Wave Propagation in Periodic Structures

Preface......Page 4
Contents......Page 6
1. Historical Background; Eighteenth Century......Page 10
2. Historical Background; Nineteenth Century. Cauchy, Baden-Powell, and Kelvin......Page 12
3. Later Work on Models Similar to That Treated in Sec. 2......Page 20
4. General Remarks......Page 26
5. A Lattice of Free Particles......Page 28
6. Longitudinal Vibration in a Row of Equidistant Coupled Oscillators......Page 30
7. Longitudinal Vibrations in a Row of Diatomic Molecules......Page 31
8. Equation of Motion of a One-dimensional Lattice of Identical Particles......Page 35
9. Rigorous Discussion for the Case of Interactions between Nearest Neighbors Only......Page 40
10. Discussion of the Distance of Interaction......Page 42
11. The Low-pass Electric Filter......Page 46
12. Analogies between Electrical and Mechanical Systems......Page 49
13. Equations of Motion for the One-dimensional NaCl Lattice......Page 53
14. Electrical Analogue of the One-dimensional Diatomic Lattice......Page 56
15. Discussion of the One-dimensional NaCl Lattice......Page 59
16. Transition from a Diatomic to a Monatomic Lattice......Page 66
17. The One-dimensional Lattice of Polyatomic Molecules......Page 74
18. General Discussion; Phase Velocity......Page 78
19. A Theorem from the Theory of Complex Variables......Page 79
20. Energy Density, Energy Flow, and Energy Velocity......Page 81
21. Group Velocity and Propagation of a Signal......Page 83
22. Preliminary Definition of Characteristic Impedance......Page 89
23. Junction of Two Lattices......Page 94
24. General Definition of Characteristic Impedance......Page 97
25. Direct and Reciprocal Lattices in Two Dimensions......Page 103
26. Doubly and Triply Periodic Functions......Page 108
27. Zones in a Two-dimensional Lattice......Page 111
28. Propagation of Waves in a Continuous Two-dimensional Medium with a Periodic Perturbation......Page 116
29. The Exceptional Waves of Case 2 and Bragg Reflection......Page 124
30. Transition Near the Discontinuity......Page 127
31. Examples and Discussion of Zones in Two Dimensions......Page 130
32. Direct and Reciprocal Lattices in Three Dimensions......Page 140
33. Zones in Three Dimensions and Bragg Reflection; Ewald's Construction......Page 145
34. General Results for a Wave Propagating in a Three-dimensional Periodic Medium......Page 148
35. Waves in a Homogeneous Isotropic Medium with a Small Periodic Perturbation......Page 152
36. General Remarks on Waves in a Discontinuous Lattice......Page 156
37. Some Examples of Zones in Three Dimensions......Page 157
38. Zones in the Direct Lattice; Principle of the Wigner-Seitz Method......Page 164
39. Frequency Distribution for Waves in an Actual Crystal......Page 166
40. The Energy of a Solid; the Characteristic Temperatures......Page 173
41. Thermal Expansion and Entropy of a Solid Body......Page 176
42. Mathieu's Equation......Page 181
43. Mathieu Functions: General Discussion......Page 184
44. Hill's Equation with a Rectangular Curve......Page 189
45. The Self-excited Oscillator......Page 195
46. Free Electrons in Metals......Page 199
47. General Remarks......Page 202
48. Expressions for Energy......Page 206
49. Definition of a Four-terminal and Equation for Its Circuit......Page 209
50. Matrix Notation for a Four-terminal......Page 210
51. Combination of Two Four-terminals; Multiplication of Matrices......Page 212
52. Inverse and Reversed Four-terminals and Transformations......Page 213
53. Four-terminal Matrices and the Group C[2]......Page 215
54. Surge, Iterative, or Characteristic Impedance of a Four-terminal......Page 218
55. Propagation along a Line of Four-terminals......Page 220
56. Application of the Theory to a Reversible Four-terminal......Page 223
57. Passing Bands and Attenuation in a Line of Four-Terminals......Page 225
58. Reflected Waves in a Line Terminated by an Impedance ζ[0]......Page 226
59. A Continuous Line Loaded with Two-terminals......Page 227
60. A Continuous Line Loaded with Four-terminals......Page 233
61. Transition from a Line of Four-terminals to a Continuous Line......Page 236
62. Examples of Four-terminal Representation of Continuous Lines......Page 238
63. Application of Hill's Equation to a Continuous Line......Page 241
64. Normalization of the Matrix (ε[ij]) and the Pauli Matrices......Page 243
65. Three-phase and Polyphase Lines......Page 245
Appendix......Page 250
Index......Page 258