Single Gaussian Pulse Research Articles

Physics-Informed Neural Network for Optical Fiber Parameter Estimation From the Nonlinear Schrödinger Equation

For any system that follows rigorous mathematical and physical theories like fiber-optic system, system parameter estimation is crucial for system detection and monitoring. In this paper, a physics-informed neural network (PINN)-based method is proposed for optical fiber parameter estimation by solving the inverse problem of the nonlinear Schrödinger equation (NLSE), i.e., inferring the unknown parameters of NLSE. The proposed method considers both the prior knowledge of physical law and the characteristics of observation data from only the transmitted and received waveforms. In PINN, the NLSE and observation data are set as the loss function, and the typical fiber parameters (attenuation, dispersion, and nonlinear coefficient) are optimized iteratively until they satisfy the inferred NLSE by learning the limited observation data. Three scenarios are validated, including single Gaussian pulse propagation, ultrashort pulse propagation in highly nonlinear fiber, and optical signal transmission in standard single-mode fiber. The launch power of the signal is embedded in PINN as a parametric feature, which makes PINN learn the signal transmissions under different powers simultaneously. The weights of mean square error terms for NLSE and observation data in the loss function are properly adjusted to balance learning difficulties. Moreover, the statistical results of 128 different signals and model performance under different signal-to-noise ratios are analyzed. As an extension, fiber length estimation is also studied, and the error is 0.375% when the launch power is 0 dBm. Our work verifiably shows that the proposed approach performs well and can be further extended to multiple applications in fiber optics.

Probing nonadiabatic dynamics with attosecond pulse trains and soft x-ray Raman spectroscopy.

Linear off-resonant x-ray Raman techniques are capable of detecting the ultrafast electronic coherences generated when a photoexcited wave packet passes through a conical intersection. A hybrid femtosecond or attosecond probe pulse is employed to excite the system and stimulate the emission of the signal photon, where both fields are components of a hybrid pulse scheme. In this paper, we investigate how attosecond pulse trains, as provided by high-harmonic generation processes, perform as probe pulses in the framework of this spectroscopic technique, instead of single Gaussian pulses. We explore different combination schemes for the probe pulse as well as the impact of parameters of the pulse trains on the signals. Furthermore, we show how Raman selection rules and symmetry consideration affect the spectroscopic signal, and we discuss the importance of vibrational contributions to the overall signal. We use two different model systems, representing molecules of different symmetries, and quantum dynamics simulations to study the difference in the spectra. The results suggest that such pulse trains are well suited to capture the key features associated with the electronic coherence.

Influence of the light excitation on energy transfer in a multi-pigments light-harvesting model of photosynthesis

Most studies on quantum effects in the process of excitation energy transfer in photosynthesis system are based on the single-excitation initial state hypothesis, which can well describe the initial state of some photosynthesis systems that people are concerned about. But for natural and artificial photosynthesis systems that do not meet the above hypothesis, the excitation process has a non-negligible impact on the system dynamics. Based on a multi-pigments model excited by Gaussian pulse, the effects of the excitation pulse width and the excitation interval on system dynamics and excitation energy transfer efficiency are studied. First, the kinetic equations for the overall evolution of the donor system and the acceptor system that can theoretically contain any number of pigments are derived. Afterwards, the relationship between the excitation energy transfer efficiency and the related parameters of the system, as well as the optimal range of the corresponding parameters are demonstrated by numerical simulation. It is found that under the condition of donor pigments being excited by a single Gaussian pulse, there exists optimal pulse width, and the optimal range of the pigment molecule numbers, the coupling strength as well as the dephasing rate can be modulated by the pulse width. The mechanism of the above modulation is also analyzed and presented. Under the condition of donor pigments being excited by two Gaussian pulses sequentially, there exists an optimal combination of pulse width and pulse interval. The kinetic equations obtained in this paper can be extended to other forms of excitation pulses. The numerical results and the related optimal design principles obtained have reference significance for the optimal design of artificial photosynthesis systems under different light conditions.

The gravitational perturbation of a Morris–Thorne wormhole and the Newman–Penrose formalism

The gravitational perturbation of the Morris–Thorne wormhole has been derived by using the Newman–Penrose formalism. We apply the Teukolsky equation to the wormhole spacetime, compute the perturbed Weyl scalars, and obtain its master equation, decomposed in spin weighted spherical harmonics with spin weight −2. For simplicity, we consider the perturbation provoked by a single Gaussian pulse of pressureless dust matter.

Numerical modeling of ship wave generation using Green’s functions based on linear dispersive wave theory

ABSTRACT In this study, an efficient numerical model for predicting ship waves was developed using Green’s functions. Avoiding detailed description of the complex boundary conditions around a ship, this model simply used an inversion technique for estimating the wave source induced by a ship as a function of the navigation route and adjacent measured water level fluctuations. The Green’s functions were determined as linear summations of the water level fluctuations generated from discrete points along the navigation route. At each point, a time-varying wave source was determined as a linear summation of Gaussian pulses introduced at segments along the longitudinal direction of the ship. The linear inversion was then applied for estimating the optimum combinations of the magnitudes of these Gaussian pulses. Linear dispersive wave theory was applied to compute the water level fluctuations generated by a single Gaussian pulse so that the model can reproduce the dispersive characteristics of ship waves. The developed model was tested against experimental data and showed satisfactorily predictive skills of water level fluctuations for cases not used in the inversion. The present model was also found to be robust in that the estimated best-fitted wave source was not sensitive to changes in the conditions of the measured data used for the inversion.

Splitting and Motions of Dissipative Soliton Resonance Pulses in Mode-Locked Fiber Lasers

We numerically investigated the splitting and motions of dissipative soliton resonance (DSR) pulses in an all-normal-dispersion Yb-doped fiber laser mode-locked by a nonlinear optical loop mirror. At certain values of the system parameters, the initial single Gaussian pulse can evolve into an unstable DSR pulse with several dark solitons inside. After collisions of dark solitons, a big intensity dip occurs at the center of the DSR pulse, leading to the splitting of the DSR pulse. After splitting, the peak-to-peak separation between two DSR pulses increases at first and finally reaches a fixed value of 193 ps, indicating a steady-state multipulse operation. The relative motions of separated DSR pulse originate from the phase shift.

Structure of Electromagnetic Fields in Crossed Gaussian Beams

Expressions for the fields of crossed Gaussian beams with foci shifted relative to the point of intersection of their axes are derived. It is shown that the linear corrections in parameter e=1/kρ0 must be taken into account in the crossed-beam intensity distribution (in contrast to the case of a single beam). The interference of crossed Gaussian beams has been investigated based on the intensity calculations taking into account linear corrections to the Poynting vector. The residual electron energy in crossed pulses is multiply increased in comparison with the case of acceleration in a single Gaussian pulse.

Stable radiation pressure acceleration of ions by suppressing transverse Rayleigh-Taylor instability with multiple Gaussian pulses

In the case of a thin plasma slab accelerated by the radiation pressure of an ultra-intense laser pulse, the development of Rayleigh-Taylor instability (RTI) will destroy the acceleration structure and terminate the acceleration process much sooner than theoretical limit. In this paper, a new scheme using multiple Gaussian pulses for ion acceleration in a radiation pressure acceleration regime is investigated with particle-in-cell simulation. We found that with multiple Gaussian pulses, the instability could be efficiently suppressed and the divergence of the ion bunch is greatly reduced, resulting in a longer acceleration time and much more collimated ion bunch with higher energy than using a single Gaussian pulse. An analytical model is developed to describe the suppression of RTI at the laser-plasma interface. The model shows that the suppression of RTI is due to the introduction of the long wavelength mode RTI by the multiple Gaussian pulses.

Optical generation of polarized photoluminescence from GaAs(100)

Polarized photoluminescence from GaAs(100) was generated using shaped ultrashort laser pulses. A train of three pulses separated by an integer multiple of the longitudinal optical phonon period produced p-polarized continuum emission, whereas trains with half-integer multiples of the phonon period as well as single Gaussian pulses produced s-polarized emission. The p-polarized emission is attributed to recombination of carriers in the L-valley, resulting from plasma generation and coherent phonon-excitation by the pulse train, whereas the s-polarized emission is caused by reflection by the melted surface of unpolarized plasma emission.

An Engineering Approach to Time-Frequency Uncertainty Criteria

The conventional formulation of the Fourier Uncertainty Principle associated with the standard deviations methodology has several drawbacks that makes this theoretical approach often useless for practical applications. Beside of that a more practical engineering approach that discusses separately the different harmonics in any time-windows and detects signal spreading in time- and frequency domains by the relative levels, may be formulated. In contrast to the single Gaussian pulse of conventional theoretical approach, the primary model task of this engineering approach is the harmonic signal in rectangular time window. The engineering approach gives possibility to formulate the simple time-frequency uncertainty product constants, for example, 1.206709 for the 50% level detection criterion in the case of rectangular time window. Ill. 6, bibl. 15, tabl. 1 (in English; abstracts in English and Lithuanian). DOI: http://dx.doi.org/10.5755/j01.eee.117.1.1043

Spectrally Efficient OFDMA Lattice Structure via Toroidal Waveforms on the Time-Frequency Plane

We investigate the performance of frequency division multiplexed (FDM) signals, where multiple orthogonal Hermite-Gaussian carriers are used to increase the bandwidth efficiency. Multiple Hermite-Gaussian functions are modulated by a data set as a multicarrier modulation scheme in a single time-frequency region constituting toroidal waveform in a rectangular OFDMA system. The proposed work outperforms in the sense of bandwidth efficiency compared to the transmission scheme where only single Gaussian pulses are used as the transmission base. We investigate theoretical and simulation results of the proposed methods.

Reducing decoherence of the confined exciton state in a quantum dot by pulse-sequence control

We study the phonon-induced dephasing of the exciton state in a quantum dot excited by a sequence of ultrashort pulses. We show that the multiple-pulse control leads to a considerable improvement of the coherence of the optically excited state. For a fixed control time window, the optimized pulsed control often leads to a higher degree of coherence than the control by a smooth, single Gaussian pulse. The reduction of dephasing is considerable already for 2--3 pulses.

Optimization of waveform and detection threshold for range and range-rate tracking in clutter

We address an optimization problem to obtain the combined sequence of waveform parameters (pulse amplitudes and lengths, and FM sweep rates) and detection thresholds for optimal range and range-rate tracking in clutter. The optimal combined sequence minimizes a tracking performance index under a set of parameter constraints. The performance index includes the probability of track loss and a function of estimation error covariances. The track loss probability and the error covariances are predicted using a hybrid conditional average algorithm. The effect of the false alarms and clutter interference is taken into account in the prediction. A measurement model in explicit form is also presented which is developed based on the resolution cell in the delay-Doppler plane for a single Gaussian pulse. Numerical experiments were performed to solve the optimization problem for several examples.

Survival of Molecular Reaction Control in a Bistable System in Condensed Phase

In this paper we are concerned with the efficiency and robustness of different optimal pulses that drive the isomerization reaction in a bistable potential. The perturbation is treated as a random-phase strong oscillation that shifts the energy barrier. We show how the reaction can be controlled by means of very intense single Gaussian pulses or linear combinations of these pulses and how the control can survive after the perturbing action. The actual resistance to the bath effects changes with the scheme used, and we concentrate on the different behaviors for different bath frequencies. In particular pump−probe schemes offer stabilizing properties at some frequency windows of the bath spectral range. We also address the problem of phase sensitivity and we find the presence of phase nodes, which are particular values of the bath frequency where the reaction dynamics is almost insensitive to the actual phase of the bath oscillations.

Gaussian pulse decomposition: an intuitive model of electrocardiogram waveforms.

This study presents a novel approach to modeling the electrocardiogram (ECG): the Gaussian pulse decomposition. Constituent waves of the ECG are decomposed into and represented by Gaussian pulses using an iterative algorithm: the chip away decomposition (ChAD) algorithm. At each iteration, a nonlinear minimization method is used to fit a portion of the ECG waveform with a single Gaussian pulse, which is then subtracted from the ECG waveform. The process iterates on the resulting residual waveform until the normalized mean square error is below an acceptable level. Three different minimization methods were compared for their applicability to the ChAD algorithm; the Nelder-Mead simplex method was found to be more noise-tolerant than the Newton-Raphson method or the steepest descent method. Using morphologically different ECG waveforms from the MIT-BIH arrhythmia database, it was demonstrated that the ChAD algorithm is capable of modeling not only normal beats, but also abnormal beats, including those exhibiting a depressed ST segment, bundle branch block, and premature ventricular contraction. An analytical expression for the spectral contributions of the constituent waves was also derived to characterize the ECG waveform in the frequency domain. The Gaussian pulse model, providing an intuitive representation of the ECG constituent waves by use of a small set of meaningful parameters, should be useful for various purposes of ECG signal processing, including signal representation and pattern recognition.

The propagation of a Gaussian pulse in sea water and its applicaiton to remote sensing

The propagation of a single Gaussian pulse in sea water and of a Gaussian pulse as an envelope for a low-frequency burst are analyzed and their anomalous behavior determined. The use of such a pulse to locate a metal cylinder submerged in the sea is studied quantitatively for two pulse widths. It is concluded that detection of the cylinder by means of its backscattered field should be possible.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>