Anderson Localization of Polar Eigenmodes in Random Planar Composites

Abstract

Anderson localization of classical waves in disordered media is a fundamental physical phenomenon that has attracted attention in the past three decades. More recently, localization of polar excitations in nanostructured metal-dielectric films (also known as random planar composite) has been subject of intense studies. Potential applications of planar composites include local near-field microscopy and spectroscopy. A number of previous studies have relied on the quasistatic approximation and a direct analogy with localization of electrons in disordered solids. Here I consider the localization problem without the quasistatic approximation. I show that localization of polar excitations is characterized by algebraic rather than by exponential spatial confinement. This result is also valid in two and three dimensions. I also show that the previously used localization criterion based on the gyration radius of eigenmodes is inconsistent with both exponential and algebraic localization. An alternative criterion based on the dipole participation number is proposed. Numerical demonstration of a localization-delocalization transition is given. Finally, it is shown that, contrary to the previous belief, localized modes can be effectively coupled to running waves.

22 pages, 7 figures. Paper was revised and a more precise definition of the participation number given, data for figures recalculated accordingly. Accepted to J. Phys.: Cond. Matt

References in corpus (6)

• Multiple scattering of classical waves: from microscopy to mesoscopy and diffusion
• Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
• Multifractality and critical fluctuations at the Anderson transition
• Fluctuations of the correlation dimension at metal-insulator transitions
• Fluctuation of the Correlation Dimension and the Inverse Participation Number at the Anderson Transition
• $f(\alpha )$ Multifractal spectrum at strong and weak disorder

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