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Metamaterial absorbers have been demonstrated across much of the electromagnetic spectrum and exhibit both broad and narrow-band absorption for normally incident radiation. Absorption diminishes for increasing angles of incidence and transverse electric polarization falls off much more rapidly than transverse magnetic. We unambiguously demonstrate that broad-angle TM behavior cannot be associated with periodicity, but rather is due to coupling with a surface electromagnetic mode that is both supported by, and well described via the effective optical constants of the metamaterial where we achieve a resonant wavelength that is 19.1 times larger than the unit cell. Experimental results are supported by simulations and we highlight the potential to modify the angular response of absorbers by tailoring the surface wave.

International audience; We computationally and experimentally investigate the use of metamaterial resonators as bandpass filters and other components that enable control of guided surface electromagnetic waves. The guided surface electromagnetic wave propagates on a planar Goubau line, launched via a coplanar waveguide coupler with 50Ω impedance. Experimental samples targeted for either microwave or terahertz frequencies are measured and shown to be in excellent agreement with simulations. Metamaterial elements are designed to absorb energy only of the planar Goubau line and yield narrow-band resonances with relatively high quality factors. Two independent configurations of coupled metamaterial elements are demonstrated that modify the otherwise flat transmission spectrum of the planar Goubau line. By physically shunting the capacitive gaps of the coupled metamaterial elements, we demonstrate the potential for a large dynamic range in transmissivity, suggesting the use of this configuration for high-bandwidth terahertz communications.

Zipf's laws are probability distributions on the positive integers which decay algebraically. Such laws have been shown empirically to describe a large class of phenomena, including frequency of words usage, populations of cities, distributions of personal incomes, and distributions of biological genera and species, to mention only a few. In this paper we present a Dirichlet–multinomial urn model for describing the above phenomena from a stochastic point of view. We derive the Zipf's law under certain regularity conditions; some limit theorems are also obtained for the urn model under consideration.

Let X 1, X 2, · ··, Xn , · ·· be independent and identically distributed non-negative integer-valued random variables with finite mean and variance. For any positive integer n and m we consider the random vector i.e., L has the same distribution as the conditional distribution of (X 1, · ··, Xm ) given the condition It is easy to see that our model includes the classical urn model, the Bose–Einstein urn model and the Pólya urn model as special cases. For any non-negative integer s define G(s) = the number of Li′s such that Li = s, and U = the number of Li′s such that Li is an even number; in this paper we study the asymptotic behaviour of the random variables considered above. Some central limit theorems and a multinormal local limit theorem are proved.