### Abstract

The topic of electromagnetism is extensive and deep. Nevertheless, we have endeavoured to restrict coverage of it to this chapter, largely by focusing only on those aspects which are needed to illuminate later chapters in this text. For example, the Maxwell equations, which are presented in their classical flux and circulation formats in Eqs. (2.1)-(2.4), are expanded into their integral forms in Sect. 2.2.1 and differential forms in Sect. 2.3. It is these differential forms, as we shall see, that are most relevant to the radiation problems encountered repeatedly in ensuing chapters.The process of gathering light from the sun to generate 'green' power generally involves collection structures (see Chap. 8) which exhibit smooth surfaces that are large in wavelength terms. The term 'smooth' is used to define a surface where any imperfections are dimensionally small relative to the wavelength of the incident electromagnetic waves, while 'large' implies a macroscopic dimension which is many hundreds of wavelengths in extent. Under these circumstances, electromagnetic wave scattering reduces to Snell's laws. In this chapter, the laws are developed fully from the Maxwell equations for a 'smooth' interface between two arbitrary non-conducting media. The transverse electromagnetic (TEM) wave equations, which represent interfering waves at such a boundary, are first formulated, and subsequently, the electromagnetic boundary conditions arising from the Maxwell equations are rigorously applied. Complete mathematical representations of the Snell's laws are the result. These are used to investigate surface polarisation effects and the Brewster angle. In the final section, the Snell's laws are employed to examine plane wave reflection at perfectly conducting boundaries. This leads to a set of powerful yet 'simple' equations defining the wave guiding of electromagnetic waves in closed structures.

Original language | English |
---|---|

Title of host publication | Green Energy and Technology |

Publisher | Springer |

Pages | 27-50 |

Number of pages | 24 |

Volume | 194 |

ISBN (Print) | 9783319085111 |

DOIs | |

Publication status | Published - 2014 |

### Publication series

Name | Green Energy and Technology |
---|---|

Volume | 194 |

ISSN (Print) | 18653529 |

ISSN (Electronic) | 18653537 |

### Fingerprint

### ASJC Scopus subject areas

- Energy Engineering and Power Technology
- Renewable Energy, Sustainability and the Environment
- Industrial and Manufacturing Engineering
- Management, Monitoring, Policy and Law

### Cite this

*Green Energy and Technology*(Vol. 194, pp. 27-50). (Green Energy and Technology; Vol. 194). Springer. https://doi.org/10.1007/978-3-319-08512-8_2

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*Green Energy and Technology.*vol. 194, Green Energy and Technology, vol. 194, Springer, pp. 27-50. https://doi.org/10.1007/978-3-319-08512-8_2

**Electromagnetic waves.** / Sangster, Alan J.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Electromagnetic waves

AU - Sangster, Alan J.

PY - 2014

Y1 - 2014

N2 - The topic of electromagnetism is extensive and deep. Nevertheless, we have endeavoured to restrict coverage of it to this chapter, largely by focusing only on those aspects which are needed to illuminate later chapters in this text. For example, the Maxwell equations, which are presented in their classical flux and circulation formats in Eqs. (2.1)-(2.4), are expanded into their integral forms in Sect. 2.2.1 and differential forms in Sect. 2.3. It is these differential forms, as we shall see, that are most relevant to the radiation problems encountered repeatedly in ensuing chapters.The process of gathering light from the sun to generate 'green' power generally involves collection structures (see Chap. 8) which exhibit smooth surfaces that are large in wavelength terms. The term 'smooth' is used to define a surface where any imperfections are dimensionally small relative to the wavelength of the incident electromagnetic waves, while 'large' implies a macroscopic dimension which is many hundreds of wavelengths in extent. Under these circumstances, electromagnetic wave scattering reduces to Snell's laws. In this chapter, the laws are developed fully from the Maxwell equations for a 'smooth' interface between two arbitrary non-conducting media. The transverse electromagnetic (TEM) wave equations, which represent interfering waves at such a boundary, are first formulated, and subsequently, the electromagnetic boundary conditions arising from the Maxwell equations are rigorously applied. Complete mathematical representations of the Snell's laws are the result. These are used to investigate surface polarisation effects and the Brewster angle. In the final section, the Snell's laws are employed to examine plane wave reflection at perfectly conducting boundaries. This leads to a set of powerful yet 'simple' equations defining the wave guiding of electromagnetic waves in closed structures.

AB - The topic of electromagnetism is extensive and deep. Nevertheless, we have endeavoured to restrict coverage of it to this chapter, largely by focusing only on those aspects which are needed to illuminate later chapters in this text. For example, the Maxwell equations, which are presented in their classical flux and circulation formats in Eqs. (2.1)-(2.4), are expanded into their integral forms in Sect. 2.2.1 and differential forms in Sect. 2.3. It is these differential forms, as we shall see, that are most relevant to the radiation problems encountered repeatedly in ensuing chapters.The process of gathering light from the sun to generate 'green' power generally involves collection structures (see Chap. 8) which exhibit smooth surfaces that are large in wavelength terms. The term 'smooth' is used to define a surface where any imperfections are dimensionally small relative to the wavelength of the incident electromagnetic waves, while 'large' implies a macroscopic dimension which is many hundreds of wavelengths in extent. Under these circumstances, electromagnetic wave scattering reduces to Snell's laws. In this chapter, the laws are developed fully from the Maxwell equations for a 'smooth' interface between two arbitrary non-conducting media. The transverse electromagnetic (TEM) wave equations, which represent interfering waves at such a boundary, are first formulated, and subsequently, the electromagnetic boundary conditions arising from the Maxwell equations are rigorously applied. Complete mathematical representations of the Snell's laws are the result. These are used to investigate surface polarisation effects and the Brewster angle. In the final section, the Snell's laws are employed to examine plane wave reflection at perfectly conducting boundaries. This leads to a set of powerful yet 'simple' equations defining the wave guiding of electromagnetic waves in closed structures.

U2 - 10.1007/978-3-319-08512-8_2

DO - 10.1007/978-3-319-08512-8_2

M3 - Chapter

SN - 9783319085111

VL - 194

T3 - Green Energy and Technology

SP - 27

EP - 50

BT - Green Energy and Technology

PB - Springer

ER -