Spin-Orbit Coupling and the Evolution of Transverse Spin

We investigate the evolution of transverse spin in tightly focused circularly polarized beams of light, where spin-orbit coupling causes a local rotation of the polarization ellipses upon propagation through the focal volume. The effect can be explained as a relative Gouy-phase shift between the circularly polarized transverse field and the longitudinal field carrying orbital angular momentum. The corresponding rotation of the electric transverse spin density is observed experimentally by utilizing a recently developed reconstruction scheme, which relies on transverse-spin-dependent directional scattering of a nano-probe.Comment: 4 pages, 2 figure

The magnetic and electric transverse spin density of spatially confined light

When a beam of light is laterally confined, its field distribution can exhibit points where the local magnetic and electric field vectors spin in a plane containing the propagation direction of the electromagnetic wave. The phenomenon indicates the presence of a non-zero transverse spin density. Here, we experimentally investigate this transverse spin density of both magnetic and electric fields, occurring in highly-confined structured fields of light. Our scheme relies on the utilization of a high-refractive-index nano-particle as local field probe, exhibiting magnetic and electric dipole resonances in the visible spectral range. Because of the directional emission of dipole moments which spin around an axis parallel to a nearby dielectric interface, such a probe particle is capable of locally sensing the magnetic and electric transverse spin density of a tightly focused beam impinging under normal incidence with respect to said interface. We exploit the achieved experimental results to emphasize the difference between magnetic and electric transverse spin densities.Comment: 7 pages, 4 figure

Optical Polarization M\"obius Strips and Points of Purely Transverse Spin Density

Tightly focused light beams can exhibit electric fields spinning around any axis including the one transverse to the beams' propagation direction. At certain focal positions, the corresponding local polarization ellipse can degenerate into a perfect circle, representing a point of circular polarization, or C-point. We consider the most fundamental case of a linearly polarized Gaussian beam, where - upon tight focusing - those C-points created by transversely spinning fields can form the center of 3D optical polarization topologies when choosing the plane of observation appropriately. Due to the high symmetry of the focal field, these polarization topologies exhibit non trivial structures similar to M\"obius strips. We use a direct physical measure to find C-points with an arbitrarily oriented spinning axis of the electric field and experimentally investigate the fully three-dimensional polarization topologies surrounding these C-points by exploiting an amplitude and phase reconstruction technique.Comment: 5 pages, 3 figures; additional supplementary materials with 4 pages, 3 figure

Weak measurement of elliptical dipole moments by C point splitting

We investigate points of circular polarization in the far field of elliptically polarized dipoles and establish a relation between the angular position and helicity of these C points and the dipole moment. In the case of highly eccentric dipoles, the C points of opposite handedness exhibit only a small angular separation and occur in the low intensity region of the emission pattern. In this regard, we introduce an optical weak measurement approach that utilizes the transverse electric (azimuthal) and transverse magnetic (radial) far-field polarization basis. Projecting the far field onto a spatially varying post-selected polarization state reveals the angular separation and the helicity of the C points. We demonstrate the applicability of this approach and determine the elliptical dipole moment of a particle sitting on an interface by measuring the C points in its far field.Comment: 5 pages, 4 figure

External financial dependence and firms' crisis performance across Europe

Economic research has often relied on a measure of external financial dependence that is constructed using U.S. data and applied to other countries under the assumption of a stable industry ranking across countries. We exploit unique survey data from seven European countries to show that correlations of financial dependence across countries are weak, questioning this assumption. We then use the novel survey-based measure to show that the global financial crisis had a disproportionately negative impact on the real performance of financially dependent firms

The photonic wheel: demonstration of a state of light with purely transverse angular momentum

The concept of angular momentum is ubiquitous to many areas of physics. In classical mechanics, a system may possess an angular momentum which can be either transverse (e.g., in a spinning wheel) or longitudinal (e.g., for a fluidic vortex) to the direction of motion. Photons, however, are well-known to exhibit intrinsic angular momentum which is longitudinal only: the spin angular momentum defining the beam polarization and the orbital angular momentum associated with a spiraling phase front. Here we show that it is possible to generate a novel state of light that contains purely transverse angular momentum, the analogue of a spinning mechanical wheel. We use an optical nano-probing technique to experimentally demonstrate its occurrence in our setup. Such a state of light can provide additional rotational degree of freedom in optical tweezers and optical manipulation.Comment: 15 pages including SO

Geometric spin Hall effect of light in tightly focused polarization tailored light beams

Recently, it was shown that a non-zero transverse angular momentum manifests itself in a polarization dependent intensity shift of the barycenter of a paraxial light beam [A. Aiello et al., Phys. Rev. Lett. 103, 100401 (2009)]. The underlying effect is phenomenologically similar to the spin Hall effect of light, but does not depend on the specific light-matter interaction and can be interpreted as a purely geometric effect. Thus, it was named the geometric spin Hall effect of light. Here, we experimentally investigate the appearance of this effect in tightly focused vector-beams. We use an experimental nano-probing technique in combination with a reconstruction algorithm to verify the relative shifts of the components of the electric energy density in the focal plane, which are linked to the intensity shift. By that, we experimentally demonstrate the geometric spin Hall effect of light in a focused light beam.Comment: 8 pages, 5 figure

Constructing a chiral dipolar mode in an achiral nanostructure

We discuss the excitation of a chiral dipolar mode in an achiral silicon nanoparticle. In particular, we make use of the electric and magnetic polarizabilities of the silicon nanoparticle to construct this chiral electromagnetic mode which is conceptually similar to the fundamental modes of 3D chiral nanostructures or molecules. We describe the chosen tailored excitation with a beam carrying neither spin nor orbital angular momentum and investigate the emission characteristics of the chiral dipolar mode in the helicity basis, consisting of parallel electric and magnetic dipole moments, phase shifted by $\pm \pi/2$. We demonstrate the wavelength dependence and measure the spin and orbital angular momentum in the emission of the excited chiral mode.Comment: 6 pages, 3 figure

Adaptive coping strategies in patients with chronic pain conditions and their interpretation of disease

<p>Abstract</p> <p>Background</p> <p>We examined which adaptive coping strategies, referring to the concept of 'locus of disease control', were of relevance for patients with chronic pain conditions, and how they were interconnected with patients' life satisfaction and interpretation of disease.</p> <p>Methods</p> <p>In a multicenter cross-sectional anonymous survey with the AKU questionnaire, we enrolled 579 patients (mean age 54 ± 14 years) with various chronic pain conditions.</p> <p>Results</p> <p>Disease as an adverse interruption of life was the prevalent interpretation of chronic pain conditions. As a consequence, patients relied on external powerful sources to control their disease (i.e., <it>Trust in Medical Help</it>; <it>Search for Information and Alternative Help</it>), but also on internal powers and virtues (i.e., <it>Conscious Way of Living</it>; <it>Positive Attitudes</it>). In contrast, <it>Trust in Divine Help </it>as an external transcendent source and <it>Reappraisal: Illness as Chance </it>as an internal (cognitive) strategy were valued moderately. Regression analyses indicated that <it>Positive Attitudes </it>and higher age were significant predictors of patients' life satisfaction, but none of the other adaptive coping strategies. While the adaptive coping strategies were not associated with negative interpretations of disease, the cognitive reappraisal attitude was of significant relevance for positive interpretations such as value and challenge.</p> <p>Conclusions</p> <p>The experience of illness may enhance intensity and depth of life, and thus one may explain the association between internal adaptive coping strategies (particularly <it>Reappraisal</it>) and positive interpretations of disease. To restore a sense of self-control over pain (and thus congruence with the situation), and the conviction that one is not necessarily disabled by disease, is a major task in patient care. In the context of health services research, apart from effective pain management, a comprehensive approach is needed which enhances the psycho-spiritual well-being of patients.</p