Nonlinear Localization in Metamaterials

Metamaterials, i.e., artificially structured ("synthetic") media comprising weakly coupled discrete elements, exhibit extraordinary properties and they hold a great promise for novel applications including super-resolution imaging, cloaking, hyperlensing, and optical transformation. Nonlinearity adds a new degree of freedom for metamaterial design that allows for tuneability and multistability, properties that may offer altogether new functionalities and electromagnetic characteristics. The combination of discreteness and nonlinearity may lead to intrinsic localization of the type of discrete breather in metallic, SQUID-based, and ${\cal PT}-$symmetric metamaterials. We review recent results demonstrating the generic appearance of breather excitations in these systems resulting from power-balance between intrinsic losses and input power, either by proper initialization or by purely dynamical procedures. Breather properties peculiar to each particular system are identified and discussed. Recent progress in the fabrication of low-loss, active and superconducting metamaterials, makes the experimental observation of breathers in principle possible with the proposed dynamical procedures.Comment: 19 pages, 14 figures, Invited (Review) Chapte

Mapping inter-element coupling in metamaterials: Scaling down to infrared

The coupling between arbitrarily positioned and oriented split ring resonators is investigated up to THz frequencies. Two different analytical approaches are used, one based on circuits and the other on field quantities that includes retardation. These are supplemented by numerical simulations and experiments in the GHz range, and by simulations in the THz range. The field approach makes it possible to determine separately the electric and magnetic coupling coefficients which, depending on orientation, may reinforce or may cancel each other. Maps of coupling are produced for arbitrary orientations of two co-planar split rings resonant at around 2 GHz and then with the geometry scaled down to be resonant at around 100 THz. We prove that the inertia of electrons at high frequencies results in a dramatic change in the maps of coupling, due to reduction of the magnetic contribution. Our approach could facilitate the design of metamaterials in a wide frequency range up to the saturation of the resonant frequency

Coupling mechanisms for split ring resonators: Theory and experiment

We study experimentally and theoretically coupling mechanisms between metamaterial elements of the split ring resonator (SRR) type. We show that, depending on the orientation of the elements relative to each other, the coupling may be either of magnetic or electric type or a combination of both. Experimental results on SRRs with resonances around 1.7 -1.9 GHz agree quantitatively with results of simulations (CST Microwave Studio). Further simulations provide analysis for a variety of SRRs both in the GHz and in the 20 THz frequency regions. The variety of coupling mechanisms can be employed in designing near field manipulating devices based on propagation of slow waves. © 2007 WILEY-VCH Verlag GmbH and Co. KGaA

Coupling mechanisms for split ring resonators: Theory and experiment

We study experimentally and theoretically coupling mechanisms between metamaterial elements of the split ring resonator (SRR) type. We show that, depending on the orientation of the elements relative to each other, the coupling may be either of magnetic or electric type or a combination of both. Experimental results on SRRs with resonances around 1.7 -1.9 GHz agree quantitatively with results of simulations (CST Microwave Studio). Further simulations provide analysis for a variety of SRRs both in the GHz and in the 20 THz frequency regions. The variety of coupling mechanisms can be employed in designing near field manipulating devices based on propagation of slow waves. © 2007 WILEY-VCH Verlag GmbH and Co. KGaA

The structure and reproduction of the virgin forest - a review of Eustace Jones 1945

Jones (1945) was a milestone paper exploring the natural forest concept with examples from the temperate and boreal ecosystems. It has become a classic because of its use of field observation of regeneration, succession and structure to assess theories about disturbance and the dynamic properties of natural forests. His main aim was to review some of the features of the structure and reproduction of the north temperate virgin forests, and this article presents, discusses and evaluates the main features of this legendary paper. Jones had international experience of both the ecological and silvicultural research communities and combined long-term field observations with theory to develop a realistic assessment of natural forest properties that formed the basis for current understanding. He demonstrated that natural disturbance regimes could generate a variety of structures and that a stable, ‘‘climax’’ forest concept was often not supported by field data. He also showed that even-aged components are common in these forest ecosystems and that the recruitment of tree species proceeds irregularly even in undisturbed stands. His work has influenced subsequent development of related subjects such as disturbance theory, gap-phase dynamics and long-term vegetation changes and has left a legacy with practical relevance for nature conservation and silviculture