Tight focal spots using azimuthally polarised light from a Fresnel cone

When focusing a light beam at high numerical aperture, the resulting electric field profile in the focal plane depends on the transverse polarisation profile, as interference between different parts of the beam needs to be taken into account. It is well known that radial polarised light produces a longitudinal polarisation component and can be focused below the conventional diffraction limit for homogeneously polarised light, and azimuthally polarised light that carries one unit of angular momentum can achieve even tighter focal spots. This is of interest for example for enhancing resolution in scanning microscopy. There are numerous ways to generate such polarisation structures, however, setups can be expensive and usually rely on birefringent components, hence prohibiting broadband operation. We have recently demonstrated a passive, low-cost technique using a simple glass cone (Fresnel cone) to generate beams with structured polarisation. We show here that the polarisation structure generated by Fresnel cones focuses better than radial polarised light at all numerical apertures. Furthermore, we investigate in detail the application of polarised light structures for two-photon microscopy. Specifically we demonstrate a method that allows us to generate the desired polarisation structure at the back aperture of the microscope by pre-compensating any detrimental phase shifts using a combination of waveplates

Exploiting boundary states of imperfect spin chains for high-fidelity state transfer

We study transfer of a quantum state through XX spin chains with static imperfections. We combine the two standard approaches for state transfer based on (i) modulated couplings between neighboring spins throughout the spin chain and (ii) weak coupling of the outermost spins to an unmodulated spin chain. The combined approach allows us to design spin chains with modulated couplings and localized boundary states, permitting high-fidelity state transfer in the presence of random static imperfections of the couplings. The modulated couplings are explicitly obtained from an exact algorithm using the close relation between tridiagonal matrices and orthogonal polynomials [Linear Algebr. Appl. 21, 245 (1978)]. The implemented algorithm and a graphical user interface for constructing spin chains with boundary states (spinGUIn) are provided as Supplemental Material.Comment: 7 pages, 3 figures + spinGUIn description and Matlab files iepsolve.m, spinGUIn.fig, spinGUIn.

Nanoarrays for the generation of complex optical wave-forms

Light beams with unusual forms of wavefront offer a host of useful features to extend the repertoire of those developing new optical techniques. Complex, non-uniform wavefront structures offer a wide range of optomechanical applications, from microparticle rotation, traction and sorting, through to contactless microfluidic motors. Beams combining transverse nodal structures with orbital angular momentum, or vector beams with novel polarization profiles, also present new opportunities for imaging and the optical transmission of information, including quantum entanglement effects. Whilst there are numerous well-proven methods for generating light with complex wave-forms, most current methods work on the basis of modifying a conventional Hermite-Gaussian beam, by passage through suitably tailored optical elements. It has generally been considered impossible to directly generate wave-front structured beams either by spontaneous or stimulated emission from individual atoms, ions or molecules. However, newly emerged principles have shown that emitter arrays, cast in an appropriately specified geometry, can overcome the obstacles: one possibility is a construct based on the electronic excitation of nanofabricated circular arrays. Recent experimental work has extended this concept to a phase-imprinted ring of apertures holographically encoded in a diffractive mask, generated by a programmed spatial light modulator. These latest advances are potentially paving the way for creating new sources of structured light

Correlations of record events as a test for heavy-tailed distributions

A record is an entry in a time series that is larger or smaller than all previous entries. If the time series consists of independent, identically distributed random variables with a superimposed linear trend, record events are positively (negatively) correlated when the tail of the distribution is heavier (lighter) than exponential. Here we use these correlations to detect heavy-tailed behavior in small sets of independent random variables. The method consists of converting random subsets of the data into time series with a tunable linear drift and computing the resulting record correlations.Comment: Revised version, to appear in Physical Review Letter

A Multi-Armed Bandit to Smartly Select a Training Set from Big Medical Data

With the availability of big medical image data, the selection of an adequate training set is becoming more important to address the heterogeneity of different datasets. Simply including all the data does not only incur high processing costs but can even harm the prediction. We formulate the smart and efficient selection of a training dataset from big medical image data as a multi-armed bandit problem, solved by Thompson sampling. Our method assumes that image features are not available at the time of the selection of the samples, and therefore relies only on meta information associated with the images. Our strategy simultaneously exploits data sources with high chances of yielding useful samples and explores new data regions. For our evaluation, we focus on the application of estimating the age from a brain MRI. Our results on 7,250 subjects from 10 datasets show that our approach leads to higher accuracy while only requiring a fraction of the training data.Comment: MICCAI 2017 Proceeding

Large-uncertainty intelligent states for angular momentum and angle

The equality in the uncertainty principle for linear momentum and position is obtained for states which also minimize the uncertainty product. However, in the uncertainty relation for angular momentum and angular position both sides of the inequality are state dependent and therefore the intelligent states, which satisfy the equality, do not necessarily give a minimum for the uncertainty product. In this paper, we highlight the difference between intelligent states and minimum uncertainty states by investigating a class of intelligent states which obey the equality in the angular uncertainty relation while having an arbitrarily large uncertainty product. To develop an understanding for the uncertainties of angle and angular momentum for the large-uncertainty intelligent states we compare exact solutions with analytical approximations in two limiting cases.Comment: 20 pages, 9 figures, submitted to J. Opt. B special issue in connection with ICSSUR 2005 conferenc

An ensemble-based approach to climate reconstructions

Data assimilation is a promising approach to obtain climate reconstructions that are both consistent with observations of the past and with our understanding of the physics of the climate system as represented in the climate model used. Here, we investigate the use of ensemble square root filtering (EnSRF) – a technique used in weather forecasting – for climate reconstructions. We constrain an ensemble of 29 simulations from an atmosphere-only general circulation model (GCM) with 37 pseudo-proxy temperature time series. Assimilating spatially sparse information with low temporal resolution (semi-annual) improves the representation of not only temperature, but also other surface properties, such as precipitation and even upper air features such as the intensity of the northern stratospheric polar vortex or the strength of the northern subtropical jet. Given the sparsity of the assimilated information and the limited size of the ensemble used, a localisation procedure is crucial to reduce "overcorrection" of climate variables far away from the assimilated information

A functional non-central limit theorem for jump-diffusions with periodic coefficients driven by stable Levy-noise

We prove a functional non-central limit theorem for jump-diffusions with periodic coefficients driven by strictly stable Levy-processes with stability index bigger than one. The limit process turns out to be a strictly stable Levy process with an averaged jump-measure. Unlike in the situation where the diffusion is driven by Brownian motion, there is no drift related enhancement of diffusivity.Comment: Accepted to Journal of Theoretical Probabilit