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ECEN 5264 Course Notes

ECEN 5264 Course Notes - Electromagnetic Absorption...

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Electromagnetic Absorption, Scattering and Propagation ECEN 5264 Course Notes A.J. Gasiewski c ° 1993, 2007
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Contents Introduction vii 0.1 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii 1 Plane Wave Propagation 1 1.1 Time Domain Maxwell°s Equations . . . . . . . . . . . . . . . . . 2 1.1.1 Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.2 Poynting°s Theorem . . . . . . . . . . . . . . . . . . . . . 7 1.2 Frequency Domain Maxwell°s Equations . . . . . . . . . . . . . . 8 1.2.1 Complex Poynting°s Theorem . . . . . . . . . . . . . . . . 10 1.2.2 Time Harmonic Wave Equation and Dispersion . . . . . . 11 1.2.3 Transverse Fields and Characteristic Impedance . . . . . 15 1.2.4 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.2.5 Power Flux and Absorption Coe¢ cient . . . . . . . . . . . 18 1.2.6 Dispersive Delay and Pulse Propagation . . . . . . . . . . 20 1.3 Boundary Conditions and Re±ection of Plane Waves . . . . . . . 20 1.3.1 Re±ection of Plane Waves from Multiply-Layered Media . 24 I Part I: Electromagnetic Absorption 25 2 Quantum Mechanical Basis for Absorption and Refraction 27 2.1 Zenith Transmission Spectrum of the Earth . . . . . . . . . . . . 29 2.2 Quantum Mechanical Theory of Polarization . . . . . . . . . . . 30 2.2.1 Schroedinger°s Equation . . . . . . . . . . . . . . . . . . . 30 2.2.2 Observables . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.2.3 Perturbation Theory for Induced Polarization . . . . . . . 35 2.2.4 State Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.2.5 State Amplitude Solution . . . . . . . . . . . . . . . . . . 40 2.2.6 State Population Statistics . . . . . . . . . . . . . . . . . 42 2.2.7 Complex Permittivity and Absorption Coe¢ cient . . . . . 42 2.3 Types of Atomic and Molecular Transitions . . . . . . . . . . . . 47 2.3.1 Electronic Transitions . . . . . . . . . . . . . . . . . . . . 48 2.3.2 Vibrational Transitions . . . . . . . . . . . . . . . . . . . 48 iii
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iv CONTENTS 2.3.3 Rotational Transitions . . . . . . . . . . . . . . . . . . . . 48 2.3.4 Spin-Rotational Coupling . . . . . . . . . . . . . . . . . . 48 2.3.5 Zeeman Splitting . . . . . . . . . . . . . . . . . . . . . . . 48 2.3.6 Inversion Spectra . . . . . . . . . . . . . . . . . . . . . . . 48 3 Dielectric Properties of Liquid and Solid Media 49 3.1 Debye Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2 Dielectric Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 II Part II: Scattering 51 4 Volume Scattering 53 4.1 Scattering from Discrete Objects . . . . . . . . . . . . . . . . . . 53 4.2 Absorption and Scattering by Hydrometeors . . . . . . . . . . . . 53 5 Surface Scattering 55 6 Scattering from Continuous Media 57 III Part III: Propagation 59 7 Propagation in the Ionospheric Plasma 61 7.1 The Classical Ionospheric Plasma . . . . . . . . . . . . . . . . . . 61 7.2 Equations of Motion and Collisions . . . . . . . . . . . . . . . . . 61 7.3 Cyclotron Resonance . . . . . . . . . . . . . . . . . . . . . . . . . 61 7.4 Magnetized Plasmas . . . . . . . . . . . . . . . . . . . . . . . . . 61 7.5 Faraday Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 7.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 8 Radiative Transfer Theory 63 8.1 Pro²le Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
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Preface This text is the dissemination of nearly three decades of experience in research, teaching, study, collaboration, and general observation in electromagnetic wave propagation. The material derives from a number of sources, for only a few of which the author can claim orginality. Accordingly, there are numerous refer- ences to contributions by many radio scientists, some of whom are household names and others less well known but whose contributions helped build a solid and modern foundation for the ²elds of remote sensing and telecommunications. The accomplishments of radio scientists in elucidating the many peculiar and valuable properties of radio waves in the natural environment has barely been surpassed by any other ²eld of human endeavor, with concessions perhaps to Einsteinian physics and moderne genetics. From the time of Maxwell, and as the result of the contributions of a legion of scientists we are in an age where the behavior of radio waves is can be reliably predicted for almost all applications in remote sensing and telecommunications. While there are most assuredly
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