An Introduction to Applied Electromagnetics and Optics by Mitin Vladimir V. & Sementsov Dmitry I

Author:Mitin, Vladimir V. & Sementsov, Dmitry I.
Language: eng
Format: epub
Publisher: CRC Press
Published: 2016-11-17T16:00:00+00:00

Section III

Electromagnetic Waves in Periodic and Waveguiding Structures

8

Waves in Periodic Structures

Diffraction by periodic structures, with period comparable with the wavelength of the incident electromagnetic radiation, has been studied extensively. Diffraction gratings, interference filters, and multilayer dielectric mirrors are some examples of such structures. Important properties of crystals are determined by the periodicity of their crystal structure. For example, the presence of periodicity in crystals leads to the appearance of “allowed” and “forbidden” bands in their energy spectrum. In this case, the period of the crystal lattice, d, is comparable to the de Broglie wavelength of electrons λe:d~λe~10−10m.

The propagation of electromagnetic waves in media with periodically changing properties results in the emergence of new phenomena. These are most noticeable when the wavelength of the wave, which propagates in the medium, becomes comparable to the medium’s spatial period. For example, in diffraction experiment, in which the wave is incident normally on a flat periodic lattice, a diffraction pattern is formed by the transmitted wave. The pattern exhibits a characteristic alternation of maxima and minima in the intensity of the diffracted wave. In an experiment with a photonic crystal with the wave propagating in the periodic medium along a periodicity axis, the characteristic allowed and forbidden photonic bands in the reflection and transmission spectra are formed. In this chapter, we will consider a number of common diffraction principles in periodic structures.

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