Abstract
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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References
P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev. 109, 1492 (1958).
T. V. Ramakrishnan, Electron localization, In: Ref.[32], pp. 213-304.
E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Scaling theory of localization: Absence of quantum diffusion in two dimensions, Phys. Rev. Lett. 42, 673 (1979).
B. Souillard, Waves and electrons in inhomogeneous media, In: Ref.[32], pp. 305-382.
M. Kaveh, What to expect from similarities between the Schrödinger and Maxwell equations, In: Ref.[9], pp. 21-34.
S. John, Electromagnetic absorption in a disordered medium near a photon mobility edge, Phys. Rev. Lett. 53, 2169 (1984).
P. W. Anderson, The question of classical localization. A theory of white paint? Phil. Mag. B 52, 505 (1985).
S. John, Strong localization of photons in certain disordered dielectric superlattices, Phys. Rev. Lett. 58, 2486 (1987).
W. van Haeringen and D. Lenstra, editors, Analogies in Optics and Micro Electronics (Kluwer, Dordrecht, 1990).
C. M. Soukoulis, editor, Photonic Band Gaps and Localization, New York, 1993. NATO ASI Series, Plenum.
E. Akkermans, P. E. Wolf, and R. Maynard, Coherent backscattering of light by disordered media: Analysis of the peak line shape, Phys. Rev. Lett. 56, 1471 (1986).
M. J. Stephen and G. Cwillich, Rayleigh scattering and weak localization: Effects of polarization, Phys. Rev. B 34, 7564 (1986).
F. C. MacKintosh and S. John, Coherent backscattering of light in the presence of time-reversal-noninvariant and parity-nonconserving media, Phys. Rev. B 37, 1884 (1988).
Y. Kuga and A. Ishimaru, Retroreflectance from a dense distribution of spherical particles, J. Opt. Soc. Am. A 1, 831 (1984).
M. P. van Albada and E. Lagendijk, Observation of weak localization of light in a random medium, Phys. Rev. Lett. 55, 2692 (1985).
P.-E. Wolf and G. Maret, Weak localization and coherent backscattering of photons in disordered media, Phys. Rev. Lett. 55, 2696 (1985).
M. P. van Albada, A. Lagendijk, and M. B. van der Mark, Towards observation of Anderson localization of light, In: Ref.[9], pp. 85-103.
G. H. Watson Jr., P. A. Fleury, and S. L. McCall, Search for photon localization in the time domain, Phys. Rev. Lett. 58, 945 (1987).
A. Z. Genack, Optical transmition in disordered media, Phys. Rev. Lett. 58, 2043 (1987).
J. M. Drake and A. Z. Genack, Observation of nonclassical optical diffusion, Phys. Rev. Lett. 63, 259 (1989).
A. Z. Genack and N. Garcia, Observation of photon localization in a three-dimensional disordered system, Phys. Rev. Lett. 66, 2064 (1991).
R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, and S. L. McCall, Microwave localization by two-dimensional random scattering, Nature 354, 53 (1991).
S. John, Localization of light, Physics Today 44, 32 (May 1991).
Barbara Goss Levi, Light travels more slowly through strongly scattering materials, Physics Today 44, 17 (June 1991).
J. Kroha, C. M. Sokoulis, and P. Wölfle, Localization of classical waves in a random medium: A self-consistent theory, Phys. Rev. B 47, 11093 (1993).
B. A. van Tiggelen and E. Kogan, Analogies between light and electrons: Density of states and Friedel’s identity, Phys. Rev. A 49, 708 (1994).
M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, Speed of propagation of classical waves in strongly scattering media, Phys. Rev. Lett. 66, 3132 (1991).
G. D. Mahan, Many-Particle Physics (Plenum, New York, 1981).
M. Born and E. Wolf, Principles of Optics (Pergamon Press, Oxford-London, 1965).
M. Rusek, A. Orlowski, and J. Mostowski, Localization of light in three-dimensional random dielectric media, Phys. Rev. E 53, 4122 (1996).
M. Rusek and A. Orlowski, Analytical approach to localization of electromagnetic waves in two-dimensional random media, Phys. Rev. E 51, R2763 (1995).
J. Souletie, J. Vannimenus, and R. Stora, editors, Chance and Matter (North-Holland, Amsterdam, 1987).
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Orłowski, A., Rusek, M. (1997). Localization of Electromagnetic Waves in 2D Random Media. In: Dowling, J.P. (eds) Electron Theory and Quantum Electrodynamics. NATO ASI Series, vol 358. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0081-4_24
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