Abstract
A practical problem of fundamental importance in electromagnetic wave theory concerns the reflection and transmission of an electromagnetic wave at an interface separating two different material media. As this problem can become rather complicated for a general pulsed wave field incident upon the surface S of a dispersive body immersed in a dispersive medium, it is best to consider first the much simpler case of a time-harmonic (monochromatic) plane wave field incident upon an infinitely extended plane surface. The general solution to this problem will then form the basis for the analysis of the more general problem of a pulsed electromagnetic beam field incident upon a planar interface separating two different dispersive media. This more general problem is treated in some detail in Volume 2.
“Do not Bodies and Light act mutually upon one another; that is to say, Bodies upon Light in emitting, reflecting, refracting and inflecting it, and Light upon Bodies for heating them, and putting their parts into a vibrating motion wherein heat consists?” Sir Isaac Newton (1704).
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Notes
- 1.
Unlike the analysis presented in Sect. 6.2 for reflection from a perfect conductor, the present analysis is conducted in a more general framework.
- 2.
Willebrord Snellius (1580–1626), a Dutch mathematician and astronomer, rediscovered the law of refraction in 1621, commonly referred to as Snell’s law but also known as the Snell–Descarte law due to Descarte’s independent heuristic derivation in his 1637 essay Dioptrics. This law of refraction was first described by the Greco-Egyptian mathematician Ptolemy (c. 100–170), was later described by the Persian mathematician Ibn Sahl (c. 940–1000) in his 984 treatise On Burning Mirrors and Lenses, and subsequently described by the Silesian friar and natural philosopher Erazmus Witelo in 1284.
- 3.
Notice that n j(ω)∕μ j(ω) = (𝜖 0 μ 0)−1∕2[𝜖 cj(ω)∕μ j(ω)]1∕2 = (c∕∥c∥)∕η j(ω) and that n j(ω)∕𝜖 cj(ω) = (𝜖 0 μ 0)−1∕2[μ j(ω)∕𝜖 cj(ω)]1∕2 = (c∕∥c∥)η j(ω) where η j(ω) is the complex impedance and n j(ω) = [(𝜖 cj(ω)∕𝜖 0)(μ j(ω)∕μ 0)]1∕2 is the complex index of refraction of medium j with complex permittivity 𝜖 cj(ω) = 𝜖(ω) + (i∕∥4π∥)σ j(ω)∕ω.
- 4.
A simpler asymptotic description of molecular optics may be found in the essential optics text Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light by M. Born and E. Wolf. [1].
- 5.
Notice that this macroscopic polarization density is derived from the spatial average of the microscopic dipoles induced by the local effective electric field.
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Oughstun, K.E. (2019). Plane Wave Reflection and Refraction. In: Electromagnetic and Optical Pulse Propagation . Springer Series in Optical Sciences, vol 224. Springer, Cham. https://doi.org/10.1007/978-3-030-20835-6_6
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