Localization of Electromagnetic Waves in 2D Random Media
Recently random dielectric structures with typical length scale matching the wavelength of electromagnetic radiation in the microwave and optical part of the spectrum have attracted much attention. Propagation of electromagnetic waves in these structures resembles the properties of electrons in disordered semiconductors. Therefore many ideas concerning transport properties of light and microwaves in such media exploit the theoretical methods and concepts of solid-state physics that were developed over many decades. One of them is the concept of electron localization in noncrystalline systems such as amorphous semiconductors or disordered insulators. As shown by Anderson1, in a sufficiently disordered infinite material an entire band of electronic states can be spatially localized. Thus for any energy from this band the stationary solution of the Schrödinger equation is localized for almost any realization of the random potential. Prior to the work due to Anderson, it was believed that electronic states in infinite media are either extended, by analogy with the Bloch picture for crystalline solids, or are trapped around isolated spatial regions such as surfaces and impurities2.
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