This chapter extends the study of electromagnetic waves from vacuum to material media, focusing on how the presence of matter modifies wave propagation. It begins by generalizing Maxwell’s equations in matter, introducing the auxiliary fields \(\textbf{D}\) (electric displacement) and \(\textbf{H}\) (magnetic excitation) to account for polarization ( \(\textbf{P}\) ) and magnetization ( \(\textbf{M}\) ) within the medium. Poynting’s theorem is also generalized to describe energy flow and dissipation in material media. A significant portion of the chapter is dedicated to the propagation of waves in dielectric media. Lorentz model is introduced to explain the frequency dependence of permittivity and, consequently, the refractive index, leading to the phenomenon of dispersion. This model describes atoms as damped harmonic oscillators, accounting for both absorption (represented by the imaginary part of the complex permittivity and refractive index) and the frequency-dependent speed of light in the medium. Concepts like phase velocity and group velocity are clearly distinguished, explaining how wave packets deform as they propagate through dispersive media. Cauchy’s law is presented as an empirical relation for normal dispersion. A significant portion of the chapter is dedicated to the propagation of waves in dielectric media. Lorentz model is introduced to explain the frequency dependence of permittivity and, consequently, the refractive index, leading to the phenomenon of dispersion. This model describes atoms as damped harmonic oscillators, accounting for both absorption (represented by the imaginary part of the complex permittivity and refractive index) and the frequency-dependent speed of light in the medium. Concepts like phase velocity and group velocity are clearly distinguished, explaining how wave packets deform as they propagate through dispersive media. Cauchy’s law is presented as an empirical relation for normal dispersion. The chapter then examines the propagation of electromagnetic waves in conductors. Using the Drude–Lorentz model, it derives the complex conductivity and demonstrates how it leads to a complex wave number, resulting in the exponential decay of wave amplitude within the conductor (the skin effect). The relationship between effective permittivity and conductivity is explored, highlighting the unified nature of charge response in both dielectrics and metals. Finally, the chapter provides an overview of practical control of light polarization using optical components. Linear polarizers are discussed, along with Malus’s Law, which quantifies the intensity of transmitted light through a polarizer. Wave plates (half-wave and quarter-wave plates) are introduced as devices that manipulate the phase difference between orthogonal polarization components, enabling transformations between linear, circular, and elliptical polarization states.

Electromagnetic Waves in Matter, Polarizers and Wave Plates

章节
发表日期：

2025年

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Fabian Cadiz,
Arnaud Couairon

摘要

This chapter extends the study of electromagnetic waves from vacuum to material media, focusing on how the presence of matter modifies wave propagation. It begins by generalizing Maxwell’s equations in matter, introducing the auxiliary fields \(\textbf{D}\) (electric displacement) and \(\textbf{H}\) (magnetic excitation) to account for polarization ( \(\textbf{P}\) ) and magnetization ( \(\textbf{M}\) ) within the medium. Poynting’s theorem is also generalized to describe energy flow and dissipation in material media. A significant portion of the chapter is dedicated to the propagation of waves in dielectric media. Lorentz model is introduced to explain the frequency dependence of permittivity and, consequently, the refractive index, leading to the phenomenon of dispersion. This model describes atoms as damped harmonic oscillators, accounting for both absorption (represented by the imaginary part of the complex permittivity and refractive index) and the frequency-dependent speed of light in the medium. Concepts like phase velocity and group velocity are clearly distinguished, explaining how wave packets deform as they propagate through dispersive media. Cauchy’s law is presented as an empirical relation for normal dispersion. A significant portion of the chapter is dedicated to the propagation of waves in dielectric media. Lorentz model is introduced to explain the frequency dependence of permittivity and, consequently, the refractive index, leading to the phenomenon of dispersion. This model describes atoms as damped harmonic oscillators, accounting for both absorption (represented by the imaginary part of the complex permittivity and refractive index) and the frequency-dependent speed of light in the medium. Concepts like phase velocity and group velocity are clearly distinguished, explaining how wave packets deform as they propagate through dispersive media. Cauchy’s law is presented as an empirical relation for normal dispersion. The chapter then examines the propagation of electromagnetic waves in conductors. Using the Drude–Lorentz model, it derives the complex conductivity and demonstrates how it leads to a complex wave number, resulting in the exponential decay of wave amplitude within the conductor (the skin effect). The relationship between effective permittivity and conductivity is explored, highlighting the unified nature of charge response in both dielectrics and metals. Finally, the chapter provides an overview of practical control of light polarization using optical components. Linear polarizers are discussed, along with Malus’s Law, which quantifies the intensity of transmitted light through a polarizer. Wave plates (half-wave and quarter-wave plates) are introduced as devices that manipulate the phase difference between orthogonal polarization components, enabling transformations between linear, circular, and elliptical polarization states.