BASIC THEORY OF ELECTROMAGNETIC SCATTERING 1 11 . 12 . . 13 14 . 2 3 4 Dyadic Green’s Function Green’s Functions Plane Wave Represent at ion Cylindrical Waves Spherical Waves Huygens’ Principle and Extinction Sensing and Bistatic Theorem Scattering 54 54 55 57 59 60 66 68 73 73 and Active Remote Coefficients Optical Reciprocity Reciprocity Reciprocal Scattering Symmetry Eulerian T-Matrix T-Matrix Unitarity Theorem | Scattering of Electromagnetic Waves Theories and Applications Leung Tsang Jin Au Kong Kung-Hau Ding Copyright 2000 John Wiley Sons Inc. ISBNs 0-471-38799-1 Hardback 0-471-22428-6 Electronic Chapter 2 BASIC THEORY OF ELECTROMAGNETIC SCATTERING 1 Dyadic Green s Function 54 Green s Functions 54 Plane Wave Representation 55 Cylindrical Waves 57 Spherical Waves 59 2 Huygens Principle and Extinction Theorem 60 3 Active Remote Sensing and Bistatic Scattering Coefficients 66 4 Optical Theorem 68 5 Reciprocity and Symmetry 73 Reciprocity 73 Reciprocal Relations for Bistatic Scattering Coefficients and Scattering Amplitudes 75 Symmetry Relations for Dyadic Green s Function 79 6 Eulerian Angles of Rotation 81 7 T-Matrix 83 T-Matrix and Relation to Scattering Amplitudes 83 Unitarity and Symmetry 88 8 Extended Boundary Condition 91 Extended Boundary Condition Technique 91 Spheres 97 Scattering and Absorption for Arbitrary Excitation 100 Mie Scattering of Coated Sphere 102 Spheroids 104 References and Additional Readings 106 - 53 - 54 2 BASIC THEORY OF ELECTROMAGNETIC SCATTERING 1 Dyadic Green s Function Green s Functions The Green s function is the solution of the field equation for a point source. Using the principle of linear superposition the solution of the field due to a general source is just the convolution of the Green s function with the source. The equation for the Green s function for the scalar wave equation is V2 k g r r S r r where 5 f r is the three-dimensional Dirac delta function with the source located at r . The solution of is Kong 1990 Ishimaru 1991 fi L Lp_ p The dyadic Green s function relates the vector electromagnetic fields to vector current sources. From the Maxwell equations in frequency domain with exp zwt time convention V x E ia p H V xH -iueE J V-pH Q V eE p it follows that the electric field obeys the vector wave equation V x V x E k2E iwp J
