Dispersion Phenomena in Dunkl-Schrödinger Equation and Applications

2000 Mathematics Subject Classification: 35Q55,42B10.

Bound dissipative-pulse evolution in the all-normal dispersion fiber laser using a 45° tilted fiber grating

The formation and evolution of bound dissipative pulses in the all-normal dispersion Yb-fiber laser based on a novel 45° tilted fiber grating (TFG) are first investigated both numerically and experimentally. Based on the nonlinear polarization rotation technique, the TFG and two polarization controllers (PCs) are exploited for stable self-started passive mode locking. Numerical results show that the formation of bound-state pulses in the all-normal dispersion region is the progress of soliton shaping through the dispersive waves and follows the soliton energy quantization effect. Theoretical and experimental results demonstrate that the formation mechanism of bound-state pulses can be attributed to the high pump strength and effective filter bandwidth. The obtained bound-state dissipative pulses with quasi-rectangular spectral profile have fixed pulse separation as a function of pump power. © 2013 Astro Ltd.

Compression spectrale dans les fibres optiques en présence de dispersion normale

Nous étudions numériquement le phénomène de compression spectrale se déroulant dans une fibre optique à dispersion normale. Les conditions conduisant à une impulsion en quasi-limite de Fourier sont déterminées et nous montrons que loin de dégrader les performances, la présence de dispersion normale permet une amélioration significative des résultats.

On the impact of Cu dispersion on CO2 photoreduction over Cu/TiO2

A family of Cu/TiO2 catalysts was prepared using a refined sol–gel method, and tested in the photocatalytic reduction of CO2 by H2O to CH4 using a stirred batch, annular reactor. The resulting photoactivity was benchmarked against pure TiO2 nanoparticles (synthesised by an identical sol–gel route). CO2 photoreduction exhibited a strong volcano dependence on Cu loading, reflecting the transition from 2-dimensional CuOx nanostructures to 3-dimensional crystallites, with optimum CH4 production observed for 0.03 wt.% Cu/TiO2.

Interaction of time-varying airy pulses with a layer

Pulses with an envelope in the form of the Airy function are obtained using Green's functions in 1D and 2D in time domain. Interaction of such pulses with a dielectric layer is investigated and expressions for reflected and transmitted pulses are obtained. © 2012 EUROPEAN MICROWAVE ASSOC.

Influence of digital dispersion equalization on phase noise enhancement in coherent optical system

The phase noise enhancement due to digital dispersion equalization is investigated, which indicates that the phase noise from transmitter laser can also interact with the dispersion depending on the choice of digital dispersion compensation methods. © OSA 2012.

Capacity of dispersion-non-compensated nonlinear fibre channels

We present the analytical description of a specific nonlinear fibre channel with non-compensated dispersion. Information theory analysis shows that capacity of such nonlinear fibre channel does not decay with growing signal-to-noise ratio. © 2012 IEEE.

Stochastic anti-resonance in a fibre Raman amplifier

Stochastic anti-resonance, that is resonant enhancement of randomness caused by polarization mode beatings, is analyzed both numerically and analytically on an example of fibre Raman amplifier with randomly varying birefringence. As a result of such anti-resonance, the polarization mode dispersion growth causes an escape of the signal state of polarization from a metastable state corresponding to the pulling of the signal to the pump state of polarization.This phenomenon reveals itself in abrupt growth of gain fluctuations as well as in dropping of Hurst parameter and Kramers length characterizing long memory in a system and noise induced escape from the polarization pulling state. The results based on analytical multiscale averaging technique agree perfectly with the numerical data obtained by direct numerical simulations of underlying stochastic differential equations. This challenging outcome would allow replacing the cumbersome numerical simulations for real-world extra-long high-speed communication systems.

An investigation of support effects on the Pt-catalysed selective transformation of α,β-unsaturated substrates

Pt catalyst series were prepared on mesoporous SBA-15, SBA-16, KIT-6, true liquidcrystal-templated meso-macroporous SBA-15 and a commercial, low surface area silicasupport. Support structure can be easily fabricated using surfactant templating as a mode ofstringent control on porosity, surface area and internal structure. The impact of varying Pt-support physicochemical properties was systematically studied for the selective transformation of allylic substrates under chemoselective oxidation and hydrogenation regimes, a class of reactions highly applicable to industry. Pt-based heterogeneous catalysts are well-known for their utilisation in the hydrogenation of α,β-unsaturated aldehydes,although the mode of action and lack of systematic studies in the literature fuels continuing debate into the role of Pt nanoparticles and support choice for this area. This project attempts to shed some light on several frequently asked questions in this field. Successful support synthesis and stability after Pt impregnation is confirmed through HRTEM, XRD and N2 porosimetry. Decreasing metal loading promoted dispersion values,regardless of support choice, with surface PtO2 content also showing visible enhancement.Increasing support surface area and mesoporosity exhibited the following trend on Pt dispersion augmentation; low surface area commercial silica < true liquid crystal-templated SBA-15 < SBA-15 < SBA-16 ~ KIT-6. For the selective oxidation of cinnamyl alcohol,increasing PtO2 surface population confers substantial rate enhancements, with turnover frequencies evidencing PtO2 to be the active species .In the Pt-catalysed hydrogenation of cinnamaldehyde, strong support insensitivity was observed towards catalytic activity; as turnover frequencies normalised to Pt metal reveal constant values. However, structure sensitivity to the desired unsaturated alcohol arose,evidencing the requirement of flat, extended Pt (111) facets for C=O hydrogenation. Pt/SBA-15 proved the most selective, reflecting suppressed cinnamyl alcohol hydrogenation, with DRIFTS and in-situ ATR-IR evidencing the key role of support polarity in re-orientation of cinnamaldehyde to favour di-σCO adsorption and C=O versus C=C hydrogenation. High pressures increased activity, whilst a dramatic shift in selectivity from dominant C=C (1 bar)to C=O hydrogenation (10 bar) was also observed, attributed to surface crowding and suppression of di-σCC and η4 di-σCO+πC=C cinnamaldehyde binding modes.

Furnace chemical vapor deposition (FCVD) method for special optical fibers fabrication

The features of the Furnace Chemical Vapor Deposition (FCVD) method of manufacturing preforms for special optical fibers are considered. It is shown that misalignment of substrate silica tube and furnace hole axes has a negative effect on the quality of fabricated preforms, leading to angular and radial asymmetry of the refractive index profile. Ways of getting rid of this and other disadvantages of the FCVD method are described. Some advantages of the FCVD method over the MCVD method are shown. It was demonstrated that the FCVD method, despite some drawbacks, allows to manufacture high-quality fiber preforms with good symmetry of the refractive index profile, and thus it is promising for fabrication of dispersion, dispersion varying and active fibers. © 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).

Gain dependent pulse regimes transitions in a dissipative dispersion-managed fibre laser

For the first time, we demonstrate the possibility to switch between three distinct pulse regimes in a dissipative dispersion-managed (DM) fibre laser by solely controlling the gain saturation energy. Nonlinear Schrödinger equation based simulations show the transitions between hyper-Gaussian similaritons, parabolic similaritons, and dissipative solitons in the same laser cavity. It is also shown that such transitions exist in a wide dispersion range from all-normal to slightly net-normal dispersion. This work demonstrates that besides dispersion and filter managements gain saturation energy can be a new degree of freedom to manage pulse regimes in DM fibre lasers, which offers flexibility in designing ultrafast fibre lasers. Also, the result indicates that in contrast to conservative soliton lasers whose intensity profiles are unique, dissipative DM lasers show diversity in pulse shapes. The findings not only give a better understanding of pulse shaping mechanisms in mode-locked lasers, but also provide insight into dissipative systems.

Filter-based dispersion-managed versatile ultrafast fibre laser

We present the operation of an ultrafast passively mode-locked fibre laser, in which flexible control of the pulse formation mechanism is readily realised by an in-cavity programmable filter the dispersion and bandwidth of which can be software configured. We show that conventional soliton, dispersion- managed (DM) soliton (stretched-pulse) and dissipative soliton mode-locking regimes can be reliably targeted by changing the filter’s dispersion and bandwidth only, while no changes are made to the physical layout of the laser cavity. Numerical simulations are presented which confirm the different nonlinear pulse evolutions inside the laser cavity. The proposed technique holds great potential for achieving a high degree of control over the dynamics and output of ultrafast fibre lasers, in contrast to the traditional method to control the pulse formation mechanism in a DM fibre laser, which involves manual optimisation of the relative length of fibres with opposite-sign dispersion in the cavity. Our versatile ultrafast fibre laser will be attractive for applications requiring different pulse profiles such as in optical signal processing and optical communications.

Time-varying airy pulses

Pulses in the form of the Airy function as solutions to an equation similar to the Schrodinger equation but with opposite roles of the time and space variables are derived. The pulses are generated by an Airy time varying field at a source point and propagate in vacuum preserving their shape and magnitude. The pulse motion is decelerating according to a quadratic law. Its velocity changes from infinity at the source point to zero in infinity. These one dimensional results are extended to the 3D+time case for a similar Airy-Bessel pulse with the same behaviour, the non-diffractive preservation and the deceleration. This pulse is excited by the field at a plane aperture perpendicular to the direction of the pulse propagation. © 2011 IEEE.

Optically tuning of chromatic dispersion compensators

We present a new tuning method for chromatic dispersion compensators, which can be optically tunable. The dispersion compensators were made in Er/Yb co-doped fiber and were pumped with 980nm laser diodes. The tunable dispersion for a chirped grating and also a uniform-period grating was successfully demonstrated in the experiment.

Az extrém ármozgások statisztikai jellemzői a magyar áramtőzsdén (The statistical characteristics of extreme price movements in the Hungarian power exchange)

2010. július 20-án megkezdte működését a magyar áramtőzsde, a HUPX. 2010. augusztus 16-án az első napokban tapasztalt 45-60 euró megawattórás ár helyett egyes órákban 2999 eurós árral szembesültek a piaci szereplők. A kiemelkedően magas árak megjelenése nem szokatlan az áramtőzsdéken a nemzetközi tapasztalatok szerint, sőt a kutatások kiemelten foglalkoznak az ún. ártüskék okainak felkutatásával, valamint megjelenésük kvantitatív és kvalitatív elemzésével. A cikkben a szerző bemutatja, milyen eredmények születtek a kiugró árak statisztikai vizsgálatai során a szakirodalomban, illetve azok következtetései hogyan állják meg a helyüket a magyar árak idősorát figyelembe véve. A szerző bemutat egy modellkeretet, amely a villamosenergia-árak viselkedését a hét órái szerint periodikusan váltakozó paraméterű eloszlásokkal írja le. A magyar áramtőzsde rövid története sajnos nem teszi lehetővé, hogy a hét minden órájára külön áreloszlást illeszthessünk. A szerző ezért a hét óráit két csoportba sorolja az ár eloszlásának jellege alapján: az ártüskék megjelenése szempontjából kockázatos és kevésbé kockázatos órákba. Ezután a HUPX-árak leírására felépít egy determinisztikus, kétállapotú rezsimváltó modellt, amellyel azonosítani lehet a kockázatos és kevésbé kockázatos órákat, valamint képet kaphatunk az extrém ármozgások jellegéről. / === / On 20th July, 2010 the Hungarian Power Exchange, the HUPX started its operation. On 16th August in certain hours the markets participants faced € 2,999 price instead of in the first days experienced 45-60 euros/mwh. According to the international experiences the appearance of the extremely high prices hasn’t been unusual in the power exchanges, the researches have focused exploring the causes of the so-called spikes and quantitative and qualitative analysis of those appearances. In this article the author describes what results were determined on statistical studies of outstanding prices in the literature, and how their conclusions stand up into account the time series of the Hungarian prices. The author presents a model framework which describes the behavior of electricity prices in the seven hours of periodically varying parameters. Unfortunately the brief history of the Hungarian Power Exchange does not allow to suit specific prices for each hour of week. Therefore the author classifies the hours of the week in the two groups based on the nature of price dispersion: according to the appearance of spikes to risky and less risky classes. Then for describing the HUPX prices the author builds a deterministic two-state, regime-changing model, which can be identified the risky and less risky hours, and to get a picture of the nature of extreme price movements.