Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Universality in the merging dynamics of parametric active contours:a study in MRI based lung segmentation

Measurement of lung ventilation is one of the most reliable techniques in diagnosing pulmonary diseases. The time-consuming and bias-prone traditional methods using hyperpolarized H 3He and 1H magnetic resonance imageries have recently been improved by an automated technique based on 'multiple active contour evolution'. This method involves a simultaneous evolution of multiple initial conditions, called 'snakes', eventually leading to their 'merging' and is entirely independent of the shapes and sizes of snakes or other parametric details. The objective of this paper is to show, through a theoretical analysis, that the functional dynamics of merging as depicted in the active contour method has a direct analogue in statistical physics and this explains its 'universality'. We show that the multiple active contour method has an universal scaling behaviour akin to that of classical nucleation in two spatial dimensions. We prove our point by comparing the numerically evaluated exponents with an equivalent thermodynamic model. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

Quantum Mechanics of Guiding Center Motion in Strong Magnetic Field (Coherent State Path Integral Approach)

A new approach is proposed for the quantum mechanics of guiding center motion in strong magnetic field. This is achieved by use of the coherent state path integral for the coupled systems of the cyclotron and the guiding center motion. We are specifically concerned with the effective action for the guiding center degree, which can be used to get the Bohr- Sommerfeld quantization scheme. The quantization rule is similar to the one for the vortex motion as a dynamics of point particles.

Wider-frequency combs generation, noise reduction, and repetition rate tuning in quantum-dot mode-locked lasers

We describe the technique allowing for generation of low-noise wider frequency combs and pulses of shorter duration in quantum-dot mode-locked lasers. We compare experimentally noise stabilization techniques in semiconductor modelocked lasers. We discuss the benefits of electrical modulation of the laser absorber voltage (hybrid mode-locking), combination of hybrid mode-locking with optical injection seeding from the narrow linewidth continues wave master source and optical injection seeding of two coherent sidebands separated by the laser repetition rate. © 2014 SPIE.

Non-Markov state model of peptide dynamics

A hidden Markov state model has been applied to classical molecular dynamics simulated small peptide in explicit water. The methodology allows increasing the time resolution of the model and describe the dynamics with the precision of 0.3 ps (comparing to 6 ps for the standard methodology). It also permits the investigation of the mechanisms of transitions between the conformational states of the peptide. The detailed description of one of such transitions for the studied molecule is presented. © 2012 Elsevier B.V. All rights reserved.

Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus

Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90

Effect of dynamical instability on timing jitter in passively mode-locked quantum-dot lasers

We study the effect of noise on the dynamics of passively mode-locked semiconductor lasers both experimentally and theoretically. A method combining analytical and numerical approaches for estimation of pulse timing jitter is proposed. We investigate how the presence of dynamical features such as wavelength bistability in a quantum-dot laser affects timing jitter.

The effect of slow passage in the pulse-pumped quantum dot laser

In recent years, quantum-dot (QD) semiconductor lasers attract significant interest in many practical applications due to their advantages such as high-power pulse generation because to the high gain efficiency. In this work, the pulse shape of an electrically pumped QD-laser under high current is analyzed. We find that the slow rise time of the pulsed pump may significantly affect the high intensity output pulse. It results in sharp power dropouts and deformation of the pulse profile. We address the effect to dynamical change of the phase-amplitude coupling in the proximity of the excited state (ES) threshold. Under 30ns pulse pumping, the output pulse shape strongly depends on pumping amplitude. At lower currents, which correspond to lasing in the ground state (GS), the pulse shape mimics that of the pump pulse. However, at higher currents the pulse shape becomes progressively unstable. The instability is greatest when in proximity to the secondary threshold which corresponds to the beginning of the ES lasing. After the slow rise stage, the output power sharply drops out. It is followed by a long-time power-off stage and large-scale amplitude fluctuations. We explain these observations by the dynamical change of the alpha-factor in the QD-laser and reveal the role of the slowly rising pumping processes in the pulse shaping and power dropouts at higher currents. The modeling is in very good agreement with the experimental observations. © 2014 SPIE.

Quantum dot-based terahertz photoconductive antennas

We present novel Terahertz (THz) emitting optically pumped Quantum Dot (QD) photoconductive (PC) materials and antenna structures on their basis both for pulsed and CW pumping regimes. Full text Quantum dot and microantenna design - Presented here are design considerations for the semiconductor materials in our novel QD-based photoconductive antenna (PCA) structures, metallic microantenna designs, and their implementation as part of a complete THz source or transceiver system. Layers of implanted QDs can be used for the photocarrier lifetime shortening mechanism[1,2]. In our research we use InAs:GaAs QD structures of varying dot layer number and distributed Bragg reflector(DBR)reflectivity range. According to the observed dependence of carrier lifetimes on QD layer periodicity [3], it is reasonable to assume that electron lifetimes can be potentially reduced down to 0.45ps in such structures. Both of these features; long excitation wavelength and short carriers lifetime predict possible feasibility of QD antennas for THz generation and detection. In general, relatively simple antenna configurations were used here, including: coplanar stripline (CPS); Hertzian-type dipoles; bow-ties for broadband and log-spiral(LS)or log-periodic(LP)‘toothed’ geometriesfor a CW operation regime. Experimental results - Several lasers are used for antenna pumping: Ti:Sapphire femtosecond laser, as well as single-[4], double-[5] wavelength, and pulsed [6] QD lasers. For detection of the THz signal different schemes and devices were used, e.g. helium-cooled bolometer, Golay cell and a second PCA for coherent THz detection in a traditional time-domain measurement scheme.Fig.1shows the typical THz output power trend from a 5 um-gap LPQD PCA pumped using a tunable QD LD with optical pump spectrum shown in (b). Summary - QD-based THz systems have been demonstrated as a feasible and highly versatile solution. The implementation of QD LDs as pump sources could be a major step towards ultra-compact, electrically controllable transceiver system that would increase the scope of data analysis due to the high pulse repetition rates of such LDs [3], allowing real-time THz TDS and data acquisition. Future steps in development of such systems now lie in the further investigation of QD-based THz PCA structures and devices, particularly with regards to their compatibilitywith QD LDs as pump sources. [1]E. U. Rafailov et al., “Fast quantum-dot saturable absorber for passive mode-locking of solid-State lasers,”Photon.Tech.Lett., IEEE, vol. 16 pp. 2439-2441(2004) [2]E. Estacio, “Strong enhancement of terahertz emission from GaAs in InAs/GaAs quantum dot structures. Appl.Phys.Lett., vol. 94 pp. 232104 (2009) [3]C. Kadow et al., “Self-assembled ErAs islands in GaAs: Growth and subpicosecond carrier dynamics,” Appl. Phys. Lett., vol. 75 pp. 3548-3550 (1999) [4]T. Kruczek, R. Leyman, D. Carnegie, N. Bazieva, G. Erbert, S. Schulz, C. Reardon, and E. U. Rafailov, “Continuous wave terahertz radiation from an InAs/GaAs quantum-dot photomixer device,” Appl. Phys. Lett., vol. 101(2012) [5]R. Leyman, D. I. Nikitichev, N. Bazieva, and E. U. Rafailov, “Multimodal spectral control of a quantum-dot diode laser for THz difference frequency generation,” Appl. Phys. Lett., vol. 99 (2011) [6]K.G. Wilcox, M. Butkus, I. Farrer, D.A. Ritchie, A. Tropper, E.U. Rafailov, “Subpicosecond quantum dot saturable absorber mode-locked semiconductor disk laser, ” Appl. Phys. Lett. Vol 94, 2511 © 2014 IEEE.

Polarization dynamics of bound state solitons in a carbon nanotubes mode locked erbium doped fiber laser

Optical solitons are important in the modern photonics. Passively mode locked erbium doped fiber lasers provide a neat platform to study soliton dynamics. Soliton interaction dynamics is important for various applications and has quite different manifestations, including e.g. such as bound state solitons [1], soliton rains [2]. Soliton interactions have been observed with different mode locking approaches such as figure-of-eight [3] and nonlinear polarization rotation [4]. Carbon nanotubes (CNT) have recently been widely applied as an efficient saturable absorber for passively mode locked fiber lasers. We have recently studied the polarization dynamics in a CNT mode locked vector soliton erbium doped fiber laser [5]. So far, the polarization dynamics of bound state solitons have yet to be investigated. In this report, we present a wide range of polarization dynamics of bound state solitons generated in a CNT mode locked erbium doped fiber laser. The fiber laser consists of ∼ 2 m highly doped erbium fiber (Liekki Er80-8/125) as the gain medium, an optical isolator to ensure unidirectional oscillation anda 980 nm laser diode is used to pump the gain through the 1550/980 nm wavelength division multiplexer. A fused 10:90 coupler is used to couple 10 % of the light out of the laser cavity and two in-line polarization controllers (NewPort) are used to control the birefringence of the cavity and polarization of the pump light respectively. The total cavity length is ∼ 7.8 m indicating a 25.7 MHz fundamental repetition rate. © 2013 IEEE.

Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1

2000 Mathematics Subject Classification: 35Q02, 35Q05, 35Q10, 35B40.

Efficient computation of decoherent quantum walks through eigenvalue perturbation

A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly,it has been shown that algorithmic properties of quantum walks with decoherence such as the spreading rate are sometimes better than their purely quantum counterparts. Not only quantum walks with decoherence provide a generalization of quantum walks that naturally encompasses both the quantum and classical case, but they also give rise to new and different probability distribution. The application of quantum walks with decoherence to large graphs is limited by the necessity of evolving state vector whose sizes quadratic in the number of nodes of the graph, as opposed to the linear state vector of the purely quantum (or classical) case. In this technical report,we show how to use perturbation theory to reduce the computational complexity of evolving a continuous-time quantum walk subject to decoherence. More specifically, given a graph over n nodes, we show how to approximate the eigendecomposition of the n2×n2 Lindblad super-operator from the eigendecomposition of the n×n graph Hamiltonian.

Quantum dot materials for terahertz generation applications

Compact and tunable semiconductor terahertz sources providing direct electrical control, efficient operation at room temperatures and device integration opportunities are of great interest at the present time. One of the most well-established techniques for terahertz generation utilises photoconductive antennas driven by ultrafast pulsed or dual wavelength continuous wave laser systems, though some limitations, such as confined optical wavelength pumping range and thermal breakdown, still exist. The use of quantum dot-based semiconductor materials, having unique carrier dynamics and material properties, can help to overcome limitations and enable efficient optical-to-terahertz signal conversion at room temperatures. Here we discuss the construction of novel and versatile terahertz transceiver systems based on quantum dot semiconductor devices. Configurable, energy-dependent optical and electronic characteristics of quantum-dot-based semiconductors are described, and the resonant response to optical pump wavelength is revealed. Terahertz signal generation and detection at energies that resonantly excite only the implanted quantum dots opens the potential for using compact quantum dot-based semiconductor lasers as pump sources. Proof-of-concept experiments are demonstrated here that show quantum dot-based samples to have higher optical pump damage thresholds and reduced carrier lifetime with increasing pump power.

Pigment dynamics and autumn leaf senescence in a New England deciduous forest, eastern USA

The leaves of woody plants at Harvard Forest in Central Massachusetts, USA, changed color during senescence; 70% (62/89) of the woody species examined anatomically contained anthocyanins during senescence. Anthocyanins were not present in summer green leaves, and appeared primarily in the vacuoles of palisade parenchyma cells. Yellow coloration was a result of the unmasking of xanthophyll pigments in senescing chloroplasts. In nine red-senescing species, anthocyanins were not detectable in mature leaves, and were synthesized de novo in senescence, with less than 20 m g cm - 2 of chlorophyll remaining. Xanthophyll concentrations declined in relation to chlorophyll to the same extent in both yellow- and red-leaved taxa. Declines in the maximum photosystem II quantum yield of leaves collected prior to dawn were only slightly less in the red-senescing species, indicating no long-term protective activity. Red-leaved species had significantly greater mass/area and lower chlorophyll a / b ratios during senescence. Nitrogen tissue concentrations in mature and senescent leaves negatively correlated to anthocyanin concentrations in senescent leaves, weak evidence for more efficient nitrogen resorption in anthocyanic species. Shading retarded both chlorophyll loss and anthocyanin production in Cornus alternifolia , Acer rubrum , Acer saccharum , Quercus rubra and Viburnum alnifolium . It promoted chlorophyll loss in yellow-senescing Fagus grandifolia . A reduced red : far-red ratio did not affect this process. Anthocyanins did not increase leaf temperatures in Q. rubra and Vaccinium corymbosum on cold and sunny days. The timing of leaf-fall was remarkably constant from year to year, and the order of senescence of individual species was consistent.