Highly efficient luminescence from a hybrid state found in strongly quantum confined PbS nanocrystals

We report that high quality PbS nanocrystals, synthesized in the strong quantum confinement regime, have quantum yields as high as 70% at room temperature. We use a combination of modelling and photoluminescence up-conversion to show that we obtain a nearly monodisperse size distribution. Nevertheless, the emission displays a large nonresonant Stokes shift. The magnitude of the Stokes shift is found to be directly proportional to the degree of quantum confinement, from which we establish that the emission results from the recombination of one quantum confined charge carrier with one localized or surface-trapped charge carrier. Furthermore, the surface state energy is found to lie outside the bulk bandgap so that surface-related emission only commences for strongly quantum confined nanocrystals, thus highlighting a regime where improved surface passivation becomes necessary.

"Magic" dispersion maps with distributed Raman amplification

We analyze pulse propagation in an optical fiber with a periodic dispersion map and distributed amplification. Using an asymptotic theory and a momentum method, we identify a family of dispersion management schemes that are advantageous for massive multichannel soliton transmission. For the case of two-step dispersion maps with distributed Raman amplification to compensate for the fiber loss, we find special schemes that have optimal (chirp-free) launch point locations that are independent of the fiber dispersion. Despite the variation of dispersion with wavelength due to the fiber dispersion slope, the transmission in several different channels can be optimized simultaneously using the same optimal launch point. The theoretical predictions are verified by direct numerical simulations. The obtained results are applied to a practical multichannel transmission system.

Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations.

Self-similar parabolic optical solitary waves

We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE.

From rogue waves to random walks:nonlinear instabilities in supercontinuum generation

The noise properties of supercontinuum generation continue to be a subject of wide interest within both pure and applied physics. Aside from immediate applications in supercontinuum source development, detailed studies of supercontinuum noise mechanisms have attracted interdisciplinary attention because of links with extreme instabilities in other physical systems, especially the infamous and destructive oceanic rogue waves. But the instabilities inherent in supercontinuum generation can also be interpreted in terms of natural links with the general field of random processes, and this raises new possibilities for applications in areas such as random number generation. In this contribution we will describe recent work where we interpret supercontinuum intensity and phase fluctuations in this way.

Self-similar parabolic optical solitary waves

We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE.

Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations. © 2005 Springer Science+Business Media, Inc.

Analysis of foveation sequences in congenital nystagmus

Congenital nystagmus (CN) is an ocular-motor disorder that appears at birth or during the first few months of life; it is characterised by involuntary, conjugated, bilateral to and fro ocular oscillations. Pathogenesis of congenital nystagmus is still unknown. Eye movement recording allow to extract and analyse nystagmus main features such as shape, amplitude and frequency; depending on the morphology of the oscillations nystagmus can be classified in different categories (pendular, jerk, horizontal unidirectional, bidirectional). In general, CN patient show a considerable decrease of the visual acuity: image fixation on the retina is disturbed by nystagmus continuous oscillations; however, image stabilisation is still achieved during the short foveation periods in which eye velocity slows down while the target image is placed onto the fovea. Visual acuity was found to be mainly dependent on foveation periods duration, but cycle-to-cycle foveation repeatability and reduction of retinal image velocities also contribute in increasing visual acuity. This study concentrate on cycle-to-cycle image position variation onto fovea, trying to characterise the sequences of foveation positions. Eye-movement (infrared oculographic or electro oculographic) recordings, relative to different gaze positions and belonging to more than 30 CN patients, were analysed. Preliminary results suggest that sequences of foveations show a cyclic pattern with a dominant frequency (around 0.3 Hz on average) much lower than that of the nystagmus (about 3.3 Hz on average). Sequences of foveations reveals an horizontal ocular swing of more than 2 degree on average, which can explain the low visual acuity of the CN patient. Current CN therapies, pharmacological treatment or surgery of the ocular muscles, mainly aim to increase the patient's visual acuity. Hence, it is fundamental to have an objective parameter (expected visual acuity) for therapy planning. The information about sequences of foveations can improve estimation of patient visual acuity. © 2008 Springer-Verlag.

PREFACE

The Conference on Partial Differential Equations and Applications, Sofia, September 14–16, 2011 (In honor of 65-th Anniversary of Professor Petar Popivanov) took place in the premises of the Institute of Mathematics and Informatics (IMI) of the Bulgarian Academy of Sciences (BAS). The conference was organized by the Section “Differential Equations and Mathematical Physics” of IMI with the participation of research groups on PDE from Universit`a di Cagliari and Universit`a di Torino (Italy), with the organizing committee – N. Kutev (IMI–BAS) – chair, G. Boyadzhiev (IMI–BAS) – secretary, T. Gramchev (Univ. Cagliari) and A. Oliaro (Univ. Torino) – members, and thefollowing program/scientific committee: T. Gramchev (chair), N. Kutev (IMI–BAS), L. Rodino (Universit`a di Torino), M. Ruzhansky (Imperial College London), A. Slavova (IMI–BAS), C. Van Der Mee (Universit`a di Cagliari).