Finite Element Time-Domain Body-of-Revolution Maxwell Solver based on Discrete Exterior Calculus

We present a finite-element time-domain (FETD) Maxwell solver for the analysis of body-of-revolution (BOR) geometries based on discrete exterior calculus (DEC) of differential forms and transformation optics (TO) concepts. We explore TO principles to map the original 3-D BOR problem to a 2-D one in the meridian plane based on a Cartesian coordinate system where the cylindrical metric is fully embedded into the constitutive properties of an effective inhomogeneous and anisotropic medium that fills the domain. The proposed solver uses a TE/TM field decomposition and an appropriate set of DEC-based basis functions on an irregular grid discretizing the meridian plane. A symplectic time discretization based on a leap-frog scheme is applied to obtain the full-discrete marching-on-time algorithm. We validate the algorithm by comparing the numerical results against analytical solutions for resonant fields in cylindrical cavities and against pseudo-analytical solutions for fields radiated by cylindrically symmetric antennas in layered media. We also illustrate the application of the algorithm for a particle-in-cell (PIC) simulation of beam-wave interactions inside a high-power backward-wave oscillator.Comment: 42 pages, 19 figure

Throughput Performance Evaluation of Multiservice Multirate OCDMA in Flexible Networks

\u3cp\u3eIn this paper, new analytical formalisms to evaluate the packet throughput of multiservice multirate slotted ALOHA optical code-division multiple-access (OCDMA) networks are proposed. The proposed formalisms can be successfully applied to 1-D and 2-D OCDMA networks with any number of user classes in the system. The bit error rate (BER) and packet correct probability expressions are derived, considering the multiple-access interference as binomially distributed. Packet throughput expressions, on the other hand, are derived considering Poisson, binomial, and Markov chain approaches for the composite packet arrivals distributions, with the latter defined as benchmark. A throughput performance evaluation is carried out for two distinct user code sequences separately, namely, 1-D and 2-D multiweight multilength optical orthogonal code (MWML-OOC). Numerical results show that the Poisson approach underestimates the throughput performance in unacceptable levels and incorrectly predicts the number of successfully received packets for most offered load values even in favorable conditions, such as for the 2-D MWML-OOC OCDMA network with a considerably large number of simultaneous users. On the other hand, the binomial approach proved to be more straightforward, computationally more efficient, and just as accurate as the Markov chain approach.\u3c/p\u3

Turing machines can be efficiently simulated by the General Purpose Analog Computer

The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and at a computational complexity level modulo polynomial reductions. However, the situation is less clear in what concerns models of computation using real numbers, and no analog of the Church-Turing thesis exists for this case. Recently it was shown that some models of computation with real numbers were equivalent from a computability perspective. In particular it was shown that Shannon's General Purpose Analog Computer (GPAC) is equivalent to Computable Analysis. However, little is known about what happens at a computational complexity level. In this paper we shed some light on the connections between this two models, from a computational complexity level, by showing that, modulo polynomial reductions, computations of Turing machines can be simulated by GPACs, without the need of using more (space) resources than those used in the original Turing computation, as long as we are talking about bounded computations. In other words, computations done by the GPAC are as space-efficient as computations done in the context of Computable Analysis

Spatial resolution effect of light coupling structures

This research project was founded by the National Council for Scientific and Technological Development (CNPq) of Brazil (302397/2014-0), by the National Natural Science Foundation of China (11204386, 11411130117, 11334015), by the Open research project of the State Key Laboratory of Optoelectronic Materials and Technologies, Sun-Yat Sen University of China (OEMT-2015-KF-12, OEMT-2015-KF-13) and by EPSRC of U.K. under grant EP/J01771X/1 (Structured Light). Kezheng Li is also supported by the aboard exchange scholar and international doctoral cooperative project of Sun Yat-sen University.The coupling of light between free space and thin film semiconductors is an essential requirement of modern optoelectronic technology. For monochromatic and single mode devices, high performance grating couplers have been developed that are well understood. For broadband and multimode devices, however, more complex structures, here referred to as "coupling surfaces", are required, which are often difficult to realise technologically. We identify general design rules based on the Fourier properties of the coupling surface and show how they can be used to determine the spatial resolution required for the coupler's fabrication. To our knowledge, this question has not been previously addressed, but it is important for the understanding of diffractive nanostructures and their technological realisation. We exemplify our insights with solar cells and UV photodetectors, where high-performance nanostructures that can be realised cost-effectively are essential.Publisher PDFPeer reviewe

Hybrid optical CDMA-FSO communications network under spatially correlated gamma-gamma scintillation

\u3cp\u3eIn this paper, we propose a new hybrid network solution based on asynchronous optical code-division multiple-access (OCDMA) and free-space optical (FSO) technologies for last-mile access networks, where fiber deployment is impractical. The architecture of the proposed hybrid OCDMA-FSO network is thoroughly described. The users access the network in a fully asynchronous manner by means of assigned fast frequency hopping (FFH)-based codes. In the FSO receiver, an equal gain-combining technique is employed along with intensity modulation and direct detection. New analytical formalisms for evaluating the average bit error rate (ABER) performance are also proposed. These formalisms, based on the spatially correlated gamma-gamma statistical model, are derived considering three distinct scenarios, namely, uncorrelated, totally correlated, and partially correlated channels. Numerical results show that users can successfully achieve error-free ABER levels for the three scenarios considered as long as forward error correction (FEC) algorithms are employed. Therefore, OCDMA-FSO networks can be a prospective alternative to deliver high-speed communication services to access networks with deficient fiber infrastructure.\u3c/p\u3

Numerical Determination of the Avalanche Exponents of the Bak-Tang-Wiesenfeld Model

We consider the Bak-Tang-Wiesenfeld sandpile model on a two-dimensional square lattice of lattice sizes up to L=4096. A detailed analysis of the probability distribution of the size, area, duration and radius of the avalanches will be given. To increase the accuracy of the determination of the avalanche exponents we introduce a new method for analyzing the data which reduces the finite-size effects of the measurements. The exponents of the avalanche distributions differ slightly from previous measurements and estimates obtained from a renormalization group approach.Comment: 6 pages, 6 figure

Sandpile Model with Activity Inhibition

A new sandpile model is studied in which bonds of the system are inhibited for activity after a certain number of transmission of grains. This condition impels an unstable sand column to distribute grains only to those neighbours which have toppled less than m times. In this non-Abelian model grains effectively move faster than the ordinary diffusion (super-diffusion). A novel system size dependent cross-over from Abelian sandpile behaviour to a new critical behaviour is observed for all values of the parameter m.Comment: 11 pages, RevTex, 5 Postscript figure

Generic Sandpile Models Have Directed Percolation Exponents

We study sandpile models with stochastic toppling rules and having sticky grains so that with a non-zero probability no toppling occurs, even if the local height of pile exceeds the threshold value. Dissipation is introduced by adding a small probability of particle loss at each toppling. Generically, for models with a preferred direction, the avalanche exponents are those of critical directed percolation clusters. For undirected models, avalanche exponents are those of directed percolation clusters in one higher dimension.Comment: 4 pages, 4 figures, minor change

Dynamically Driven Renormalization Group Applied to Sandpile Models

The general framework for the renormalization group analysis of self-organized critical sandpile models is formulated. The usual real space renormalization scheme for lattice models when applied to nonequilibrium dynamical models must be supplemented by feedback relations coming from the stationarity conditions. On the basis of these ideas the Dynamically Driven Renormalization Group is applied to describe the boundary and bulk critical behavior of sandpile models. A detailed description of the branching nature of sandpile avalanches is given in terms of the generating functions of the underlying branching process.Comment: 18 RevTeX pages, 5 figure