A methodology for hierarchical image segmentation evaluation

This paper proposes a method to evaluate hierarchical image segmentation procedures, in order to enable comparisons between different hierarchical algorithms and of these with other (non-hierarchical) segmentation techniques (as well as with edge detectors) to be made. The proposed method builds up on the edge-based segmentation evaluation approach by considering a set of reference human segmentations as a sample drawn from the population of different levels of detail that may be used in segmenting an image. Our main point is that, since a hierarchical sequence of segmentations approximates such population, those segmentations in the sequence that best capture each human segmentation level of detail should provide the basis for the evaluation of the hierarchical sequence as a whole. A small computational experiment is carried out to show the feasibility of our approach.

High-resolution spatial-response measurements of optical nano-antennas in the visible

A few years ago, some of the authors of the paper demonstrated the resonance of optical antennas in the visible frequencies. The results of that paper were obtained using experimental techniques that were primarily developed for the measurement of antenna-coupled detectors in the infrared. In the present paper, we show the results of spatial-response mapping obtained by using a dedicated measurement station for the characterization of optical antennas in the visible. At the same time, the bottleneck in the spatial responsivity calculation represented by the beam characterization has been approached from a different perspective. The proposed technique uses a collection of knife edge measurements in order to avoid the use of any model of the laser beam irradiance. By taking all this into account we present the spatial responsivity of optical antennas measured with high spatial resolution in the visible.

Generic helical edge states due to Rashba spin-orbit coupling in a topological insulator

We study the helical edge states of a two-dimensional topological insulator without axial spin symmetry due to the Rashba spin-orbit interaction. Lack of axial spin symmetry can lead to so-called generic helical edge states, which have energy-dependent spin orientation. This opens the possibility of inelastic backscattering and thereby nonquantized transport. Here we find analytically the new dispersion relations and the energy dependent spin orientation of the generic helical edge states in the presence of Rashba spin-orbit coupling within the Bernevig-Hughes-Zhang model, for both a single isolated edge and for a finite width ribbon. In the single-edge case, we analytically quantify the energy dependence of the spin orientation, which turns out to be weak for a realistic HgTe quantum well. Nevertheless, finite size effects combined with Rashba spin-orbit coupling result in two avoided crossings in the energy dispersions, where the spin orientation variation of the edge states is very significantly increased for realistic parameters. Finally, our analytical results are found to compare well to a numerical tight-binding regularization of the model.

Measurement limitations in knife-edge tomographic phase retrieval of focused IR laser beams

An experimental setup to measure the three-dimensional phase-intensity distribution of an infrared laser beam in the focal region has been presented. It is based on the knife-edge method to perform a tomographic reconstruction and on a transport of intensity equation-based numerical method to obtain the propagating wavefront. This experimental approach allows us to characterize a focalized laser beam when the use of image or interferometer arrangements is not possible. Thus, we have recovered intensity and phase of an aberrated beam dominated by astigmatism. The phase evolution is fully consistent with that of the beam intensity along the optical axis. Moreover, this method is based on an expansion on both the irradiance and the phase information in a series of Zernike polynomials. We have described guidelines to choose a proper set of these polynomials depending on the experimental conditions and showed that, by abiding these criteria, numerical errors can be reduced.

Micromachined silicon lenses for terahertz applications

Silicon microlenses are a very important tool for coupling terahertz (THz) radiation into antennas and detectors in integrated circuits. They can be used in a large array structures at this frequency range reducing considerably the crosstalk between the pixels. Drops of photoresist have been deposited and their shape transferred into the silicon by means of a Reactive Ion Etching (RIE) process. Large silicon lenses with a few mm diameter (between 1.5 and 4.5 mm) and hundreds of μm height (between 50 and 350 μm) have been fabricated. The surface of such lenses has been characterized using Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM), resulting in a surface roughness of about ∼3 μm, good enough for any THz application. The beam profile at the focal plane of such lenses has been measured at a wavelength of 10.6 μm using a tomographic knife-edge technique and a CO2 laser.

Topological massive Dirac edge modes and long-range superconducting Hamiltonians

We discover novel topological effects in the one-dimensional Kitaev chain modified by long-range Hamiltonian deformations in the hopping and pairing terms. This class of models display symmetry-protected topological order measured by the Berry/Zak phase of the lower-band eigenvector and the winding number of the Hamiltonians. For exponentially decaying hopping amplitudes, the topological sector can be significantly augmented as the penetration length increases, something experimentally achievable. For power-law decaying superconducting pairings, the massless Majorana modes at the edges get paired together into a massive nonlocal Dirac fermion localized at both edges of the chain: a new topological quasiparticle that we call topological massive Dirac fermion. This topological phase has fractional topological numbers as a consequence of the long-range couplings. Possible applications to current experimental setups and topological quantum computation are also discussed.