New recursions for genus-zero Gromov-Witten invariants

New relations among the genus-zero Gromov-Witten invariants of a complex projective manifold X are exhibited. When the cohomology of X is generated by divisor classes and classes “with vanishing one-point invariants,” the relations determine many-point invariants in terms of one-point invariants.     

Iterative calculation, manufacture and investigation of DOE forming unimodal complex distribution

We present results of iterative calculation, manufacture and experimental as well as theoretical investigations of a novel diffractive optical element (DOE) which transforms a Gaussian TEM₀₀ input beam into a unimodal Gauss–Hermite (1, 0) complex distribution. The iterative calculation procedure is based on the application of the method of generalized projections. The projection operator onto a set of modal functions is implemented through partition of the focal plane into a ‘useful’ and an ‘auxiliary’ domain. This element is manufactured as a 16 level surface profile by (variable dose) electron-beam direct-writing into a PMMA resist film, and a subsequent development procedure of the resist. The final element consists of a fused-silica substrate coated with the structured PMMA film. Both computational and experimental results are presented and demonstrate a good conformity with each other. The achieved results show good prospects of such an approach for the formation of unimodal distributions.     

Comparison of femtosecond laser-induced damage on unstructured vs. nano-structured Au-targets

The combination of high-field physics with nano-plasmonics has proven to be feasible in producing high harmonics of intense laser radiation from noble gases, assisted by the field-enhancement effect in the proximity of metallic nano-antennas. However, the intensity region where harmonics can be generated without irreversible damage to these delicate structures is rather narrow. We explore the damage threshold of gold targets that exhibit regular structures on a nanoscopic scale, either explicitly resonant to the used laser frequency, or off-resonance. These are compared to values for bulk material in order to gain insight into the role of plasmonic resonances in the response of solid targets on intense laser radiation. We find that the presence of such a resonance lowers the threshold fluence (J/cm²) where global structural damage sets in by about an order of magnitude. Statistical deviations either in local pulse energy of the damage inducing laser radiation or in the exact resonance behaviour of singular structures prove to be limited. These results should serve as a guideline for future experiments working near the damage threshold of more sophisticated antenna designs.     

High performance diffraction gratings made by e-beam lithography

Gratings are essential components in different high performance optical set-ups such as spectrometers in space missions or ultrashort-pulse laser compression arrangements. Often such kinds of applications require gratings operating close to the technological accessible limits of today??s fabrication technology. Typical critical parameters are the diffraction efficiency and its polarization dependency, the wave-front error introduced by the grating, and the stray-light performance. Additionally, space applications have specific environmental requirements and laser application typically demand a high damage threshold. All these properties need to be controlled precisely on rather large grating areas. Grating sizes of 200?mm or even above are not unusual anymore. The paper provides a review on how such high performance gratings can be realized by electron-beam lithography and accompanying technologies. The approaches are demonstrated by different examples. The first example is the design and fabrication of the grating for the Radial-Velocity-Spectrometer of the GAIA-mission of the ESA. The second grating is a reflective pulse compression element with no wavelength resonances due to an optimized design. The last example shows a three level blazed grating in resonance domain with a diffraction efficiency of approximately 86?%.     

External-cavity diode laser in second-order Littrow configuration

In this Letter, we propose and demonstrate an external-cavity diode laser in second-order Littrow configuration. This topology utilizes a low-efficiency diffraction grating to establish a high-finesse external cavity, strong optical feedback, a high polarization discrimination, and a circular TEM₀₀ output mode. In our proof-of-concept experiment, we realized a cavity with a finesse of 1855, being, to the best of our knowledge, the highest value ever reported for a three-port-grating-coupled cavity. With optical feedback, the laser threshold of the laser diode employed was reduced by a factor of 4.     

An ultra‐black silicon absorber

An ultra‐black (A > 99%) broadband absorber concept on the basis of a needle‐like silicon nanostructure called Black Silicon is proposed. The absorber comprises Black Silicon established by inductively coupled plasma reactive ion etching (ICP‐RIE) on a highly doped, degenerated silicon substrate. Improved absorbers also incorporate an additional oxide capping layer on the nanostructures and reach an absorptance of A > 99.5% in the range of 350 to 2000 nm and A ∼ 99.8% between 1000 and 1250 nm. Fabrication of the absorbers is consistent with CMOS standards and requires no lithography. (Picture: Kasper, Friedrich‐Schiller‐University Jena)     

Analysing the isotopic life history of the alpine ungulates Capra ibex and Rupicapra rupicapra rupicapra through their horns

The horn of ungulate grazers offers a valuable isotopic record of their diet and environment. However, there have been no reports of the spatio‐temporal variation of the isotopic composition of horns. We investigated patterns of carbon (δ¹³C) and nitrogen (δ¹⁵N) isotopic composition along and perpendicular to the horn axis in Capra ibex and Rupicapra rupicapra rupicapra to assess the effects of animal age, within‐year (seasonal) and inter‐annual variation, natural contamination and sampling position on horn isotope composition. Horns of male C. ibex (n = 23) and R. r. rupicapra (n = 1) were sampled longitudinally on the front (only R. r. rupicapra) and back side and on the surface and sub‐surface. The sides of the R. r. rupicapra horn did not differ in δ¹³C. In both species, the horn surface had a 0.15‰ lower δ¹³C and a higher carbon‐to‐nitrogen (C/N) ratio than the sub‐surface. Washing the horn with water and organic solvents removed material that caused these differences. With age, the δ¹⁵N of C. ibex horns increased (+0.1‰ year^?1), C/N ratio increased, and ¹³C discrimination relative to atmospheric CO₂ (¹³Δ) increased slightly (+0.03‰ year^?1). Geostatistical analysis of one C. ibex horn revealed systematic patterns of inter‐annual and seasonal ¹³C changes, but ¹⁵N changed only seasonally. The work demonstrates that isotopic signals in horns are influenced by natural contamination (δ¹³C), age effects (¹³Δ and δ¹⁵N), and seasonal (δ¹³C and δ¹⁵N) and inter‐annual variation (δ¹³C). The methods presented allow us to distinguish between these effects and thus allow the use of horns as isotopic archives of the ecology of these species and their habitat. Copyright © 2009 John Wiley & Sons, Ltd.     

Corrugated neat thin-film conjugated polymer distributed-feedback lasers

Wave-guided thin-film distributed-feedback (DFB) polymer lasers are fabricated by spin coating a PPV-derived semiconducting polymer, thianthrene-DOO-PPV, onto oxidised silicon wafers with corrugated second-order periodic gratings. The gratings are written by reactive ion beam etching. Laser action is achieved by transverse pumping with picosecond laser pulses (wavelength 347.15 nm, duration 35 ps). The DFB-laser surface emission and edge emission are analysed. Outside the grating region the polymer film is used for comparative wave-guided travelling wave laser (amplified spontaneous emission (ASE)) studies. The pump pulse threshold energy density for wave-guided DFB-laser action (4–9 μJ cm^-2) is found to be approximately a factor of two lower than the threshold for wave-guided travelling wave laser action. The spectral width of the DFB laser (down to Δλ_DFB≈0.07 nm) is considerably narrower than that of the travelling wave laser (Δλ_TWL≈14 nm). The DFB-laser emission is highly linearly polarised transverse to the grating axis (TE mode). Only at high pump pulse energy densities does an additional weak TM mode build up. The surface-emitted DFB-laser radiation has a low divergence along the grating direction. For both the DFB lasers and the travelling wave lasers, gain saturation occurs at high excitation energy densities. Received: 7 January 2002 / Revised version: 15 February 2002 / Published online: 14 March 2002     

Bounds for randomly shared risk of heavy-tailed loss factors

For a risk vector V, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents’ exposure risk and the aggregated risk in the market. Risk is measured by Value-at-Risk or Conditional Tail Expectation. We assume Pareto tails for the components of V and arbitrary dependence structure in a multivariate regular variation setting. Upper and lower bounds are given by asymptotically independent and fully dependent components of V with respect to the tail index α being smaller or larger than 1. Counterexamples, where for non-linear aggregation functions no bounds are available, complete the picture.