Adaptive split-step Fourier method for simulating ultrashort laser pulse propagation in photonic crystal fibres

In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre （PCF） parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.

Pulse Propagation with Self-Phase Modulation in Nonlinear Chiral Fiber and Its Applications

From Maxwell＇s equations and Post＇s formalism, a generalized chiral nonlinear Schr6dinger equation （CNLSE） is obtained for the nonlinear chiral fiber. This equation governs light transmission through a dispersive nonlinear chiral fiber with joint action of chirality in linear and nonlinear ways. The generalized CNLSE shows a modu- lation of chirality to the effect of attenuation and nonlinearity compared with the case for a conventional fiber. Simulations based on the split-step beam propagation method reveal the role of nonlinearity with cooperation to chirality playing in the pulse evolution. By adjusting its strength the role of chirality in forming solitons is demonstrated for a given circularly polarized component. The application of nonlinear optical rotation is also discussed in an all-optical switch.

Simulation of Chirped Pulse Propagation in Silicon Nanowires: Shape and Spectrum Analysis

In this paper, we simulate the propagation of chirped pulses in silicon nanowires by solving the nonlinear Schrodinger equation (NLSE) using the split-step Fourier (SSF) method. The simulations are performed both for the pulse shape (time domain) and for the pulse spectrum (frequency domain), and various linear and nonlinear effects changing the shape and the spectrum of the pulse are analyzed. Owing to the high nonlinear coefficient and a very small effective-mode area, the required length for observing nonlinear effects in nanowires is much shorter than that of conventional optical fibers. The impacts of loss, nonlinear effects, second- and third-order dispersion coefficients and the chirp parameter on pulse propagation along the nanowire are investigated. The results show that the sign and the value of the chirp parameter have important role in pulse propagation so that in the anomalous dispersion regime, the compression occurs for the up- chirped pulses, whereas the broadening takes place for the down-chirped pulses. The opposite situation happens for up- and down-chirped pulses propagating in the normal dispersion regime.

Short pulse propagation in dense dispersion compensated systems

The short Hermite-Gaussian optical pulse transmission over 1440 km in a dense dispersion compensated system is investigated based on numerical simulation. In the simulation, compensation is made not only for the group-velocity dispersion but also for the third order dispersion. It is demonstrated that the pulse with reasonably lower power can propagate steadily in net zero, positive and negative dispersion system.

Analytical Characterization on Pulse Propagation in a Semiconductor Optical Amplifier Based on Homotopy Analysis Method

Starting from the basic equations describing the evolution of the carriers and photons inside a semiconductor optical amplifier （SOA）, the equation governing pulse propagation in the SOA is derived. By employing homotopy analysis method （HAM）, a series solution for the output pulse by the SOA is obtained, which can effectively characterize the temporal features of the nonlinear process during the pulse propagation inside the SOA. Moreover, the analytical solution is compared with numerical simulations with a good agreement. The theoretical results will benefit the future analysis of other problems related to the pulse propagation in the SOA.

On the Hybrid Model of Nerve Pulse: Mathematical Analysis and Numerical Results

Amongst the important phenomena in neurophysiology, nerve pulse generation and propagation is fundamental. Scientists have studied this phenomena using mathematical models based on experimental observations on the physiological processes in the nerve cell. Widely used models include: the Hodgkin-Huxley (H-H) model, which is based entirely on the electrical activity of the nerve cell;and the Heimburg and Jackson (H-J), model based on the thermodynamic activity of the nerve cell. These classes of models do not, individually, give a complete picture of the processes that lead to nerve pulse generation and propagation. Recently, a hybrid model proposed by Mengnjo, Dikandé and Ngwa (M-D-N), takes into consideration both the electrical and thermodynamic activities of the nerve cell. In their work, the first three bound states of the model are analytically computed and they showed great resemblance to some of the experimentally observed pulse profiles. With these bound states, the M-D-N model reduces to an initial value problem of a linear parabolic partial differential equation with variable coefficients. In this work we consider the resulting initial value problem and, using the theory of function spaces, propose and prove conditions under which such equations will admit unique solutions. We then verify that the resulting initial value problem from the M-D-N model satisfies these conditions and so has a unique solution. Given that the derived initial value problem is complex and there are no known analytic techniques that can be deployed to obtain its solution, we designed a numerical experiment to estimate the solutions. The simulations revealed that the unique solution is a stable pulse that propagates in the x-t plane with constant velocity and maintains the shape of the initial profile.

Experimental Observation of the Pulsed High Pressure Gas Puffing on HL-2A Tokamak

The pulse propagations of both the electron temperature and the electron density have been observed during pulse-modulated molecular beam injection experiments on HL-2A. The propagation depth of the cold pulse in the low field side is much longer than that in the high field side. The cold pulses cannot propagate to the plasma center from either the low field side or the high field side. The electron temperature in the plasma center does not change during MBI, but the electron density pulse perturbations can be observed in the plasma center.

Quantitative relationship between the maximum streamer length and discharge voltage of a pulsed positive streamer discharge in water

A linear relationship has been realized between the maximum streamer length and discharge voltage of a pulsed positive streamer discharge by measuring the streamer length in water with conductivity of 100 μS cm-1using high-speed photography. Based on Ohm＇s law, a quantitative equation has been derived for the dependence of the maximum streamer length on the discharge voltage of a pulsed positive streamer discharge in water. According to the equation, our results suggest that the streamers spontaneously stop propagating through water due to the voltage at the streamer head dropping below the ignition voltage of a pulsed positive streamer discharge.

Propagation of Solitary Pulses in Optical Fibers with Both Self-Steepening and Quintic Nonlinear Effects

Pulse dynamics and stability in optical fibers in the presence of both self-steepening and quintic nonlinear effects are analyzed. Propagating profiles of the quintic derivative nonlinear Schr¨odinger model are isolated via two invariants of motion. The resulting canonical equation admits exact periodic propagating patterns in terms of the Jacobi elliptic functions, and solitary pulses are recovered in the long wave limit, i.e. degenerate cases of periodic profiles where each pulse is widely separated from the adjacent ones. Two families of such exact wave profiles are identified. The first one has a precise constraint concerning the magnitude of self-steepening and quintic nonlinear effects, while the second one permits more freedom. The reduction to the well established temporal soliton in an optical fiber waveguide in the absence of self-steepening and quintic nonlinearity is demonstrated explicitly. Numerical simulations are performed to identify regimes of parameter values where robust propagation patterns exist.

Spatiotemporal evolution of continuous-wave field and dark soliton formation in a microcavity with normal dispersion

Stable dark soliton and dark pulse formation in normally dispersive and red-detuned microcavities are investigated by numerically solving the normalized Lugiato-Lefever equation. The soliton essence is proved by fitting the calculated field intensity profile with the analytical formula of a dark soliton. Meanwhile, we find that a dark soliton can be generated either from the nonlinear evolution of an optical shock wave or narrowing of a locally broad dark pulse with smoother fronts. Explicit analytical expression is obtained to describe the oscillatory fronts of the optical shock wave. Furthermore,from the calculation results, we show that for smaller frequency detunings, e.g., α 3, in addition to the dark soliton formation, a single dark pulse with an oscillatory dip can also arise and propagate stably in the microcavity under proper pump detuning and pump strength combination. The existence region together with various field intensity profiles and the corresponding spectra of single dark pulse are demonstrated.

Preliminary Results of Sawtooth Behaviour and Electron Heat Transport During ECRH Experiment on HL-2A

An electron cyclotron resonance heating （ECRH） system with a maximum output power of 1 MW, a frequency of 68 GHz and a duration of ls was operated on HL-2A tokamak. The temperature profile control and the sawtooth behaviour during ECRH experiments are investigated. ‘Density pumpout＇ during on-axis ECRH is analysed. Features of confinement and electron heat transport during ECRH are studied.

Behaviors of Electron Heat Transportation in HT-7 Sawtoothing Plasma

It is found that in HT-7 ohmic plasma, main energy loss comes from electron heat conduction, hence quantitative data of electron heat diffusivity is a very important issue for investigation of electron heat transportation behavior in different target plasmas so as to get high performance plasma. A time-to-peak method of the heat pulse propagation originating from the sawtooth activity on the soft x-ray intensity signal has been adopted to experimentally determine electron heat diffusivity XeHP on the HT-7 tokamak. Aiming to improve the signal-to-noise (S/N) ratio of the original signal to get a stable and reasonable electron heat diffusivity XeHD value, some data processing methods, including average of tens of sawteeth, is discussed. The electron heat diffusivity XeHP is larger than XePB which is determined from the balance of background plasma power. Based on variation of the measured electron heat diffusivity XeHP, performances of different high confinement plasmas are analyzed.

The Effect of the Width of the Incident Pulse to the Dielectric Transition Layer in the Scattering of an Electromagnetic Pulse–a Qubit Lattice Algorithm Simulation

The effect of the thickness of the dielectric boundary layer that connects amaterial of refractive index n1 to another of index n2 is considered for the propagation of an electromagnetic pulse.A qubit lattice algorithm(QLA),which consists of a specially chosen non-commuting sequence of collision and streaming operators acting on a basis set of qubits,is theoretically determined that recovers theMaxwell equations to second-order in a small parameterǫ.For very thin but continuous boundary layer the scattering properties of the pulse mimics that found from the Fresnel discontinuous jump conditions for a plane wave-except that the transmission to incident amplitudes are augmented by a factor of√n2/n1.As the boundary layer becomes thicker one finds deviations away from the discontinuous Fresnel conditions and eventually one approaches the expectedWKB limit.However there is found a small but unusual dip in part of the transmitted pulse that persists in time.Computationally,the QLA simulations still recover the solutions to Maxwell equations even when this parameterǫ→1.On examining the pulse propagation in medium n1,ǫcorresponds to the dimensionless speed of the pulse(in lattice units).

Primary Results of ECRH Experiment and Electron Heat Transport on the HL-2A Tokamak

As an ordinary mainly auxiliary heating on tokamak plasma, electron cyclotron resonance heating （ ECRH ） is an useful method to the study of electron heat transport and confinement performance. In this work, primary results of ECRH experiments on the HL-2A tokamak are presented. The features of confinement and electron heat transport during ECRH are analyzed.

NONLINEAR MOTION MECHANICS MODEL OF CURVED BLOOD VESSEL

A geometric model of curved blood vessels is established based on some reasonable hypotheses; the nonlinear motion mechanics model of the curved blood vessel is established according to basic mechanics laws. This model includes much more physiological factors. It couples the interaction of blood flow with mechanical factors such as the displacement, deformation, strain and stress etc. of the curved blood vessel. It is of great importance for investigating the circulation rules of the cardiovascular system and the nonlinear pulse wave propagation in curved blood vessels.

Propagation of quasi-periodic random sound pulse sequence signals in shallow-water waveguides

It is an efficient method to model ship radiated noise as quasi-periodic random sound pulse sequences. Based on the model, this paper discusses the characteristics change of ship noise after through shallow-water waveguides. Theoretical analysis and numerical simulation show that random waveguides and multi-path effects can bring much additional transmission loss for the noise line spectra, demonstrating the instability of ship radiated noise line spectra to a certain extent, and providing some theoretical support for advanced studies of ship radiated noise.

What causes the superluminal propagation of light pulses

In this paper, we discuss what causes the superluminal propagation of a pulse through dispersion by solving Maxwell's equations without any approximation. The coherence of the pulse plays an important role for superluminal propagation. When the pulse becomes partially coherent, the propagation changes from superluminal to sublumiiial. The energy velocity is always less than the vacuum velocity. The shape of the pulse is changed during the propagation.

The WKBZ mode approach to pulsed propagation in ocean channels

In the paper, the WKBZ normal mode approach has been applied to the propagation of the pulsed energy and waveform in ocean channels. The numerical results in two different channels are given. Comparison between the WKBZ and conventional normal mode codes shows that the WKBZ mode approach is a fast and accurate method and the running time by the WKBZ approach is reduced by about two orders of magnitude.

Stability and a fast calculation method of travel speed of pulse peak in convergence zone

A long-range sound propagation experiment was conducted in the West Pacific Ocean in summer 2013.The signals received by a towed array indicate that the travel speed of pulse peak(TSPP)in the convergence zones is stable.Therefore,an equivalent sound speed can be used at all ranges in the convergence zones.A fast calculation method based on the beam-displace-ment ray-mode(BDRM)theory and convergence zone theory is proposed to calculate this equivalent sound speed.The computation speed of this proposed method is over 1000 times faster than that of the conventional calculation method based on the normal mode theory,with the computation error less than 0.4%compared with the experimental result.Also,the effect of frequency and sound speed profile on the TSPP is studied with the conventional and fast calculation methods,showing that the TSPP is almost independent of the frequency and sound speed profile in the ocean surface layer.