Localization of electromagnetic waves in a two-dimensional random medium

Abstract

Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied ab initio for a system consisting of many randomly distributed two dimensional dipoles. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is derived from first principles and then solved numerically for the total electromagnetic field. The results show that spatially localized electromagnetic waves are possible in such a simple but realistic disordered system. When localization occurs, a coherent behavior appears and is revealed as a unique property differentiating localization from either the residual absorption or the attenuation effects.PACS numbers: 42.25. Hz, 41.90.+e When propagating through a medium consisting of many scatterers, waves will be scattered by each scatterer. The scattered waves will be again scattered by other scatterers. Such a process will be repeated to establish an infinite recursive pattern of multiple scattering. As a result, the wave propagation may be significantly altered 1 . It is now well-known that the multiple scattering of waves is responsible for many fascinating phenomena, ranging from phenomena of macroscopic scales such as twinkling lights in the evening sky, modulation of ambient noise in the oceans, and electromagnetic scintillation of turbulence in the atmosphere, to phenomena of microscopic or mesoscopic scales including random lasers 2 and electronic resistivity in disordered solids 3 . It has also been proposed that under certain conditions, the multiple scattering can lead to the unusual phenomenon of wave localization, a concept originally introduced to describe disorder induced metal-insulator transitions in electronic systems 4 .Over the past two decades, localization of classical waves has been under intensive investigations, leading to a very large body of literature(e. g. 5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21 ). Such a localization phenomenon has been characterized by two levels. One is the weak localization associated with the enhanced backscattering. That is, waves which propagate in the two opposite directions along a loop will obtain the same phase and interfere constructively at the emission site, thus enhancing the backscattering. The second is the strong localization, without confusion often just termed as localization, in which a significant inhibition of transmission appears and the energy is mostly confined spatially in the vicinity of the emission site.While the weak localization, regarded as a precursor to the strong localization, has been well studied both theoretically (e. g. the monograph 3,18 ) and experimentally (e. g. 19 ), observation of strong localization of classical waves for higher than one dimension remains a subject of debate 20,21,22 , primarily because a suitable system is hard to find and the observation is often obscured by such effects as the residual absorption 22 and scatt...

Simulation study of localization of electromagnetic waves in two-dimensional random dipolar systems

“…Although much of the following materials can be referred to in [30], we repeat the important parts here for the sake of convenience and completeness.…”

“…Second, localization effects are often entangled with other effects such as dissipation, wave deflection, or boundary effects [12], making data interpretation often ambiguous. In a recent communication, a simple but seemingly realistic model system has been proposed to study EM localization in 2D random media [30]. This model originated from the previous study of the radiative effects of the electric dipoles embedded in structured cavities [31].…”

“…With the present paper, we wish to explore further the localization properties of the system outlined in [30]. We will investigate the dependence of localization behavior on a numbers of parameters including frequency, filling factor, scattering strength, damping effect, and two different ways of measuring localization.…”

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“…In a recent communication, a simple but seemingly realistic model system has been proposed to study EM localization in 2D random media [33]. This model originated from the previous study of the radiative effects of the electric dipoles embedded in structured cavities [34].…”