Part I: Introductory Foundations |
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1 Essentials of Electricity and Magnetism |
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3 | (40) |
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1.1 Maxwell's static equations in vacuum |
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3 | (3) |
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1.1.1 Electrostatic equations |
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4 | (1) |
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1.1.2 Magnetostatic equations |
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5 | (1) |
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6 | (1) |
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1.2 Maxwell's static equations in matter |
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6 | (8) |
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1.2.1 Response of material to fields |
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7 | (2) |
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1.2.2 Bound charges and currents |
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9 | (1) |
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10 | (1) |
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1.2.4 Polarizability and Susceptibility |
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11 | (2) |
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1.2.5 The canonical constitutive relations |
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13 | (1) |
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1.2.6 Electric fields and free charges in materials |
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13 | (1) |
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1.3 Energy of static charge and current configurations |
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14 | (4) |
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1.3.1 Electrostatic field energy |
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14 | (2) |
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1.3.2 Magnetic field energy |
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16 | (2) |
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1.4 Maxwell's dynamic equations in vacuum |
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18 | (4) |
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1.4.1 Faraday's contribution |
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19 | (1) |
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1.4.2 Conservation of charge and the continuity equation |
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20 | (1) |
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1.4.3 Maxwell's contribution |
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21 | (1) |
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1.5 Maxwell's dynamic equations in matter |
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22 | (2) |
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1.5.1 Origin of material currents |
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22 | (2) |
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1.6 Plane wave propagation in vacuum |
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24 | (5) |
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1.6.1 Polarization of plane waves |
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26 | (3) |
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1.7 E&M propagation within simple media |
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29 | (1) |
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1.8 Electromagnetic conservation laws |
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30 | (4) |
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30 | (1) |
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31 | (1) |
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1.8.3 Linear momentum density |
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31 | (2) |
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1.8.4 Maxwell stress tensor |
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33 | (1) |
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34 | (4) |
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1.9.1 Field amplitude as a function of distance from the source |
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35 | (1) |
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1.9.2 Decoupling of radiation fields from the source |
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35 | (1) |
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1.9.3 Illustration of coupled and decoupled fields from an accelerated charge |
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36 | (2) |
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38 | (1) |
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39 | (4) |
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43 | (20) |
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2.1 The magnetic and electric fields in terms of potentials |
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43 | (1) |
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44 | (1) |
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2.3 The wave equations prescribing the potentials using the Lorenz gauge |
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45 | (1) |
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46 | (3) |
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2.4.1 Potentials with retarded time |
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48 | (1) |
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2.5 Moments of the retarded potential |
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49 | (6) |
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49 | (2) |
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2.5.2 General expansion of the retarded potential |
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51 | (4) |
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55 | (1) |
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55 | (8) |
Part II Origins of Radiation Fields |
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3 General Relations between Fields and Sources |
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63 | (22) |
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3.1 Relating retarded potentials to observable fields |
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63 | (4) |
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3.1.1 Spatial derivatives of retarded potentials |
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65 | (2) |
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3.2 Jefimenko's equations from the retarded potentials |
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67 | (2) |
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3.3 Graphical representation of transverse fields arising from acceleration |
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69 | (2) |
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3.4 Jefimenko's equations without regard to retarded potentials: |
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71 | (3) |
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3.4.1 Field characteristics |
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74 | (1) |
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3.4.2 Example: fields directly from Jefimenko's equations |
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75 | (4) |
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79 | (1) |
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80 | (5) |
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4 Fields in Terms of the Multipole Moments of the Source |
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85 | (28) |
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4.1 Multipole radiation using Jefimenko's equations |
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85 | (6) |
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4.1.1 Approximate spatial dependence |
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85 | (2) |
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4.1.2 Radiation from zeroth order moments |
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87 | (2) |
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4.1.3 Radiation from first order moments |
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89 | (2) |
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4.2 Multipole radiation from the scalar expansion of the vector potential |
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91 | (8) |
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4.2.1 Fields from an electric dipole moment |
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92 | (2) |
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4.2.2 Fields from magnetic dipole moment |
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94 | (4) |
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4.2.3 Fields from electric quadrupole moment |
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98 | (1) |
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4.3 Power radiated in terms of multipole moments of the source |
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99 | (4) |
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4.3.1 Power radiated by electric dipole moment |
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99 | (1) |
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4.3.2 Power radiated by magnetic dipole moment |
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100 | (1) |
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4.3.3 Power radiated by electric quadrupole moment |
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101 | (2) |
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103 | (3) |
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106 | (7) |
Part III: Electromagnetism and Special Relativity |
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5 Introduction to Special Relativity |
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113 | (71) |
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5.1 Historical introduction-1666 to 1905 |
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115 | (6) |
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5.1.1 The nature of space and time |
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115 | (2) |
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5.1.2 The nature of light |
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117 | (4) |
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5.1.3 Michelson-Morley experiments |
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121 | (1) |
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5.2 Einstein and the Lorentz transformation |
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121 | (9) |
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5.2.1 Einstein's approach |
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122 | (3) |
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5.2.2 The Lorentz transformation: covariance among inertial frames |
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125 | (5) |
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5.3 The invariant interval and the geometry of space-time |
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130 | (9) |
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5.3.1 Minkowski space-time diagrams |
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131 | (4) |
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5.3.2 Physical consequences of special relativity |
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135 | (4) |
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5.4 Vector space concepts |
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139 | (11) |
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5.4.1 Contravariant and covariant vectors |
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141 | (7) |
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148 | (1) |
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5.4.3 Generation of other 4-vectors and 4-tensors |
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149 | (1) |
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5.5 Some important general 4-vectors |
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150 | (9) |
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5.5.1 The 4-gradient operator |
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151 | (2) |
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5.5.2 The 4-vector velocity |
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153 | (1) |
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5.5.3 The 4-vector momentum |
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154 | (3) |
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157 | (2) |
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5.6 Some important "E&M" 4-vectors |
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159 | (3) |
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159 | (2) |
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5.6.2 The 4-current density |
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161 | (1) |
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5.6.3 The 4-potential (in Lorenz Gauge) |
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161 | (1) |
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5.7 Other covariant and invariant quantities |
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162 | (2) |
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5.7.1 The angular momentum 4-tensor |
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162 | (1) |
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163 | (1) |
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5.7.3 Space-time delta function |
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164 | (1) |
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5.8 Summary of 4-vector results |
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164 | (1) |
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5.9 Maxwell's equations and special relativity |
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165 | (8) |
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5.9.1 Manifest covariance of Maxwell's equations |
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165 | (1) |
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5.9.2 The electromagnetic field tensor |
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166 | (3) |
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5.9.3 Simple field transformation examples |
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169 | (4) |
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5.10 The Einstein stress-energy tensor |
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173 | (2) |
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175 | (1) |
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176 | (8) |
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6 Radiation from Charges Moving at Relativistic Velocities |
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184 | (45) |
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6.1 Lienard-Wiechert potentials |
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185 | (5) |
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6.1.1 Derivation by integral transform |
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187 | (1) |
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6.1.2 Derivation by geometric construction |
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188 | (2) |
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6.2 Radiation fields from a single charge undergoing acceleration |
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190 | (6) |
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6.2.1 Moving charge general field characteristics |
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195 | (1) |
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6.3 Power radiated from an accelerated charge |
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196 | (4) |
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6.3.1 Low velocities and classical Larmor's formula |
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197 | (1) |
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6.3.2 Radiated power for relativistic particles |
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198 | (2) |
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6.4 Acceleration parallel and perpendicular to velocity |
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200 | (5) |
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6.4.1 Angular distribution for acceleration to velocity |
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200 | (2) |
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6.4.2 Angular distribution for acceleration to velocity |
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202 | (1) |
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6.4.3 Total radiated power for acceleration and to velocity |
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203 | (2) |
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6.5 Spectral distribution of radiation from an accelerated charge |
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205 | (4) |
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6.6 Synchrotron radiation |
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209 | (5) |
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6.7 Fields from a single charge moving with constant velocity |
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214 | (9) |
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6.7.1 Parametrization of the fields |
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218 | (2) |
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6.7.2 Spectral energy density of the fields |
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220 | (2) |
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6.7.3 Number of photons associated with fields of a passing charge |
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222 | (1) |
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223 | (4) |
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227 | (1) |
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228 | (1) |
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7 Relativistic Electrodynamics |
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229 | (38) |
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7.1 Dynamics using action principles: Lagrangian and Hamiltonian mechanics |
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229 | (5) |
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230 | (4) |
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7.2 Relativistic mechanics of single point-like particles |
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234 | (9) |
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7.2.1 The relativistic mechanics of a free particle |
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234 | (2) |
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7.2.2 Free particle canonical 4-momentum |
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236 | (1) |
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7.2.3 Free particle angular momentum 4-tensor |
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237 | (2) |
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7.2.4 A charged particle in an external electromagnetic field |
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239 | (4) |
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7.3 The action principle description of the electromagnetic field |
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243 | (11) |
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7.3.1 Equations of motion |
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245 | (2) |
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7.3.2 Lagrangian density function |
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247 | (2) |
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7.3.3 Recovery of Maxwell's equations |
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249 | (1) |
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250 | (2) |
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7.3.5 The Proca Lagrangian |
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252 | (2) |
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7.4 The Hamiltonian density and canonical stress-energy tensor |
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254 | (7) |
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7.4.1 From the Maxwell stress tensor to the 4D stress-energy tensor |
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254 | (1) |
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7.4.2 Hamiltonian density: the "00" canonical stress-energy tensor component |
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255 | (1) |
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7.4.3 Canonical stress-energy tensor and conservation laws |
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256 | (1) |
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7.4.4 Canonical electromagnetic stress-energy tensor |
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257 | (1) |
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7.4.5 Symmetric electromagnetic stress-energy tensor |
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258 | (1) |
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7.4.6 Angular momentum density of fields |
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259 | (2) |
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7.4.7 Electromagnetic stress-energy tensor including source terms |
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261 | (1) |
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261 | (2) |
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263 | (4) |
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8 Field Reactions to Moving Charges |
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267 | (36) |
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8.1 Electromagnetic field masses |
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268 | (1) |
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8.2 Field reaction as a self-force |
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269 | (7) |
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8.2.1 Lorentz calculation of the self-force |
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270 | (4) |
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8.2.2 Some qualitative arguments for the self-force |
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274 | (2) |
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8.3 Abraham-Lorentz formula and the equations of motion |
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276 | (8) |
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8.3.1 The equations of motion |
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278 | (4) |
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8.3.2 Landau-Lifshitz approximation |
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282 | (1) |
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8.3.3 Characteristic time |
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283 | (1) |
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8.4 The 4/3 problem, instability, and relativity |
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284 | (7) |
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8.5 Infinite mass of the Abraham-Lorentz model |
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291 | (3) |
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294 | (2) |
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296 | (7) |
Part IV Radiation in Materials |
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9 Properties of Electromagnetic Radiation in Materials |
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303 | (63) |
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9.1 Polarization, magnetization, and current density |
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304 | (2) |
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9.2 A practical convention for material response |
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306 | (1) |
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9.3 E&M propagation within simple media |
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307 | (3) |
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310 | (12) |
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9.4.1 ω moving towards infinity |
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310 | (2) |
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312 | (1) |
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9.4.3 Plane waves versus diffusion |
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313 | (3) |
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9.4.4 Transient response in a conductor |
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316 | (1) |
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9.4.5 Temporal wave-packet |
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317 | (2) |
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9.4.6 Group velocity versus phase velocity |
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319 | (1) |
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320 | (2) |
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9.5 Plane waves at interfaces |
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322 | (13) |
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322 | (3) |
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9.5.2 Fresnel transmission and reflection amplitude coefficients |
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325 | (3) |
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9.5.3 Total internal reflection |
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328 | (4) |
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9.5.4 Fresnel transmission and reflection intensity coefficients |
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332 | (1) |
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9.5.5 Fresnel transmission and reflection: vacuum/material interface |
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333 | (2) |
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9.6 Some practical applications |
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335 | (4) |
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9.6.1 The two-surface problem |
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335 | (3) |
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9.6.2 Lossy dielectrics and metals |
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338 | (1) |
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9.7 Frequency and time domain polarization response to the fields |
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339 | (4) |
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342 | (1) |
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9.8 Kramers-Kronig relationships |
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343 | (3) |
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9.9 Measuring the response of matter to fields |
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346 | (12) |
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9.9.1 Measuring the optical constants of a material |
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347 | (1) |
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9.9.2 Single frequency measurements |
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348 | (7) |
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9.9.3 Spectral measurements |
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355 | (3) |
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358 | (2) |
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360 | (6) |
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10 Models of Electromagnetic Response of Materials |
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366 | (32) |
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10.1 Classical models of Drude and Lorentz |
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366 | (10) |
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10.1.1 The Drude model of free electrons |
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368 | (2) |
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10.1.2 The Lorentz model of bound electrons |
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370 | (4) |
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10.1.3 The combined model: Lorentz-Drude |
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374 | (1) |
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10.1.4 Lorentz and Drude model response functions |
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375 | (1) |
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376 | (8) |
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10.2.1 Multiple binding frequencies |
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383 | (1) |
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10.3 Drude metals and plasmas |
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384 | (4) |
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10.4 Measuring the Lorentz-drude response of matter to fields |
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388 | (6) |
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10.4.1 Single frequency measurements |
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388 | (1) |
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10.4.2 Dual polarization Fresnel reflectivity measurement |
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389 | (2) |
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10.4.3 Broadband measurements and response models |
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391 | (3) |
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394 | (4) |
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11 Scattering of Electromagnetic Radiation in Materials |
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398 | (69) |
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398 | (4) |
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11.2 Scattering by dielectric small particles |
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402 | (9) |
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11.2.1 Scattering by a free electron: Thomson scattering |
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404 | (1) |
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11.2.2 Scattering by a harmonically bound electron |
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405 | (2) |
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11.2.3 Scattering near resonance |
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407 | (1) |
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408 | (3) |
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11.3 Integral equations, the Born approximation and optical theorem |
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411 | (12) |
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413 | (4) |
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417 | (6) |
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11.4 Partial wave analysis |
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423 | (20) |
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424 | (5) |
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11.4.2 Vector partial wave analysis |
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429 | (9) |
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11.4.3 Solution of scattering from a homogeneous sphere: Mie scattering |
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438 | (5) |
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443 | (12) |
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11.5.1 The long wavelength limit |
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443 | (2) |
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11.5.2 Scattering off dielectric spheres: water droplets |
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445 | (10) |
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455 | (1) |
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456 | (11) |
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12 Diffraction and the Propagation of Light |
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467 | (56) |
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467 | (3) |
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12.2 Geometric optics and the eikonal equation |
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470 | (1) |
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12.3 Kirchhoff's diffraction theory |
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471 | (17) |
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12.3.1 Kirchhoff's integral theorem |
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471 | (2) |
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12.3.2 Kirchhoff's diffraction theory: boundary conditions |
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473 | (2) |
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12.3.3 Alternate boundary conditions: Rayleigh-Sommerfeld diffraction |
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475 | (4) |
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12.3.4 Babinet's principle |
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479 | (2) |
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12.3.5 Fresnel approximation |
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481 | (2) |
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12.3.6 Fraunhofer (far-field) diffraction |
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483 | (2) |
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12.3.7 Fresnel diffraction of rectangular slit: the near-field |
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485 | (3) |
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12.4 The angular spectrum representation |
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488 | (26) |
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491 | (4) |
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12.4.2 Fourier optics (far-field) |
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495 | (1) |
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12.4.3 Tight focusing of fields |
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496 | (10) |
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12.4.4 Diffraction limits on microscopy |
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506 | (8) |
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514 | (2) |
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516 | (7) |
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13 Radiation Fields in Constrained Environments |
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523 | (49) |
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13.1 Constrained environments |
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523 | (4) |
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13.2 Mode counting: the density of electromagnetic modes in space |
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527 | (3) |
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530 | (2) |
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532 | (5) |
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13.5 Spontaneous emission: the Einstein A and B coefficients |
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537 | (3) |
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540 | (3) |
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13.7 Microwave waveguides |
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543 | (5) |
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13.7.1 General features of waveguides |
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543 | (2) |
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13.7.2 Rectangular conducting waveguides |
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545 | (1) |
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13.7.3 Transmission lines and coaxial cables: TEM modes |
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546 | (2) |
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13.8 One-dimensional optical waveguides: the ray optic picture |
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548 | (17) |
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13.8.1 The three-layer planar waveguide: the wave solutions of Maxwell's equations |
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553 | (4) |
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13.8.2 Fiber optics: the step-index circular waveguide |
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557 | (5) |
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13.8.3 Higher order modes, single mode fibers, and dispersion |
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562 | (3) |
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565 | (6) |
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571 | (1) |
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572 | (41) |
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A Vector Multipole Expansion of the Fields |
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583 | (30) |
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A.1 Vector spherical harmonics |
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583 | (1) |
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A.1.1 VSH expansion of general radiation fields |
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584 | (1) |
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A.2 Multipole expansion of electromagnetic radiation |
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584 | (5) |
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A.2.1 Non-homogeneous field wave equations |
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584 | (1) |
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A.2.2 VSH expansion of the field wave equations |
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585 | (2) |
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A.2.3 Parity considerations |
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587 | (1) |
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A.2.4 Multipole expansion in a source-free region |
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588 | (1) |
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A.3 Multipole radiation: energy and angular momentum |
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589 | (5) |
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A.3.1 Energy density and the Poynting vector |
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589 | (2) |
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A.3.2 Momentum density and angular momentum density |
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591 | (3) |
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A.4 Multipole fields from vector harmonic expansion |
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594 | (19) |
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A.4.1 Multipole expansion including sources |
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594 | (4) |
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A.4.2 The small source approximation: near and far zones |
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598 | (15) |
References |
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613 | (4) |
Index |
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617 | |