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Electromagnetism: Maxwell Equations, Wave Propagation and Emission by Tamer Bécherrawy

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Chapter 11

Reflection, Interference, Diffraction and Diffusion

In this chapter we study the laws of reflection and transmission of electromagnetic waves at the interface of two mediums (one of them may be the vacuum). The wave may be totally or partially reflected, a part being transmitted across the interface. The amplitudes of the reflected wave and the transmitted wave, as well as their possible phase shifts, are determined by the boundary conditions at the interface. First, we formulate the laws determining the direction of propagation of the reflected wave and the transmitted wave in the case of two dispersive mediums. These laws hold for any type of wave. Then, we study the reflection and refraction of electromagnetic waves on the interface of two dielectrics, of a dielectric with a conductor and of a dielectric with a plasma. In the second part of this chapter, we study the interference of two and several waves, the diffraction, and the diffusion of waves.

11.1. General laws of reflection and refraction

The laws of reflection and refraction of light, which were initially established experimentally, were interpreted by Huygens for any type of wave. To simplify, we consider a scalar wave u, which propagates in a medium (1). If it meets the interface of this medium with another medium (2), generally there is a reflected wave u′ back toward the medium (1) and a transmitted wave u″ in the medium (2) (Figure 11.1). Huygens’ principle assumes that each point P of a wavefront Σ ...

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