Accelerated rogue waves generated by soliton fusion at the advanced stage of supercontinuum formation in photonic crystal fibers

Soliton fusion is a fascinating and delicate phenomenon that manifests itself in optical fibers in case of interaction between co-propagating solitons with small temporal and wavelengths separation. We show that the mechanism of acceleration of trailing soliton by dispersive waves radiated from the preceding one provides necessary conditions for soliton fusion at the advanced stage of supercontinuum generation in photonic crystal fibers. As a result of fusion large intensity robust light structures arise and propagate over significant distances. In presence of small random noise the delicate condition for the effective fusion between solitons can easily be broken, making the fusion induced giant waves a rare statistical event. Thus oblong-shaped giant accelerated waves become excellent candidates for optical rogue waves.Comment: Optics Letters Journal. In pres

Every Hilbert space frame has a Naimark complement

Naimark complements for Hilbert space Parseval frames are one of the most fundamental and useful results in the field of frame theory. We will show that actually all Hilbert space frames have Naimark complements which possess all the usual properties for Naimark complements with one notable exception. So these complements can be used for equiangular frames, RIP property, fusion frames etc. Along the way, we will correct a mistake in a recent fusion frame paper where chordal distances for Naimark complements are computed incorrectly.Comment: Changes after Refereein

Spectral self-action of THz emission from ionizing two-color laser pulses in gases

The spectrum of terahertz (THz) emission in gases via ionizing two-color femtosecond pulses is analyzed by means of a semi-analytic model and finite-difference-time-domain simulations in 1D and 2D geometries. We show that produced THz signals interact with free electron trajectories and thus influence significantly further THz generation upon propagation, i.e., make the process inherently nonlocal. This self-action plays a key role in the observed strong spectral broadening of the generated THz field. Diffraction limits the achievable THz bandwidth by efficiently depleting the low frequency amplitudes in the propagating field.Comment: 12 pages, 6 figure

Determinants of share-based compensation plans in Central and Eastern European public companies: An institutional analysis

This paper discusses the adoption of share-based compensation plans among Central and Eastern European (CEE) public companies composing major national stock exchange indices in Poland (WIG 20), the Czech Republic (PX) and Hungary (BUX). The analysis shows that the spread of such pay practices depends on the characteristics of major shareholders of the company, the state and foreign parent companies being the most prominent influencing factors. The results are discussed in the light of the legal environment in respective countries.Im Zentrum des vorliegenden Artikels stehen aktienbasierte Vergütungspläne in mittel- und osteuropäischen (MOE) Aktiengesellschaften, die in den nationalen Leitindizes in Polen (WIG 20), der Tschechischen Republik (PX) und Ungarn (BUX) vertreten sind. Die Analyse zeigt, dass die Verbreitung dieser Praktiken wesentlich von den Charakteristika der Hauptaktionäre der Unternehmen abhängt. Hier stellen der Staat und die ausländischen Unternehmen die wichtigsten Einflussfaktoren dar. Die Ergebnisse der Studie werden vor dem Hintergrund des regulativen Kontextes in den jeweiligen Ländern diskutiert

Multifunctional Cascaded Metamaterials: Integrated Transmitarrays

Control of electromagnetic waves using engineered materials is very important in a wide range of applications, therefore there is always a continuous need for new and more efficient solutions. Known natural and artificial materials and surfaces provide a particular functionality in the frequency range they operate but cast a "shadow" and produce reflections at other frequencies. Here, we introduce a concept of multifunctional engineered materials that possess different predetermined functionalities at different frequencies. Such response can be accomplished by cascading metasurfaces (thin composite layers) that are designed to perform a single operation at the desired frequency and are transparent elsewhere. Previously, out-of-band transparent metasurfaces for control over reflection and absorption were proposed. In this paper, to complete the full set of functionalities for wave control, we synthesize transmitarrays that tailor transmission in a desired way, being "invisible" beyond the operational band. The designed transmitarrays for wavefront shaping and anomalous refraction are tested numerically and experimentally. To demonstrate our concept of multifunctional engineered materials, we have designed a cascade of three metasurfaces that performs three different functions for waves at different frequencies. Remarkably, applied to volumetric metamaterials, our concept can enable a single composite possessing desired multifunctional response.Comment: 9 pages, 9 figures, journal pape

Community-based curriculum for inter-ethnic education and violence prevention

While Belarus has been uniquely marked in its region by a history of productive coexistence between the majority of the population and the country's diverse ethnic, religious and national minorities the country is now faced by new challenges from an influx of recent refugees from the republics of the Former Soviet Union. It is important that action is taken now to implant the lessons of historic coexistence in the emerging generation of Belarusian citizens. For that reason the Belarus National Institute of Education and think tank SCAF have created a proactive program that supports grassroots initiatives in inter-ethnic confidence building education

Every Hilbert space frame has a Naimark complement

Naimark complements for Hilbert space Parseval frames are one of the most fundamental and useful results in the field of frame theory. We will show that actually all Hilbert space frames have Naimark complements which possess all the usual properties for Naimark complements with one notable exception. So these complements can be used for equiangular frames, RIP property, fusion frames etc. Along the way, we will correct a mistake in a recent fusion frame paper where chordal distances for Naimark complements are computed incorrectly.Comment: Changes after Refereein