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.

Probing polarization and dielectric function of molecules with higher order harmonics in scattering-near-field scanning optical microscopy

The idealized system of an atomically flat metallic surface [highly oriented pyrolytic graphite (HOPG)] and an organic monolayer (porphyrin) was used to determine whether the dielectric function and associated properties of thin films can be accessed with scanning-near-field scanning optical microscopy (s-NSOM). Here, we demonstrate the use of harmonics up to fourth order and the polarization dependence of incident light to probe dielectric properties on idealized samples of monolayers of organic molecules on atomically smooth substrates. An analytical treatment of light/sample interaction using the s-NSOM tip was developed in order to quantify the dielectric properties. The theoretical analysis and numerical modeling, as well as experimental data, demonstrate that higher order harmonic scattering can be used to extract the dielectric properties of materials with tens of nanometer spatial resolution. To date, the third harmonic provides the best lateral resolution (∼50 nm) and dielectric constant contrast for a porphyrin film on HOPG. © 2009 American Institute of Physics.

Mechanisms of Cdc42 Polarization in Yeast

Polarization is important for the function and morphology of many different cell types. The keys regulators of polarity in eukaryotes are the Rho-family GTPases. In the budding yeast Saccharomyces cerevisiae, which must polarize in order to bud and to mate, the master regulator is the highly conserved Rho GTPase, Cdc42. During polarity establishment, active Cdc42 accumulates at a site on the plasma membrane characterizing the “front” of the cell where the bud will emerge. The orientation of polarization is guided by upstream cues that dictate the site of Cdc42 clustering. However, in the absence of upstream cues, yeast can still polarize in a random direction during symmetry breaking. Symmetry breaking suggests cells possess an autocatalytic polarization mechanism that can amplify stochastic fluctuations of polarity proteins through a positive feedback mechanism.

Two different positive feedback mechanisms have been proposed to polarize Cdc42 in budding yeast. One model posits that Cdc42 activation must be localized to a site at the plasma membrane. Another model posits that Cdc42 delivery must be localized to a particular site at the plasma membrane. Although both mechanisms could work in parallel to polarize Cdc42, it is unclear which mechanism is critical to polarity establishment. We directly tested the predictions of the two positive feedback models using genetics and live microscopy. We found that localized Cdc42 activation is necessary for polarity establishment.

While this explains how active Cdc42 localizes to a particular site at the plasma membrane, it does not address how Cdc42 concentrates at that site. Several different mechanisms have been proposed to concentrate Cdc42. The GDI can extract Cdc42 from membranes and selective mobilize GDP-Cdc42 in the cytoplasm. It was proposed that selectively mobilizing GDP-Cdc42 in combination with local activation could locally concentrate total Cdc42 at the polarity site. Although the GDI is important for rapid Cdc42 accumulation at the polarity site, it is not essential to Cdc42 concentration. It was proposed that delivery of Cdc42 by actin-mediated vesicle can act as a backup pathway to concentrate Cdc42. However, we found no evidence for an actin-dependent concentrating pathway. Live microscopy experiments reveal that prenylated proteins are not restricted to membranes, and can enter the cytoplasm. We found that the GDI-independent concentrating pathway still requires Cdc42 to exchange between the plasma membrane and the cytoplasm, which is supported by computational modeling. In the absence of the GDI, we found that Cdc42 GAP became essential for polarization. We propose that the GAP limits GTP-Cdc42 leak into the cytoplasm, which would be prohibitive to Cdc42 polarization.