Unified theory for Goos-H\"{a}nchen and Imbert-Fedorov effects

A unified theory is advanced to describe both the lateral Goos-H\"{a}nchen (GH) effect and the transverse Imbert-Fedorov (IF) effect, through representing the vector angular spectrum of a 3-dimensional light beam in terms of a 2-form angular spectrum consisting of its 2 orthogonal polarized components. From this theory, the quantization characteristics of the GH and IF displacements are obtained, and the Artmann formula for the GH displacement is derived. It is found that the eigenstates of the GH displacement are the 2 orthogonal linear polarizations in this 2-form representation, and the eigenstates of the IF displacement are the 2 orthogonal circular polarizations. The theoretical predictions are found to be in agreement with recent experimental results.Comment: 15 pages, 3 figure

Fresnel laws at curved dielectric interfaces of microresonators

We discuss curvature corrections to Fresnel's laws for the reflection and transmission of light at a non-planar refractive-index boundary. The reflection coefficients are obtained from the resonances of a dielectric disk within a sequential-reflection model. The Goos-H\"anchen effect for curved light fronts at a planar interface can be adapted to provide a qualitative and quantitative extension of the ray model which explains the observed deviations from Fresnel's laws.Comment: submitted to Phys. Rev.

Kaspar Schott’s “encyclopedia of all mathematical sciences”

In 1661, Kaspar Schott published his comprehensive textbook “Cursus mathematicus” in Würzburg for the first time, his “Encyclopedia of all mathematical sciences”. It was so successful that it was published again in 1674 and 1677. In its 28 books, Schott gave an introduction for beginners in 22 mathematical disciplines by means of 533 figures and numerous tables. He wanted to avoid the shortness and the unintelligibility of his predecessors Alsted and Hérigone. He cited or recommended far more than hundred authors, among them Protestants like Michael Stifel and Johannes Kepler, but also Catholics like Nicolaus Copernicus. The paper gives a survey of this work and explains especially interesting aspects: The dedication to the German emperor Leopold I., Athanasius Kircher’s letter of recommendation as well as Schott’s classification of sciences, explanations regarding geometry, astronomy, and algebra

Geometric Spin Hall Effect of Light at Polarizing Interfaces

The geometric Spin Hall Effect of Light (geometric SHEL) amounts to a polarization-dependent positional shift when a light beam is observed from a reference frame tilted with respect to its direction of propagation. Motivated by this intriguing phenomenon, the energy density of the light beam is decomposed into its Cartesian components in the tilted reference frame. This illustrates the occurrence of the characteristic shift and the significance of the effective response function of the detector. We introduce the concept of a tilted polarizing interface and provide a scheme for its experimental implementation. A light beam passing through such an interface undergoes a shift resembling the original geometric SHEL in a tilted reference frame. This displacement is generated at the polarizer and its occurrence does not depend on the properties of the detection system. We give explicit results for this novel type of geometric SHEL and show that at grazing incidence this effect amounts to a displacement of multiple wavelengths, a shift larger than the one introduced by Goos-H\"anchen and Imbert-Fedorov effects.Comment: 6 pages, 4 figure

Technoscientia est Potentia?: Contemplative, interventionist, constructionist and creationist idea(l)s in (techno)science

Within the realm of nano-, bio-, info- and cogno- (or NBIC) technosciences, the ‘power to change the world’ is often invoked. One could dismiss such formulations as ‘purely rhetorical’, interpret them as rhetorical and self-fulfilling or view them as an adequate depiction of one of the fundamental characteristics of technoscience. In the latter case, a very specific nexus between science and technology, or, the epistemic and the constructionist realm is envisioned. The following paper focuses on this nexus drawing on theoretical conceptions as well as empirical material. It presents an overview of different technoscientific ways to ‘change the world’—via contemplation and representation, intervention and control, engineering, construction and creation. It further argues that the hybrid character of technoscience makes it difficult (if not impossible) to separate knowledge production from real world interventions and challenges current science and technology policy approaches in fundamental ways

Electronic beam shifts in monolayer graphene superlattice

Electronic analogue of generalized Goos-H\"{a}nchen shifts is investigated in the monolayer graphene superlattice with one-dimensional periodic potentials of square barriers. It is found that the lateral shifts for the electron beam transmitted through the monolayer graphene superlattice can be negative as well as positive near the band edges of zero-$\bar{k}$ gap, which are different from those near the band edges of Bragg gap. These negative and positive beam shifts have close relation to the Dirac point. When the condition $q_A d_A= -q_B d_B= m \pi$ ($m=1,2,3...$) is satisfied, the beam shifts can be controlled from negative to positive when the incident energy is above the Dirac point, and vice versa. In addition, the beam shifts can be greatly enhanced by the defect mode inside the zero-$\bar{k}$ gap. These intriguing phenomena can be verified in a relatively simple optical setup, and have potential applications in the graphene-based electron wave devices.Comment: 5 pages, 4 figures, submitted on Oct. 15, 201

Interplay between n-3 and n-6 long-chain polyunsaturated fatty acids and the endocannabinoid system in brain protection and repair.

The brain is enriched in arachidonic acid (ARA) and docosahexaenoic acid (DHA), long-chain polyunsaturated fatty acids (LCPUFA) of the n-6 and n-3 series, respectively. Both are essential for optimal brain development and function. Dietary enrichment with DHA and other long-chain n-3 PUFA, such as eicosapentaenoic acid (EPA) have shown beneficial effects on learning and memory, neuroinflammatory processes and synaptic plasticity and neurogenesis. ARA, DHA and EPA are precursors to a diverse repertoire of bioactive lipid mediators, including endocannabinoids. The endocannabinoid system comprises cannabinoid receptors, their endogenous ligands, the endocannabinoids, and their biosynthetic and degradation enzymes. Anandamide (AEA) and 2-archidonoylglycerol (2-AG) are the most widely studied endocannabinoids, and are both derived from phospholipid-bound ARA. The endocannabinoid system also has well established roles in neuroinflammation, synaptic plasticity and neurogenesis, suggesting an overlap in the neuroprotective effects observed with these different classes of lipids. Indeed, growing evidence suggests a complex interplay between n-3 and n-6 LCPUFA and the endocannabinoid system. For example, long-term DHA and EPA supplementation reduces AEA and 2-AG levels, with reciprocal increases in levels of the analogous endocannabinoid-like DHA and EPA-derived molecules. This review summarises current evidence of this interplay and discusses the therapeutic potential for brain protection and repair