Time delay in thin slabs with self-focusing Kerr-type nonlinearity

Time delays for an intense transverse electric (TE) wave propagating through a Kerr-type nonlinear slab are investigated. The relation between the bidirectional group delay and the dwell time is derived and it is shown that the difference between them can be separated into three terms. The first one is the familiar self interference time, due to the dispersion of the medium surrounding the slab. The other two terms are caused by the nonlinearity and oblique incidence of the TE wave. It is shown that the electric field distribution along the slab may be expressed in terms of Jacobi elliptic functions while the phase difference introduced by the slab is given in terms of incomplete elliptic integrals. The expressions for the field intensity dependent complex reflection and transmission coefficients are derived and the multivalued oscillatory behavior of the delay times for the case of a thin slab is demonstrated

Towards automated design of quantum cascade lasers

We present an advanced technique for the design and optimization of GaAs/AlGaAs quantum cascade laser structures. It is based on the implementation of the simulated annealing algorithm with the purpose of determining a set of design parameters that satisfy predefined conditions, leading to an enhancement of the device output characteristics. Two important design aspects have been addressed: improved thermal behavior, achieved by the use of higher conduction band offset materials, and a more efficient extraction mechanism, realized via a ladder of three lower laser states, with subsequent pairs separated by the optical phonon energy. A detailed analysis of performance of the obtained structures is carried out within a full self-consistent rate equations model of the carrier dynamics. The latter uses wave functions calculated by the transfer matrix method, and evaluates all relevant carrier–phonon and carrier–carrier scattering rates from each quantized state to all others within the same and neighboring periods of the cascade. These values are then used to form a set of rate equations for the carrier density in each state, enabling further calculation of the current density and gain as a function of the applied field and temperature. This paper addresses the application of the described procedure to the design of lambda~9 µm GaAs-based mid-infrared quantum cascade lasers and presents the output characteristics of some of the designed optimized structures. © 2005 American Institute of Physic

Hopping dynamics for localized Lyapunov vectors in many-hard-disk systems

The dynamics of the localized region of the Lyapunov vector for the largest Lyapunov exponent is discussed in quasi-one-dimensional hard-disk systems at low density. We introduce a hopping rate to quantitatively describe the movement of the localized region of this Lyapunov vector, and show that it is a decreasing function of hopping distance, implying spatial correlation of the localized regions. This behavior is explained quantitatively by a brick accumulation model derived from hard-disk dynamics in the low density limit, in which hopping of the localized Lyapunov vector is represented as the movement of the highest brick position. We also give an analytical expression for the hopping rate, which is obtained us a sum of probability distributions for brick height configurations between two separated highest brick sites. The results of these simple models are in good agreement with the simulation results for hard-disk systems.Comment: 28 pages, 13 figure

Time-dependent mode structure for Lyapunov vectors as a collective movement in quasi-one-dimensional systems

Time dependent mode structure for the Lyapunov vectors associated with the stepwise structure of the Lyapunov spectra and its relation to the momentum auto-correlation function are discussed in quasi-one-dimensional many-hard-disk systems. We demonstrate mode structures (Lyapunov modes) for all components of the Lyapunov vectors, which include the longitudinal and transverse components of their spatial and momentum parts, and their phase relations are specified. These mode structures are suggested from the form of the Lyapunov vectors corresponding to the zero-Lyapunov exponents. Spatial node structures of these modes are explained by the reflection properties of the hard-walls used in the models. Our main interest is the time-oscillating behavior of Lyapunov modes. It is shown that the largest time-oscillating period of the Lyapunov modes is twice as long as the time-oscillating period of the longitudinal momentum auto-correlation function. This relation is satisfied irrespective of the particle number and boundary conditions. A simple explanation for this relation is given based on the form of the Lyapunov vector.Comment: 39 pages, 21 figures, Manuscript including the figures of better quality is available from http://www.phys.unsw.edu.au/~gary/Research.htm

Boundary effects in the stepwise structure of the Lyapunov spectra for quasi-one-dimensional systems

Boundary effects in the stepwise structure of the Lyapunov spectra and the corresponding wavelike structure of the Lyapunov vectors are discussed numerically in quasi-one-dimensional systems consisting of many hard-disks. Four kinds of boundary conditions constructed by combinations of periodic boundary conditions and hard-wall boundary conditions are considered, and lead to different stepwise structures of the Lyapunov spectra in each case. We show that a spatial wavelike structure with a time-oscillation appears in the spatial part of the Lyapunov vectors divided by momenta in some steps of the Lyapunov spectra, while a rather stationary wavelike structure appears in the purely spatial part of the Lyapunov vectors corresponding to the other steps. Using these two kinds of wavelike structure we categorize the sequence and the kinds of steps of the Lyapunov spectra in the four different boundary condition cases.Comment: 33 pages, 25 figures including 10 color figures. Manuscript including the figures of better quality is available from http://newt.phys.unsw.edu.au/~gary/step.pd

Procena ekološkog rizika u funkciji zaštite životne sredine

This paper proposes an appropriate methodology for ecological risk assessment. The methodology has been applied in the region of Boka Kotorska Bay (Bay), Montenegro. The emphasis of the research is on the analysis of the impact of various stressors on the ecological components of Bay. The consequences of that impact can be seen in an increased level of eutrophication of water environment, mostly through the influence of nitrogen and its compounds. The actual research at/about the region of Boka Kotorska Bay was performed in the period of 2008. The study emphasized the importance of the acquisition, processing and analysis of various ecologically related data for more efficient monitoring and management of the environment. The suggested methodology of the ecological risk assessment is, therefore, a remarkable scientific and expert contribution in the area of environmental protection in our country and in general.U radu je predstavljena primena metodologije procene ekološkog rizika. Metodologija je primenjena na primeru Bokokotorskog zaliva (Zaliv). Istraživanjem je razmatrana procena uticaja većeg broja stresora na ekološke komponente Zaliva. Posledice ovih uticaja ispoljene su kroz povećan stepen eutrofikacije vodene sredine i dovode se u vezu sa koncentracijom azotnih jedinjenja (nitrata i nitrita) Konkretna merenja vršena su u 2008. godini. Istraživanjem je posebno ukazano na značaj razvoja sistema prikupljanja i obrade ekoloških i drugih informacija radi efikasnijeg upravljanja životnom sredinom datog prostora. Primenjena metodologija procene ekološkog rizika trebalo bi da u naučnom i stručnom pogledu predstavlja doprinos u oblasti zaštite životne sredine,kako kod nas, tako i u svetu

Magnetotunnelling in resonant tunnelling structures with spin-orbit interaction

Magnetotunnelling spectroscopy of resonant tunnelling structures provides information on the nature of the two-dimensional electron gas in the well. We describe a model based on nonequilibrium Green's functions that allows for a comprehensive study of the density of states, tunnelling currents and current spin polarization. The investigated effects include the electron-phonon interaction, interface roughness scattering, Zeeman effect and the Rashba spin-orbit interaction. A qualitative agreement with experimental data is found regarding the satellite peaks. The spin polarization is predicted to be larger than ten percent for magnetic fields above 2 Tesla and having a structure even at the satellite peaks. The Rashba effect is confirmed to be observable as a beating pattern in the density of states but found to be too small to affect the tunnelling current.Comment: 31 pages, 11 figure

A new method for assessing squash tactics using 15 court areas for ball locations

Tactics in squash have typically been assessed using the frequency of different shot types played at different locations on the court either without reference to other relevant information or on the basis of the preceding shot. This paper presents a new squash specific method for categorising court locations in which the ball was played, a novel techniques for assessing the reliability of this method and presents typical shots responses in these new areas controlled for preceding shot as well as the time between shots and the handedness of the players. Twelve games were viewed using the SAGIT/Squash software and 2907 shots viewed a second time from a video image taken from behind the court with an overall agreement of 88.90% for the court location data and 99.52% for shot type. 3,192 shots from 9 matches from the 2003 World Team Championships were analysed in SAGIT/Squash. In the court areas analysed between 2 and 7 shot responses were predominant suggesting tactical patterns were evident. This was supported by differences evident between shot responses played from the two back corners where the backhand side was characterised by a predominance of straight drives whereas straight and crosscourt drives were played on the forehand side. These results tended to confirm that tactics i.e. consistent shot types, are played although these are only apparent when factors that determine shot selection are accounted for. This paper has controlled for some of these factors but others need to be considered e.g. if individual player profiles are to be ascertaine

Position-dependent mass models and their nonlinear characterization

We consider the specific models of Zhu-Kroemer and BenDaniel-Duke in a sech$^{2}$-mass background and point out interesting correspondences with the stationary 1-soliton and 2-soliton solutions of the KdV equation in a supersymmetric framework.Comment: 8 Pages, Latex version, Two new references are added, To appear in J.Phys.A (Fast Track Communication

Nonparabolicity effects and the spin-split electron dwell time in symmetric III-V double-barrier structures

We start from the fourth order nonparabolic and anisotropic conduction band bulk dispersion relation to obtain an one-band effective Hamiltonian which we apply to an AlGaSb symmetric double-barrier structure with resonant energies significantly (more than 200meV) above the well bottom. The spin-splitting is described by the k3 Dresselhaus spin-orbit coupling term modifying only the effective mass of the spin eigenstates in the investigated structure. Apart from the bulk-like resonant energy shift due to the band nonparabolicity, we obtain a substantial shift depending on the choice of boundary conditions for the envelope functions at interfaces between different materials. The shift of resonant energy levels leads to the change of spin-splitting and the magnitude of the dwell times. We attempt to explain the influence of both the nonparabolicity and boundary conditions choice by introducing various effective masses