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TO ELECTROMAGNETIC BY A SINGLE PARTICLE Parameters and Cross Sections Matrix 2 2 6 9 by a Small by a Sphere by an Ellipsoid Particle 9 10 12 14 of Scattering Amplitude and 16 16 18 Waves, and 21 21 22 24 30 Cylinders, Cylinder and Disks Using the Infinite 41 Disk Approximation 46 52 32 32 Length Basic Scattering Amplitudes Amplitude Scattering Scattering Scattering Scattering Dyads Scattering Scattering Rayleigh Rayleigh Rayleigh Rayleigh Scattering 22 . 23 . 24 . 3 . 31 32 . 4 . 41 42 . 43 . 5 6 61 . 62 . 63 . . | 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 1 INTRODUCTION TO ELECTROMAGNETIC SCATTERING BY A SINGLE PARTICLE 1 Basic Scattering Parameters 2 1.1 Scattering Amplitudes and Cross Sections 2 1.2 Scattering Amplitude Matrix 6 2 Rayleigh Scattering 9 2.1 Rayleigh Scattering by a Small Particle 9 2.2 Rayleigh Scattering by a Sphere 10 2.3 Rayleigh Scattering by an Ellipsoid 12 2.4 Scattering Dyads 14 3 Integral Representations of Scattering and Born Approximation 16 3.1 Integral Expression for Scattering Amplitude 16 3.2 Born Approximation 18 4 Plane Waves Cylindrical Waves and Spherical Waves 21 4.1 Cartesian Coordinates Plane Waves 21 4.2 Cylindrical Waves 22 4.3 Spherical Waves 24 5 Acoustic Scattering 30 6 Scattering by Spheres Cylinders and Disks 32 6.1 Mie Scattering 32 6.2 Scattering by a Finite Length Cylinder Using the Infinite Cylinder Approximation 41 6.3 Scattering by a Disk Based on the Infinite Disk Approximation 46 References and Additional Readings 52 - 1 - 2 1 ELECTROMAGNETIC SCATTERING BY SINGLE PARTICLE A major topic in this book is the study of propagation and scattering of waves by randomly distributed particles. We first consider scattering by a single particle. This chapter and the next discuss and derive the scattering characteristics of a single particle. Both exact and solutions are studied. Scattering by a single particle is an important subject in electromagnetics and optics. There exist several excellent textbooks on this subject van de Hulst 1957 Kerker 1969 Bohren and Huffman 1983 . We will treat those topics that are pertinent to later chapters of multiple scattering by random discrete scatterers. 1 Basic Scattering Parameters 1.1 Scattering Amplitudes and Cross Sections Consider an electromagnetic plane wave impinging upon a particle which has permittivity ep r that is different from .