Far-field analysis of axially symmetric three-dimensional directional cloaks.

Axisymmetric radiating and scattering structures whose rotational invariance is broken by non-axisymmetric excitations present an important class of problems in electromagnetics. For such problems, a cylindrical wave decomposition formalism can be used to efficiently obtain numerical solutions to the full-wave frequency-domain problem. Often, the far-field, or Fraunhofer region is of particular interest in scattering cross-section and radiation pattern calculations; yet, it is usually impractical to compute full-wave solutions for this region. Here, we propose a generalization of the Stratton-Chu far-field integral adapted for 2.5D formalism. The integration over a closed, axially symmetric surface is analytically reduced to a line integral on a meridional plane. We benchmark this computational technique by comparing it with analytical Mie solutions for a plasmonic nanoparticle, and apply it to the design of a three-dimensional polarization-insensitive cloak.

Fermion bag approach to lattice field theories

We propose a new approach to the fermion sign problem in systems where there is a coupling U such that when it is infinite the fermions are paired into bosons, and there is no fermion permutation sign to worry about. We argue that as U becomes finite, fermions are liberated but are naturally confined to regions which we refer to as fermion bags. The fermion sign problem is then confined to these bags and may be solved using the determinantal trick. In the parameter regime where the fermion bags are small and their typical size does not grow with the system size, construction of Monte Carlo methods that are far more efficient than conventional algorithms should be possible. In the region where the fermion bags grow with system size, the fermion bag approach continues to provide an alternative approach to the problem but may lose its main advantage in terms of efficiency. The fermion bag approach also provides new insights and solutions to sign problems. A natural solution to the "silver blaze problem" also emerges. Using the three-dimensional massless lattice Thirring model as an example, we introduce the fermion bag approach and demonstrate some of these features. We compute the critical exponents at the quantum phase transition and find ν=0.87(2) and η=0.62(2). © 2010 The American Physical Society.

A subcortical source of visual input to the frontal eye field

Many neurons in the frontal eye field (FEF) exhibit visual responses and are thought to play important roles in visuosaccadic behavior. The FEF, however, is far removed from striate cortex. Where do the FEF's visual signals come from? Usually they are reasonably assumed to enter the FEF through afferents from extrastriate cortex. Here we show that, surprisingly, visual signals also enter the FEF through a subcortical route: a disynaptic, ascending pathway originating in the intermediate layers of the superior colliculus (SC). We recorded from identified neurons at all three stages of this pathway (n=30-40 in each sample): FEF recipient neurons, orthodromically activated from the SC; mediodorsal thalamus (MD) relay neurons, antidromically activated from FEF and orthodromically activated from SC; and SC source neurons, antidromically activated from MD. We studied the neurons while monkeys performed delayed saccade tasks designed to temporally resolve visual responses from presaccadic discharges. We found, first, that most neurons at every stage in the pathway had visual responses, presaccadic bursts, or both. Second, we found marked similarities between the SC source neurons and MD relay neurons: in both samples, about 15% of the neurons had only a visual response, 10% had only a presaccadic burst, and 75% had both. In contrast, FEF recipient neurons tended to be more visual in nature: 50% had only a visual response, none had only a presaccadic burst, and 50% had both a visual response and a presaccadic burst. This suggests that in addition to their subcortical inputs, these FEF neurons also receive other visual inputs, e.g. from extrastriate cortex. We conclude that visual activity in the FEF results not only from cortical afferents but also from subcortical inputs. Intriguingly, this implies that some of the visual signals in FEF are pre-processed by the SC.