Initial Pulse Amplitude Research Articles

Management of the discrete eigenvalues of the nonlinear Schrödinger equation using periodic dispersion perturbation

The effect of the periodic oscillation of the coefficient at the second-order derivative of the nonlinear Schrödinger equation on the soliton content of propagating pulses is studied numerically. Resonant fission of multisoliton pulses and soliton fusion are described in terms of eigenvalues of the Zakharov–Shabat spectral problem. Resonant conditions are connected with internal periodicity of solitons and breathers. The resonance can be changed by variation of initial pulse parameters. When the propagation distance does not exceeds a few oscillation periods of the coefficient, a wide resonances can be obtained. With a large number of the oscillation periods, the output pulse shapes and corresponding set of the complex eigenvalues of the Zakharov–Shabat spectral problem become extremely sensitive to the initial pulse parameters. The change in the pulse propagation process is described as a bifurcation. Two types of bifurcations were are found. The first bifurcation type is connected with the join of two imaginary eigenvalues in the single point and then the split of these eigenvalues in real parts symmetrically, so their imaginary part becomes the same. The second one is described by the joining of two eigenvalues with symmetrical real parts in the single complex point and their subsequent splitting. After splitting, the eigenvalues have zero real parts and different imaginary parts. I have found that transformations of the initial pulses are described by pairwise interaction of the eigenvalues. The eigenvalue bifurcations under effect of the change of the initial pulse amplitude and separation between pulses are studied. A periodically modulated media can be used both to control soliton pulse shapes and eigenvalues of the Zakharov–Shabat spectral problem.

Propagation of instability fronts in modulationally unstable systems

We study the evolution of pulses propagating through focusing nonlinear media. A small disturbance of a smooth initial non-uniform pulse amplitude leads to formation of a region of strong nonlinear oscillations. We develop here an asymptotic method for finding the law of motion of the front of this region. The method is based on the conjecture that instability fronts propagate with the minimal group velocity of linear waves. To support this conjecture, at first we review several physical situations where this statement was obtained as a result of direct calculations. Then we generalize it to situations with a non-uniform flow and apply it to the focusing nonlinear Schrödinger equation for the particular cases of Talanov and Akhmanov-Sukhorukov-Khokhlov initial distributions. The approximate analytical results agree very well with the exact numerical solutions for these two problems.

Neuromorphic Applications of a Multivalued [SnI4{(C6H5)2SO}2] Memristor Incorporated in the Echo State Machine

The operation of an FTO/[SnI4{(C6H5)2SO}2]/Cu memristor is based on the Schottky barrier modulation due to electron trapping/detrapping at the interface states. The presented memristive bipolar device has an asymmetric current–voltage characteristic and multiple resistance states, which can be achieved by the application of impulses with different amplitudes and durations. STDP measurement performed with symmetric sawtooth voltage pulses results in the asymmetric Hebbian-like learning pattern. The incorporation of the device in a particular type of the reservoir system—a single node echo state machine—allowed observation of signal processing in a feedback-loop equipped system: classification according to the initial pulse amplitude and generation of pulse sequences of a random length.

Extremely Short Optical Pulses and Ads/CFT Compliance

Dynamics of few cycle optical pulses in non-Fermi liquid was considered. Energy spectrum of non-Fermi liquid was taken from the AdS/CFT compliance. Conditions of quasiparticle excitation existence were defined. Non-Fermi liquid parameters impact on the shape of few cycle pulses were estimated. It was shown that extremely short optical pulse propagation in the non-Fermi liquid is a stable pattern. The value of chemical potential has a significant impact on extremely short pulse shape. An increase in initial pulse amplitude does not result in pulse-shape distortions under its propagation in considered medium that is why the non-Fermi liquid can be used in applications inherent in extremely short pulse processing.

Study of femtosecond soliton dynamics in photonic crystal fiber using the moment method

We investigate the dynamics of femtosecond solitons in photonic crystal fibers (PCFs) by including high-order dispersion terms until to sixth-order in the generalized nonlinear Schrödinger equation, in addition to the nonlinear effects of the self phase modulation, self steepening and Raman scattering. We calculate theoretically the pulse parameters using the moment method. In the case of the fundamental soliton, our computed equations are coupled and difficult to solve analytically. However, we use the finite difference method to calculate numerically pulse parameters using an initially hyperbolic secant pulse at 1550-nm with different peak powers along 10m-PCF. Our numerical results show that the nonlinear regimes allow obtaining pulse compressions and initial pulse amplitudes. Furthermore, we remark a pulse broadening, and weak shifts of the peak power positions and frequencies in the critical and dispersive regimes. The use of an initial chirp provides a better pulse compressions and especially for low input powers. Also, the initial positive chirp reduces the optimal compression position lengths, while the negative one increases them. Therefore, we conclude that our theoretical calculations and numerical simulation results show that the moment method associated with the finite differences method is effective for the study of femtosecond pulse dynamics in PCFs.

Summary and difference frequency radiation generation in the field of few-cycle laser pulse propagating in GaSe

The results of numerical study of the generation process of summary and difference frequency radiations (SFR and DFR) arising via interaction of linearly polarized a few cycle laser pulses propagating in a GaSe crystal is present. The interaction of pulse having the central wavelengths of 1.98 μm, duration of 30 fs with the electric field amplitude 100 MV/m, propagating along the optical axis is considered. The thickness of GaSe crystal in numerical simulations is 198 μm. For study the pulse dynamic spectrum evolution the smoothed pseudo Wigner distribution (SPWVD) transformation was applied. In order to increase the time and frequency resolution of the pulse dynamic spectrum the Mexican-hat wavelet based continuous wavelet transform (CWT) was applied. The dependences of SFR and DFR generation efficiency versus propagation distance inside of crystal at fixed values of initial pump pulse amplitude 10, 50 and 100 MV/m are obtained. The SFR and DFR generation efficiency dependences versus initial pump pulse amplitude are obtained. It's shown that the maximum values of SFR and DFR generation efficiencies at initial pump pulse amplitude 100 MV/m are 4.8 × 10?3% and 2.7 × 10?3% respectively.

Effect of the intrinsic nonlinearity on the propagation of ultrashort optical pulses in carbon nanotubes in dispersive nonmagnetic dielectric media

The Maxwell equations for the electromagnetic field that propagates in carbon nanotubes (CNTs) placed in dispersive nonmagnetic dielectric media are analyzed with allowance for the intrinsic nonlinearity of the medium. The dependences of the pulse on the initial pulse amplitude, dispersion constants, and nonlinearity are revealed.

Generation of Solitons and Train of Soliton Pulses in Three Level Λ-Type Cold Atom Electromagnetically Induced Transparency System

We point out that a train of optical solitons can be generated in a cold-atom system by modulational instability (MI). By numerical simulation, we not only prove that the MI analysis of equations of motion for the atomic-state amplitudes and probe field can be replaced with that of one nonlinear Schrodinger equation, but also give the similarities and differences in the generation of the soliton wave train between the original Maxwell–Schrodinger equations and the nonlinear Schrodinger equation. Through the numerical simulation of the original equation of motion, we found that the generation of a single soliton or a couple of solitons can be achieved by adjusting the initial pulse amplitude, and propose a quantitative relationship. These results are different from those in previous reports, which mainly focus on the kind of nonlinear pulse that can propagate stably in an electromagnetically induced transparency (EIT) medium. The merits and shortages of our scheme are also shown by comparing what with a fi...

Propagation of extremely short optical pulses in impurity carbon nanotubes in dispersive and nonlinear media

Maxwell equations describing an extremely short pulse propagating in impurity carbon nanotubes placed in a dispersive nonmagnetic medium are analyzed with allowance for the nonlinearity of the medium. The dependences of the magnetic field intensity on the initial pulse amplitude and the parameters of the medium are revealed.

Dynamic transition from complete population transfer to self-induced transparency

We explore the connection between adiabatic rapid passage, a technique that allows for robust complete population transfer (CPT) in a resonant absorber, and self-induced transparency solitons. We employ the auxiliary differential equation finite-difference time-domain method to fully resolve the dynamics of femtosecond light pulses propagating through an absorbing two-level medium. Using the example of linearly chirped Gaussian pulses we find that the pulses achieving robust CPT for a single two-level system are also pulses that will transform into solitary waves when incident on a resonantly absorbing medium. At the entrance into the absorber strongly chirped, adiabatic pulses completely transfer the electronic population from the ground to the upper state. As the pulses suffer absorption they undergo a dynamic transition and quickly split into an off-resonant radiation part and one or several unchirped solitary pulses that may carry away some of the initially achieved population inversion. This spectral and temporal transformation process limits the spatial depths of the region of CPT in a dense absorber regardless of the initial pulse amplitude. We also show that the frequency-domain pulse area, defined as the spectral amplitude at the resonance frequency, allows for a better distinction between the regimes of $2\ensuremath{\pi}$-pulse and $0\ensuremath{\pi}$-pulse formation than time-domain measurements.

EXTREMELY SHORT OPTICAL PULSES IN CARBON NANOTUBES IN DISPERSIVE NONMAGNETIC DIELECTRIC MEDIA

We consider Maxwell equations for an electromagnetic field propagating in carbon nanotubes (CNTs) placed on a dispersive nonmagnetic dielectric medium. We obtain the effective equation analogous to the classical sine-Gordon equation. Then it has been analyzed numerically. We have revealed the dependence of the pulse on the type of CNT and on the initial pulse amplitude, as well as on the medium dispersion constants.

Ultimately short optical pulses in carbon nanotubes in dispersive nonmagnetic dielectric media

We consider Maxwell’s equations for an electromagnetic field propagating in carbon nanotubes placed in dispersive nonmagnetic dielectric media. An effective equation having the form of an analog of the classical sine-Gordon equation was obtained and analyzed numerically. The dependence of the pulse on the type of carbon nanotubes, initial pulse amplitude, and dispersion constants of the medium was revealed.

Optimization of high-voltage devices for energy compression of nanosecond pulses

Designs of compact converters intended for compression of high-voltage pulses with durations of a few nanoseconds and operating in a traveling wave mode were examined. The energy compression unit contained two lines-high-impedance and forming-with a high -pressure gas spark discharger used as a switch. A traditional serial connection of lines was replaced by a parallel connection to increase the energy compression efficiency. The power of the initial pulse (amplitude, 145 kV; half-height duration, 4 ns; and rise time, 1.5 ns) at a load of 45 Ω was increased by a factor of 1.8, while the calculated value was 2.5. The amplitude was as great as -195 kV, and the power was 17% higher relative to the circuit with a serial connection of lines. When shaped, the pulse was compressed in time to 0.8 ns. Two modifications of devices converting the initial pulse with an amplitude of -160 kV and a rise time of 0.3 ns into pulses with amplitudes of -210 and -250 kV and durations of 0.80 and 0.45 ns, respectively, were tested. Waveguide components of the converters were developed, with which it was possible to minimize the dimensions of the device in order to avoid excitation of higher harmonics while maintaining the electric strength.

Electromagnetic pulse reflection at self-generated plasma mirrors: Laser pulse shaping and high order harmonic generation

A thin layer of overdense plasma is created when an electromagnetic pulse interacts with a rapidly ionizing thin foil. This layer will reflect the incoming pulse, forming a so-called plasma mirror. A simple realistic model based on paired kinetic and wave equations is used to analytically describe the process of mirror formation and the reflection and transmission of the incident pulse. The model incorporates the exact description of the ionization process in the foil and the polarization and conduction currents that follow. The analytical description of the reflected and transmitted pulses as well as their dependence on foil parameters, and initial pulse amplitude and form are presented. Possible application and effectiveness of this process to improve laser pulse contrast are discussed. In the case of the linearly polarized incident pulse, harmonic generation occurs, that is absent in the case of the circular polarization. The spectra of the reflected pulses for different initial forms and amplitudes are studied.

IS AQUEDUCTAL STROKE VOLUME, MEASURED WITH CINE PHASE-CONTRAST MAGNETIC RESONANCE IMAGING SCANS USEFUL IN PREDICTING OUTCOME OF SHUNT SURGERY IN SUSPECTED NORMAL PRESSURE HYDROCEPHALUS?

To evaluate clinical usefulness of cerebrospinal fluid stroke volume (SV) assessed in the cerebral aqueduct, via cine phase-contrast magnetic resonance imaging, for predicting outcome after shunt surgery in suspected normal pressure hydrocephalus. Thirty-eight patients with suspected normal pressure hydrocephalus were included. SV was assessed using cine phase-contrast magnetic resonance imaging, and the results were kept blinded until postoperative follow-up after 7 +/- 5.8 months (mean +/- standard deviation). Selection to surgery was based on a positive lumbar infusion test or cerebrospinal fluid tap test, and outcome was evaluated with objective tests. Six patients were excluded from SV measurements because of technical difficulties. Eight patients were not operated (negative lumbar infusion test and cerebrospinal fluid tap test). SV in the not operated patients (mean, 66 +/- 53 microl) did not differ from the operated patients (95 +/- 78 microl; P = 0.335). Operated patients showed statistically significant improvements in walk (P = 0.020), reaction time (P = 0.006), and memory (P = 0.001) tests. Patients were divided into three groups according to SV range: low (0-50 microl), middle (51-100 microl), and high (>100 microl). No statistically significant (P > 0.05) improvements in any of the objective tests were found in any of the SV ranges. The numbers of individually improved patients were similar in the different SV ranges: six out of seven in the low, nine out of nine in the middle, and five out of eight in the high range. Weak correlations were found between SV and the initial pulse amplitude (Rs = 0.043; P = 0.014) as well as the plateau pulse amplitude (Rs = 0.043; P = 0.014) as measured with the lumbar infusion test. The data from this study show no evidence that cine phase-contrast magnetic resonance imaging measurements of SV in the cerebral aqueduct are useful for selecting patients with normal pressure hydrocephalus symptoms to shunt surgery.

Nonlinear propagation of ultrasound through microbubble contrast agents and implications for imaging

Microbubble contrast agents produce nonlinear echoes under ultrasound insonation, and current imaging techniques detect these nonlinear echoes to generate contrast agent images accordingly. For these techniques, there is a potential problem in that bubbles along the ultrasound transmission path between transducer and target can alter the ultrasound transmission nonlinearly and contribute to the nonlinear echoes. This can lead to imaging artefacts, especially in regions at depth. In this paper we provide insight, through both simulation and experimental measurement, into the nonlinear propagation caused by microbubbles and the implications for current imaging techniques. A series of investigations at frequencies below, at, and above the resonance frequency of microbubbles were performed. Three specific effects on the pulse propagation (i.e., amplitude attenuation, phase changes, and harmonic generation) were studied. It was found that all these effects are dependent on the initial pulse amplitude, and their dependence on the initial phase of the pulse is shown to be insignificant. Two types of imaging errors are shown to result from this nonlinear propagation: first, that tissue can be misclassified as microbubbles; second, the concentration of microbubbles in the image can be misrepresented. It is found that these imaging errors are significant for all three pulse frequencies when the pulses transmit through a microbubble suspension of 6 cm in path length. It also is found that the first type of error is larger at the bubble resonance frequency.

INVERSE PROBLEM OF A LASER AMPLIFIER SYSTEM CONTAINING A SPATIAL FILTER

Starting from the Frantz-Nodvik equation and Huygens-Fresnel diffraction integral and using the fast Fourier transform and successive iteration method, we studied the inverse problem of a laser amplifier system containing a spatial filter, i-e-, to find the initial input temporal pulse profile, am-plitude and phase distributions from the required output temporal, spatial pulse profile and fluence, as well as the given amplifier and spatial filter parameters-

The visual response to increased ocular blood flow in normal pressure glaucoma

The vascular reactivity to breathing carbon dioxide represents a widely used method in neurology to diagnose microvascular cerebral disorders. Fifteen eyes of 15 patients suffering from confirmed normal pressure glaucoma were included in the study. The ocular carbon dioxide reactivity was determined by recording ocular pulse amplitudes (OPA) by means of oculo-oscillo-dynamography (OODG). The initial pulse amplitudes were found to be comparable to healthy subjects. According to the results obtained during breathing increased carbon dioxide concentrations (95% O2; 5% CO 2; endtidal CO 2 approx. 6.5%), the collective of 15 patients could be subdivided into two subgroups. One group (n = 9) showed a carbon dioxide reactivity that was comparable to healthy subjects, i.e., an increase of ocular pulse amplitudes of 57%. The remaining six eyes, however, showed a statistically significantly higher OPA increase compared to the first subgroup. According to the results obtained and to evaluate the hypothesis that these hemodynamic changes are accompanied by functional improvements, central visual fields were performed during breathing room air or increased inspiratory carbon dioxide concentrations. After exposure to carbon dioxide the visual fields improved significantly in patients who showed a significant increase in OPA. An increased carbon dioxide reactivity in some normal pressure glaucoma patients, i.e., a significant increase of OPA and a significant improvement of the central visual field during exposure to increased inspiratory carbon dioxide concentrations, may be due to an initial ocular vasospasm in these patients, which can be released by induced vasodilation due to carbon dioxide exposure.

Numerical modeling of soliton-dragging logic gates

The soliton-dragging logic gate is based on the soliton-dragging effect, which occurs when pulses of opposite polarization states in a birefringent optical fiber collide. The central frequencies of the two pulses and hence their velocities are shifted. The soliton-dragging effect is studied here for two solitons of the same amplitude, two solitons of different amplitudes, and two pulses that are not solitons. The dependences of the effect on the initial pulse separation, the initial pulse amplitudes, and the initial pulse profiles are all determined. The pulse interaction is studied by means of several different methods: (1) a complete solution of the coupled nonlinear Schrodinger equation, (2) a solution of ordinary differential equations that includes the effect of frequency chirp, (3) a solution of ordinary differential equations that neglects the effect of frequency chirp, and (4) the Born approximation. We compare the last three approaches with the first. We find that the second approach accurately predicts the velocity and the time shifts for the larger amplitude pulse in all cases of practical interest that we studied. Thus the second approach is useful in the design of soliton logic-based networks. The third approach is significantly less accurate, while the fourth approach is the least accurate of all.

Nonlinear self-phase modulation in optical soliton systems with lumped amplifiers

The nonlinear Schrödinger equation, governing pulse propagation in lossy optical fibers with periodic amplification, is analyzed under the average soliton concept. Bright and dark solitons solutions, corresponding to separatrices of one-dimensional hamiltonian dynamical systems, have been derived. The shift of the soliton velocity, relative to the group velocity, as well as the effect of nonlinear self-phase modulation on the angular frequency and the wavenumber are investigated. The obtained results are connected with the initial pulse amplitude and its spatial and temporal derivatives.