4. 12 Interpretation of the spatial transform 4. 13 Spatial Fourier decomposition 4. 13.1 Boundary value problems using the spatial Fourier representation 4. 14 Periodic fields and Floquet's theorem 4.14.1 Floquet's theorem 4.14.2 Examples of periodic systems 4.15 Problems 5 Field decompositions and the eM potentials 5.1 Spatial symmetry decomposition 5.1.1 Planar field symmetry 5.2 Solenoidal-lamellar decomposition 5.2.1 Solution for potentials in an unbounded medium: the retarded potentials 5.2.2 Solution for potential functions in a bounded medium 5.3 Transverse-longitudinal decomposition 5.3.1 Transverse-longitudinal decomposition in terms of fields 5.4 TE-TM decomposition 5.4.1 TE-TM decomposition in terms of fields 5.4.2 TE-TM decomposition in terms of Hertzian potentials 5.4.3 Application: hollow-pipe waveguides 5.4.4 TE-TM decomposition in spherical coordinates 5.5 Problems 6 Integral solutions of Maxwells equations 6.1 Vector Kirchoff solution 6.1.1 The Stratton-Chu formula 1.2 The Sommerfeld radiation condition 6 6.1.3 Fields in the excluded region: the extinction theorem 2 Fields in an unbounded medium 6.2.1 The far-zone fields produced by sources in unbounded space 6.3 Fields in a bounded, source-free region 6.3.1 The vector Huygens principle 3.2 The franz formula 6.3.3 Love's equivalence principle 3.4 The Schelkunoff equivalence principle 6.3.5 Far-zone fields produced by equivalent sources 6.4 Problems a Mathematical appendix A.1 The fourier transform A2 Vector transport theorems 1.3 analysis ary value probl B Useful identities c Some Fourier transform pairs 0 2001 by CRC Press LLC4.12 Interpretation of the spatial transform 4.13 Spatial Fourier decomposition 4.13.1 Boundary value problems using the spatial Fourier representation 4.14 Periodic fields and Floquet’s theorem 4.14.1 Floquet’s theorem 4.14.2 Examples of periodic systems 4.15 Problems 5 Field decompositions and the EM potentials 5.1 Spatial symmetry decompositions 5.1.1 Planar field symmetry 5.2 Solenoidal–lamellar decomposition 5.2.1 Solution for potentials in an unbounded medium: the retarded potentials 5.2.2 Solution for potential functions in a bounded medium 5.3 Transverse–longitudinal decomposition 5.3.1 Transverse–longitudinal decomposition in terms of fields 5.4 TE–TM decomposition 5.4.1 TE–TM decomposition in terms of fields 5.4.2 TE–TM decomposition in terms of Hertzian potentials 5.4.3 Application: hollow-pipe waveguides 5.4.4 TE–TM decomposition in spherical coordinates 5.5 Problems 6 Integral solutions of Maxwell’s equations 6.1 Vector Kirchoff solution 6.1.1 The Stratton–Chuformula 6.1.2 The Sommerfeld radiation condition 6.1.3 Fields in the excluded region: the extinction theorem 6.2 Fields in an unbounded medium 6.2.1 The far-zone fields produced by sources in unbounded space 6.3 Fields in a bounded, source-free region 6.3.1 The vector Huygens principle 6.3.2 The Franz formula 6.3.3 Love’s equivalence principle 6.3.4 The Schelkunoff equivalence principle 6.3.5 Far-zone fields produced by equivalent sources 6.4 Problems A Mathematical appendix A.1 The Fourier transform A.2 Vector transport theorems A.3 Dyadic analysis A.4 Boundary value problems B Useful identities C Some Fourier transform pairs