighboring Atoms 1256.3 Periodic One-dimensional System with Two Different Atoms and Spatial Period l = 4a 1266.4 Reduced Zone Scheme 1296.5 Problems 130Chapter 7: Disordered Models 1377.1 Random Tight Binding Model 1387.2 Random Kronig-Penney Model 1507.3 Supplementary Notes 1597.4 Problems 168Chapter 8: Numerical Solution of the Schrodinger Equation 1738.1 Numerical Procedure 1738.2 Accuracy of Numerical Data 1748.3 Numerical Data for Transmission 1778.4 Problems 179Chapter 9: Transmission and Reflection of Plane Electromagnetic Waves on an Interface 1819.1 Plane Wave at the Interface 1819.2 Transmission and Reflection Coefficients 1849.3 Interface between Two Dielectric Materials 1899.4 Interface between a Dielectric Material and a Metal 1909.5 Total Transmission 1959.6 Total Reflection 1989.7 Problems 200Chapter 10: Transmission and Reflection Coefficients for a Slab 20510.1 Transmission and Reflection Amplitudes: TE and TM modes 20610.2 Dielectric Slab Embedded in Vacuum 20910.3 Transmission through a Metallic Slab 22010.4 Problems 223Chapter 11: Surface Waves 22511.1 Surface Waves at the Interface between Two Media 22611.2 Surface Modes on a Slab 23311.3 Experimental Observation of Surface Waves 23711.4 Problems 241Chapter 12: Resonant Tunneling through Double-Layer Structures 24312.1 Transmission through Two Dielectric Layers 24312.2 Transmission through Two Metallic Layers 24612.3 Problems 248Chapter 13: Layered Electromagnetic Medium: Photonic Crystals 24913.1 Photonic Crystals: Infinite Periodic Layered Medium 25013.2 Periodic Arrangement of Dielectric Layers 25213.3 Band Structure of Photonic Crystals 25413.4 Coupling to a Finite Photonic Crystal 25813.5 Layered Dispersive Media 26313.6 Kronig-Penney Model of a Photonic Crystal 26913.7 Problems 271Chapter 14: Effective Parameters 27514.1 Effective Parameters of a Layered Medium 27614.2 Retrieval Procedure 27914.3 Alternating Layers with Negative Permittivity and Negative Permeability 28214.4 Problem 285Chapter 15: Wave Propagation in Nonlinear Structures 28615.1 Single Î´-Function Layer of a Nonlinear Dielectric 28615.2 Nonlinear Kronig-Penney Î´-Function Model 29015.3 Problems 296Chapter 16: Left-Handed Materials 29816.1 Electromagnetic Properties of Left-Handed Materials 29916.2 Transmission through a Slab of Left-Handed Material 30316.3 Structure of Left-Handed Materials 30916.4 Problems 317Appendix A: Matrix Operations 321A.1 The Determinant and the Trace of the Matrix 321A.2 Inverse, Transpose, and Unitary Matrices 322A.3 Eigenvalues and Eigenvectors 324A.4 Similarity Transformations 324A.5 Degeneracy 325Appendix B: Summary of Electrodynamics Formulas 327B.1 Maxwell's Equations 327B.2 Wave Equation 330B.3 Group Velocity and Phase Velocity 331B.4 Poynting Vector 333B.5 Boundary Condition at an Interface 334B.6 Permitivity and Permeability 335B.7 Metals 337Bibliography 341Index 349.
- (source: Nielsen Book Data)9780691130033 20170814
(source: Nielsen Book Data)9780691130033 20170814
- Book
- 1 online resource (xi, 352 pages) : illustrations
- Preface ixChapter 1: Transfer Matrix 11.1 A Scattering Experiment 21.2 Scattering Matrix and Transfer Matrix 31.3 Transmission and Reflection Amplitudes 101.4 Properties of the Transfer Matrix 121.5 Supplementary Notes 191.6 Problems 24Chapter 2: Rectangular Potentials 282.1 Transfer Matrix 292.2 Transmission Coefficient: E > V0 322.3 Tunneling: 0 < E < V0 382.4 Current Density 422.5 Bound States: V0 < E < 0 452.6 Inverse Problem for Rectangular Potential 472.7 Problems 49Chapter 3: Î´ -Function Potential 563.1 Single Î´-Function Potential 563.2 Two Î´-Function Repulsive Potentials 603.3 Bound States of Double Î´-Function Attractive Potentials 623.4 N Identical Î´-Function Barriers 643.5 Supplementary Notes 683.6 Problems 69Chapter 4: Kronig-Penney Model 744.1 The Periodic Model 754.2 Allowed Energy Bands 764.3 The Density of States 814.4 Wave Function 834.5 Single Impurity 844.6 N Î´-Function Barriers versus Infinite Kronig-Penney Model 874.7 Supplementary Notes 884.8 Problems 91Chapter 5: Tight Binding Model 985.1 Periodic Model 1005.2 The Transfer Matrix 1045.3 Transmission Coefficient 1065.4 Single Impurity 1075.5 Transmission through Impurities 1085.6 Coupled Pendulum Analogy of the Tight Binding Model 1115.7 Problems 114Chapter 6: Tight Binding Models of Crystals 1206.1 Periodic One-Dimensional System with Two Different Atoms 1206.2 Periodic Model with Different Distances between Neighboring Atoms 1256.3 Periodic One-dimensional System with Two Different Atoms and Spatial Period l = 4a 1266.4 Reduced Zone Scheme 1296.5 Problems 130Chapter 7: Disordered Models 1377.1 Random Tight Binding Model 1387.2 Random Kronig-Penney Model 1507.3 Supplementary Notes 1597.4 Problems 168Chapter 8: Numerical Solution of the Schrodinger Equation 1738.1 Numerical Procedure 1738.2 Accuracy of Numerical Data 1748.3 Numerical Data for Transmission 1778.4 Problems 179Chapter 9: Transmission and Reflection of Plane Electromagnetic Waves on an Interface 1819.1 Plane Wave at the Interface 1819.2 Transmission and Reflection Coefficients 1849.3 Interface between Two Dielectric Materials 1899.4 Interface between a Dielectric Material and a Metal 1909.5 Total Transmission 1959.6 Total Reflection 1989.7 Problems 200Chapter 10: Transmission and Reflection Coefficients for a Slab 20510.1 Transmission and Reflection Amplitudes: TE and TM modes 20610.2 Dielectric Slab Embedded in Vacuum 20910.3 Transmission through a Metallic Slab 22010.4 Problems 223Chapter 11: Surface Waves 22511.1 Surface Waves at the Interface between Two Media 22611.2 Surface Modes on a Slab 23311.3 Experimental Observation of Surface Waves 23711.4 Problems 241Chapter 12: Resonant Tunneling through Double-Layer Structures 24312.1 Transmission through Two Dielectric Layers 24312.2 Transmission through Two Metallic Layers 24612.3 Problems 248Chapter 13: Layered Electromagnetic Medium: Photonic Crystals 24913.1 Photonic Crystals: Infinite Periodic Layered Medium 25013.2 Periodic Arrangement of Dielectric Layers 25213.3 Band Structure of Photonic Crystals 25413.4 Coupling to a Finite Photonic Crystal 25813.5 Layered Dispersive Media 26313.6 Kronig-Penney Model of a Photonic Crystal 26913.7 Problems 271Chapter 14: Effective Parameters 27514.1 Effective Parameters of a Layered Medium 27614.2 Retrieval Procedure 27914.3 Alternating Layers with Negative Permittivity and Negative Permeability 28214.4 Problem 285Chapter 15: Wave Propagation in Nonlinear Structures 28615.1 Single Î´-Function Layer of a Nonlinear Dielectric 28615.2 Nonlinear Kronig-Penney Î´-Function Model 29015.3 Problems 296Chapter 16: Left-Handed Materials 29816.1 Electromagnetic Properties of Left-Handed Materials 29916.2 Transmission through a Slab of Left-Handed Material 30316.3 Structure of Left-Handed Materials 30916.4 Problems 317Appendix A: Matrix Operations 321A.1 The Determinant and the Trace of the Matrix 321A.2 Inverse, Transpose, and Unitary Matrices 322A.3 Eigenvalues and Eigenvectors 324A.4 Similarity Transformations 324A.5 Degeneracy 325Appendix B: Summary of Electrodynamics Formulas 327B.1 Maxwell's Equations 327B.2 Wave Equation 330B.3 Group Velocity and Phase Velocity 331B.4 Poynting Vector 333B.5 Boundary Condition at an Interface 334B.6 Permitivity and Permeability 335B.7 Metals 337Bibliography 341Index 349.
- (source: Nielsen Book Data)9780691130033 20170814
(source: Nielsen Book Data)9780691130033 20170814
- Preface ixChapter 1: Transfer Matrix 11.1 A Scattering Experiment 21.2 Scattering Matrix and Transfer Matrix 31.3 Transmission and Reflection Amplitudes 101.4 Properties of the Transfer Matrix 121.5 Supplementary Notes 191.6 Problems 24Chapter 2: Rectangular Potentials 282.1 Transfer Matrix 292.2 Transmission Coefficient: E > V0 322.3 Tunneling: 0 < E < V0 382.4 Current Density 422.5 Bound States: V0 < E < 0 452.6 Inverse Problem for Rectangular Potential 472.7 Problems 49Chapter 3: Î´ -Function Potential 563.1 Single Î´-Function Potential 563.2 Two Î´-Function Repulsive Potentials 603.3 Bound States of Double Î´-Function Attractive Potentials 623.4 N Identical Î´-Function Barriers 643.5 Supplementary Notes 683.6 Problems 69Chapter 4: Kronig-Penney Model 744.1 The Periodic Model 754.2 Allowed Energy Bands 764.3 The Density of States 814.4 Wave Function 834.5 Single Impurity 844.6 N Î´-Function Barriers versus Infinite Kronig-Penney Model 874.7 Supplementary Notes 884.8 Problems 91Chapter 5: Tight Binding Model 985.1 Periodic Model 1005.2 The Transfer Matrix 1045.3 Transmission Coefficient 1065.4 Single Impurity 1075.5 Transmission through Impurities 1085.6 Coupled Pendulum Analogy of the Tight Binding Model 1115.7 Problems 114Chapter 6: Tight Binding Models of Crystals 1206.1 Periodic One-Dimensional System with Two Different Atoms 1206.2 Periodic Model with Different Distances between Neighboring Atoms 1256.3 Periodic One-dimensional System with Two Different Atoms and Spatial Period l = 4a 1266.4 Reduced Zone Scheme 1296.5 Problems 130Chapter 7: Disordered Models 1377.1 Random Tight Binding Model 1387.2 Random Kronig-Penney Model 1507.3 Supplementary Notes 1597.4 Problems 168Chapter 8: Numerical Solution of the Schrodinger Equation 1738.1 Numerical Procedure 1738.2 Accuracy of Numerical Data 1748.3 Numerical Data for Transmission 1778.4 Problems 179Chapter 9: Transmission and Reflection of Plane Electromagnetic Waves on an Interface 1819.1 Plane Wave at the Interface 1819.2 Transmission and Reflection Coefficients 1849.3 Interface between Two Dielectric Materials 1899.4 Interface between a Dielectric Material and a Metal 1909.5 Total Transmission 1959.6 Total Reflection 1989.7 Problems 200Chapter 10: Transmission and Reflection Coefficients for a Slab 20510.1 Transmission and Reflection Amplitudes: TE and TM modes 20610.2 Dielectric Slab Embedded in Vacuum 20910.3 Transmission through a Metallic Slab 22010.4 Problems 223Chapter 11: Surface Waves 22511.1 Surface Waves at the Interface between Two Media 22611.2 Surface Modes on a Slab 23311.3 Experimental Observation of Surface Waves 23711.4 Problems 241Chapter 12: Resonant Tunneling through Double-Layer Structures 24312.1 Transmission through Two Dielectric Layers 24312.2 Transmission through Two Metallic Layers 24612.3 Problems 248Chapter 13: Layered Electromagnetic Medium: Photonic Crystals 24913.1 Photonic Crystals: Infinite Periodic Layered Medium 25013.2 Periodic Arrangement of Dielectric Layers 25213.3 Band Structure of Photonic Crystals 25413.4 Coupling to a Finite Photonic Crystal 25813.5 Layered Dispersive Media 26313.6 Kronig-Penney Model of a Photonic Crystal 26913.7 Problems 271Chapter 14: Effective Parameters 27514.1 Effective Parameters of a Layered Medium 27614.2 Retrieval Procedure 27914.3 Alternating Layers with Negative Permittivity and Negative Permeability 28214.4 Problem 285Chapter 15: Wave Propagation in Nonlinear Structures 28615.1 Single Î´-Function Layer of a Nonlinear Dielectric 28615.2 Nonlinear Kronig-Penney Î´-Function Model 29015.3 Problems 296Chapter 16: Left-Handed Materials 29816.1 Electromagnetic Properties of Left-Handed Materials 29916.2 Transmission through a Slab of Left-Handed Material 30316.3 Structure of Left-Handed Materials 30916.4 Problems 317Appendix A: Matrix Operations 321A.1 The Determinant and the Trace of the Matrix 321A.2 Inverse, Transpose, and Unitary Matrices 322A.3 Eigenvalues and Eigenvectors 324A.4 Similarity Transformations 324A.5 Degeneracy 325Appendix B: Summary of Electrodynamics Formulas 327B.1 Maxwell's Equations 327B.2 Wave Equation 330B.3 Group Velocity and Phase Velocity 331B.4 Poynting Vector 333B.5 Boundary Condition at an Interface 334B.6 Permitivity and Permeability 335B.7 Metals 337Bibliography 341Index 349.
- (source: Nielsen Book Data)9780691130033 20170814
(source: Nielsen Book Data)9780691130033 20170814
- Book
- 1 online resource ( xi, 352 pages) : illustrations.
- Preface ixChapter 1: Transfer Matrix 11.1 A Scattering Experiment 21.2 Scattering Matrix and Transfer Matrix 31.3 Transmission and Reflection Amplitudes 101.4 Properties of the Transfer Matrix 121.5 Supplementary Notes 191.6 Problems 24Chapter 2: Rectangular Potentials 282.1 Transfer Matrix 292.2 Transmission Coefficient: E > V0 322.3 Tunneling: 0 < E < V0 382.4 Current Density 422.5 Bound States: V0 < E < 0 452.6 Inverse Problem for Rectangular Potential 472.7 Problems 49Chapter 3: Î´ -Function Potential 563.1 Single Î´-Function Potential 563.2 Two Î´-Function Repulsive Potentials 603.3 Bound States of Double Î´-Function Attractive Potentials 623.4 N Identical Î´-Function Barriers 643.5 Supplementary Notes 683.6 Problems 69Chapter 4: Kronig-Penney Model 744.1 The Periodic Model 754.2 Allowed Energy Bands 764.3 The Density of States 814.4 Wave Function 834.5 Single Impurity 844.6 N Î´-Function Barriers versus Infinite Kronig-Penney Model 874.7 Supplementary Notes 884.8 Problems 91Chapter 5: Tight Binding Model 985.1 Periodic Model 1005.2 The Transfer Matrix 1045.3 Transmission Coefficient 1065.4 Single Impurity 1075.5 Transmission through Impurities 1085.6 Coupled Pendulum Analogy of the Tight Binding Model 1115.7 Problems 114Chapter 6: Tight Binding Models of Crystals 1206.1 Periodic One-Dimensional System with Two Different Atoms 1206.2 Periodic Model with Different Distances between Neighboring Atoms 1256.3 Periodic One-dimensional System with Two Different Atoms and Spatial Period l = 4a 1266.4 Reduced Zone Scheme 1296.5 Problems 130Chapter 7: Disordered Models 1377.1 Random Tight Binding Model 1387.2 Random Kronig-Penney Model 1507.3 Supplementary Notes 1597.4 Problems 168Chapter 8: Numerical Solution of the Schrodinger Equation 1738.1 Numerical Procedure 1738.2 Accuracy of Numerical Data 1748.3 Numerical Data for Transmission 1778.4 Problems 179Chapter 9: Transmission and Reflection of Plane Electromagnetic Waves on an Interface 1819.1 Plane Wave at the Interface 1819.2 Transmission and Reflection Coefficients 1849.3 Interface between Two Dielectric Materials 1899.4 Interface between a Dielectric Material and a Metal 1909.5 Total Transmission 1959.6 Total Reflection 1989.7 Problems 200Chapter 10: Transmission and Reflection Coefficients for a Slab 20510.1 Transmission and Reflection Amplitudes: TE and TM modes 20610.2 Dielectric Slab Embedded in Vacuum 20910.3 Transmission through a Metallic Slab 22010.4 Problems 223Chapter 11: Surface Waves 22511.1 Surface Waves at the Interface between Two Media 22611.2 Surface Modes on a Slab 23311.3 Experimental Observation of Surface Waves 23711.4 Problems 241Chapter 12: Resonant Tunneling through Double-Layer Structures 24312.1 Transmission through Two Dielectric Layers 24312.2 Transmission through Two Metallic Layers 24612.3 Problems 248Chapter 13: Layered Electromagnetic Medium: Photonic Crystals 24913.1 Photonic Crystals: Infinite Periodic Layered Medium 25013.2 Periodic Arrangement of Dielectric Layers 25213.3 Band Structure of Photonic Crystals 25413.4 Coupling to a Finite Photonic Crystal 25813.5 Layered Dispersive Media 26313.6 Kronig-Penney Model of a Photonic Crystal 26913.7 Problems 271Chapter 14: Effective Parameters 27514.1 Effective Parameters of a Layered Medium 27614.2 Retrieval Procedure 27914.3 Alternating Layers with Negative Permittivity and Negative Permeability 28214.4 Problem 285Chapter 15: Wave Propagation in Nonlinear Structures 28615.1 Single Î´-Function Layer of a Nonlinear Dielectric 28615.2 Nonlinear Kronig-Penney Î´-Function Model 29015.3 Problems 296Chapter 16: Left-Handed Materials 29816.1 Electromagnetic Properties of Left-Handed Materials 29916.2 Transmission through a Slab of Left-Handed Material 30316.3 Structure of Left-Handed Materials 30916.4 Problems 317Appendix A: Matrix Operations 321A.1 The Determinant and the Trace of the Matrix 321A.2 Inverse, Transpose, and Unitary Matrices 322A.3 Eigenvalues and Eigenvectors 324A.4 Similarity Transformations 324A.5 Degeneracy 325Appendix B: Summary of Electrodynamics Formulas 327B.1 Maxwell's Equations 327B.2 Wave Equation 330B.3 Group Velocity and Phase Velocity 331B.4 Poynting Vector 333B.5 Boundary Condition at an Interface 334B.6 Permitivity and Permeability 335B.7 Metals 337Bibliography 341Index 349.
- (source: Nielsen Book Data)9780691130033 20170814
(source: Nielsen Book Data)9780691130033 20170814
- Preface ixChapter 1: Transfer Matrix 11.1 A Scattering Experiment 21.2 Scattering Matrix and Transfer Matrix 31.3 Transmission and Reflection Amplitudes 101.4 Properties of the Transfer Matrix 121.5 Supplementary Notes 191.6 Problems 24Chapter 2: Rectangular Potentials 282.1 Transfer Matrix 292.2 Transmission Coefficient: E > V0 322.3 Tunneling: 0 < E < V0 382.4 Current Density 422.5 Bound States: V0 < E < 0 452.6 Inverse Problem for Rectangular Potential 472.7 Problems 49Chapter 3: Î´ -Function Potential 563.1 Single Î´-Function Potential 563.2 Two Î´-Function Repulsive Potentials 603.3 Bound States of Double Î´-Function Attractive Potentials 623.4 N Identical Î´-Function Barriers 643.5 Supplementary Notes 683.6 Problems 69Chapter 4: Kronig-Penney Model 744.1 The Periodic Model 754.2 Allowed Energy Bands 764.3 The Density of States 814.4 Wave Function 834.5 Single Impurity 844.6 N Î´-Function Barriers versus Infinite Kronig-Penney Model 874.7 Supplementary Notes 884.8 Problems 91Chapter 5: Tight Binding Model 985.1 Periodic Model 1005.2 The Transfer Matrix 1045.3 Transmission Coefficient 1065.4 Single Impurity 1075.5 Transmission through Impurities 1085.6 Coupled Pendulum Analogy of the Tight Binding Model 1115.7 Problems 114Chapter 6: Tight Binding Models of Crystals 1206.1 Periodic One-Dimensional System with Two Different Atoms 1206.2 Periodic Model with Different Distances between Neighboring Atoms 1256.3 Periodic One-dimensional System with Two Different Atoms and Spatial Period l = 4a 1266.4 Reduced Zone Scheme 1296.5 Problems 130Chapter 7: Disordered Models 1377.1 Random Tight Binding Model 1387.2 Random Kronig-Penney Model 1507.3 Supplementary Notes 1597.4 Problems 168Chapter 8: Numerical Solution of the Schrodinger Equation 1738.1 Numerical Procedure 1738.2 Accuracy of Numerical Data 1748.3 Numerical Data for Transmission 1778.4 Problems 179Chapter 9: Transmission and Reflection of Plane Electromagnetic Waves on an Interface 1819.1 Plane Wave at the Interface 1819.2 Transmission and Reflection Coefficients 1849.3 Interface between Two Dielectric Materials 1899.4 Interface between a Dielectric Material and a Metal 1909.5 Total Transmission 1959.6 Total Reflection 1989.7 Problems 200Chapter 10: Transmission and Reflection Coefficients for a Slab 20510.1 Transmission and Reflection Amplitudes: TE and TM modes 20610.2 Dielectric Slab Embedded in Vacuum 20910.3 Transmission through a Metallic Slab 22010.4 Problems 223Chapter 11: Surface Waves 22511.1 Surface Waves at the Interface between Two Media 22611.2 Surface Modes on a Slab 23311.3 Experimental Observation of Surface Waves 23711.4 Problems 241Chapter 12: Resonant Tunneling through Double-Layer Structures 24312.1 Transmission through Two Dielectric Layers 24312.2 Transmission through Two Metallic Layers 24612.3 Problems 248Chapter 13: Layered Electromagnetic Medium: Photonic Crystals 24913.1 Photonic Crystals: Infinite Periodic Layered Medium 25013.2 Periodic Arrangement of Dielectric Layers 25213.3 Band Structure of Photonic Crystals 25413.4 Coupling to a Finite Photonic Crystal 25813.5 Layered Dispersive Media 26313.6 Kronig-Penney Model of a Photonic Crystal 26913.7 Problems 271Chapter 14: Effective Parameters 27514.1 Effective Parameters of a Layered Medium 27614.2 Retrieval Procedure 27914.3 Alternating Layers with Negative Permittivity and Negative Permeability 28214.4 Problem 285Chapter 15: Wave Propagation in Nonlinear Structures 28615.1 Single Î´-Function Layer of a Nonlinear Dielectric 28615.2 Nonlinear Kronig-Penney Î´-Function Model 29015.3 Problems 296Chapter 16: Left-Handed Materials 29816.1 Electromagnetic Properties of Left-Handed Materials 29916.2 Transmission through a Slab of Left-Handed Material 30316.3 Structure of Left-Handed Materials 30916.4 Problems 317Appendix A: Matrix Operations 321A.1 The Determinant and the Trace of the Matrix 321A.2 Inverse, Transpose, and Unitary Matrices 322A.3 Eigenvalues and Eigenvectors 324A.4 Similarity Transformations 324A.5 Degeneracy 325Appendix B: Summary of Electrodynamics Formulas 327B.1 Maxwell's Equations 327B.2 Wave Equation 330B.3 Group Velocity and Phase Velocity 331B.4 Poynting Vector 333B.5 Boundary Condition at an Interface 334B.6 Permitivity and Permeability 335B.7 Metals 337Bibliography 341Index 349.
- (source: Nielsen Book Data)9780691130033 20170814
(source: Nielsen Book Data)9780691130033 20170814
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