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9: Electromagnetic Waves

Last updated

Jun 7, 2025
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- 8.3: Distortions due to loss and dispersion
- 9.1: Waves at planar boundaries at normal incidence

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Chapter 9 treats the propagation of plane waves in vacuum and simple media, at planar boundaries, and in combinations confined between sets of planar boundaries, as in waveguides or cavity resonators. Chapter 10 then discusses how such waves can be generated and received by antennas and antenna arrays. More specifically, Section 9.1 explains how plane waves are reflected from planar boundaries at normal incidence, and Section 9.2 treats reflection and refraction when the waves are incident at arbitrary angles. Section 9.3 then explains how linear combinations of such waves can satisfy all boundary conditions when they are confined within parallel plates or rectangular cylinders acting as waveguides. By adding planar boundaries at the ends of such waveguides, waves can be trapped at the resonant frequencies of the resulting cavity, as explained in Section 9.4. Sections 9.5 then treat waves in anisotropic, dispersive, and ionized media, respectively.

9.1: Waves at planar boundaries at normal incidence
This page explores boundary value problems in electromagnetics, emphasizing the uniqueness of solutions from Maxwell's equations and boundary conditions. It presents a four-step method for solving these problems and uses practical examples, including wave reflection at a perfect conductor and power reflection at a dielectric interface.
9.2: Waves incident on planar boundaries at angles
This page covers the determination of electromagnetic fields through boundary value problems, examining wave propagation at boundaries and using complex notation for frequency-dependent phenomena. It discusses TE and TM wave behavior, boundary conditions, and Snell's law. The text further details evanescent waves, lossy media impact on wave propagation, and reflection/transmission characteristics in conductors.
9.3: Waves Guided within Cartesian Boundaries
This page covers wave propagation in parallel-plate and rectangular waveguides, emphasizing Transverse Electric (TE) and Transverse Magnetic (TM) modes. It explains the conditions for modes to propagate, including cut-off frequencies and their implications for wave behavior, such as evanescent modes.
9.4: Cavity resonators
This page examines rectangular cavity resonators, which are hollow conducting structures operating at discrete resonant frequencies determined by their dimensions. The fundamental mode TE101 marks the lowest frequency, with energy decay characterized by a quality factor Q. Physical alterations of the resonator, influenced by electromagnetic forces, affect resonant frequency and energy storage.
9.5: Waves in complex media
This page explores wave behavior in anisotropic media and birefringent materials, emphasizing how direction-dependent properties affect wave propagation and polarization. It delves into plasma dynamics, including phase and group velocities, dispersion phenomena, and the implications of wave behavior relative to the plasma frequency. Additionally, it discusses exponential decay of waves, particularly the delay between electric and magnetic fields, leading to unique energy storage characteristics.

Thumbnail: Sinusoidal traveling plane wave entering a region of lower wave velocity at an angle, illustrating the decrease in wavelength and change of direction (refraction) that results. (CC BY-SA 3.0 Unported; Richard F. Lyon via Wikipedia)

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