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Academic literature on the topic 'Multi-Mode non-Linear Schrödinger equation'
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Journal articles on the topic "Multi-Mode non-Linear Schrödinger equation"
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BOGOLUBOV, N. N., M. Yu. RASULOVA, and I. A. TISHABOEV. "QUANTUM DYNAMICS OF TWO-LEVEL ATOMS INTERACTING WITH AN ELECTROMAGNETIC FIELD." International Journal of Modern Physics B 28, no. 08 (2014): 1450060. http://dx.doi.org/10.1142/s021797921450060x.
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We consider the dynamics of a system consisting of N two-level atoms interacting with a multi-mode cavity field. For the given system, the generalized kinetic equation (GKE) is obtained and conditions are given under which its solution is reduced to solution of a linear equation, and of the one-dimensional nonlinear Schrödinger equation, respectively.
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Misra, Shikha, Sanjay K. Mishra, and P. Brijesh. "Coaxial propagation of Laguerre–Gaussian (LG) and Gaussian beams in a plasma." Laser and Particle Beams 33, no. 1 (2015): 123–33. http://dx.doi.org/10.1017/s0263034615000142.
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AbstractThis paper investigates the non-linear coaxial (or coupled mode) propagation of Laguerre–Gaussian (LG) (in particular L01 mode) and Gaussian electromagnetic (em) beams in a homogeneous plasma characterized by ponderomotive and relativistic non-linearities. The formulation is based on numerical solution of non-linear Schrödinger wave equation under Jeffreys–Wentzel–Kramers–Brillouin approximation, followed by paraxial approach applicable in the vicinity of intensity maximum of the beams. A set of coupled differential equations for spot size (beam width) and phase evolution with space corresponding to coupled mode has been derived and numerically solved to determine the propagation dynamics. Using focusing equation a critical condition describing the self-trapped (i.e., spatial soliton) mode of laser beam propagation in the plasma has been discussed; as a consequence oscillatory focusing/defocusing of the beams in coupled mode propagation have been analyzed and presented graphically. As an important outcome, significant enhancement in the intensity of LG beam is noticed when it is coupled with the Gaussian mode.
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Sakhabutdinov, Airat Zh, Vladimir I. Anfinogentov, Oleg G. Morozov, et al. "Numerical Method for Coupled Nonlinear Schrödinger Equations in Few-Mode Fiber." Fibers 9, no. 1 (2021): 1. http://dx.doi.org/10.3390/fib9010001.
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This paper discusses novel approaches to the numerical integration of the coupled nonlinear Schrödinger equations system for few-mode wave propagation. The wave propagation assumes the propagation of up to nine modes of light in an optical fiber. In this case, the light propagation is described by the non-linear coupled Schrödinger equation system, where propagation of each mode is described by own Schrödinger equation with other modes’ interactions. In this case, the coupled nonlinear Schrödinger equation system (CNSES) solving becomes increasingly complex, because each mode affects the propagation of other modes. The suggested solution is based on the direct numerical integration approach, which is based on a finite-difference integration scheme. The well-known explicit finite-difference integration scheme approach fails due to the non-stability of the computing scheme. Owing to this, here we use the combined explicit/implicit finite-difference integration scheme, which is based on the implicit Crank–Nicolson finite-difference scheme. It ensures the stability of the computing scheme. Moreover, this approach allows separating the whole equation system on the independent equation system for each wave mode at each integration step. Additionally, the algorithm of numerical solution refining at each step and the integration method with automatic integration step selection are used. The suggested approach has a higher performance (resolution)—up to three times or more in comparison with the split-step Fourier method—since there is no need to produce direct and inverse Fourier transforms at each integration step. The key advantage of the developed approach is the calculation of any number of modes propagated in the fiber.
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Zhu, Junyan, Jiang Cao, Chen Song, Bo Li, and Zhengsheng Han. "Numerical investigation on the convergence of self-consistent Schrödinger-Poisson equations in semiconductor device transport simulation." Nanotechnology 35, no. 31 (2024): 315001. http://dx.doi.org/10.1088/1361-6528/ad4558.
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Abstract Semiconductor devices at the nanoscale with low-dimensional materials as channels exhibit quantum transport characteristics, thereby their electrical simulation relies on the self-consistent solution of the Schrödinger-Poisson equations. While the non-equilibrium Green’s function (NEGF) method is widely used for solving this quantum many-body problem, its high computational cost and convergence challenges with the Poisson equation significantly limit its applicability. In this study, we investigate the stability of the NEGF method coupled with various forms of the Poisson equation, encompassing linear, analytical nonlinear, and numerical nonlinear forms Our focus lies on simulating carbon nanotube field-effect transistors (CNTFETs) under two distinct doping scenarios: electrostatic doping and ion implantation doping. The numerical experiments reveal that nonlinear formulas outperform linear counterpart. The numerical one demonstrates superior stability, particularly evident under high bias and ion implantation doping conditions. Additionally, we investigate different approaches for presolving potential, leveraging solutions from the Laplace equation and a piecewise guessing method tailored to each doping mode. These methods effectively reduce the number of iterations required for convergence.
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Dabas, Bhawana, Jivesh Kaushal, Monika Rajput, and R. K. Sinha. "Study of Self Phase Modulation in Chalcogenide Glass Photonic Crystal Fiber." Applied Mechanics and Materials 110-116 (October 2011): 53–56. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.53.
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In this paper, Self Phase Modulation (SPM) in chalcogenide As2Se3glass Photonic Crystal Fiber (PCF) is numerically studied by combining the fully vectorial effective index method (FVEIM) and Split Step Fourier Method (SSFM). The FVEIM is used to calculate the variation of effective refractive index of guided mode (neff), effective area (Aeff), dispersion and non-linear coefficient (γ) with wavelength for different designs of chalcogenide As2Se3PCF. The FVEIM solves the vector wave equations and SSFM solves non linear Schrödinger Equation (NLSE) for the different designing parameter of As2Se3PCF. In case of Self Phase Modulation (SPM), spectral width of the obtained output pulse at d/Λ=0.7 is 1.5 times greater than width of the output pulse obtained at d/L=0.3 using SSFM. Thus we can get the desired spectral broadening just by tailoring the design parameters of the PCF.
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Niedda, Jacopo, Luca Leuzzi, and Giacomo Gradenigo. "Intensity pseudo-localized phase in the glassy random laser." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 5 (2023): 053302. http://dx.doi.org/10.1088/1742-5468/acd2c4.
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Abstract Evidence of an emergent pseudo-localized phase characterizing the low-temperature replica symmetry breaking phase of the complex disordered models for glassy light is provided in the mode-locked random laser model. A pseudo-localized phase corresponds to a state in which the intensity of light modes is neither equipartited among all modes nor strictly condensed on few of them. Such a hybrid phase, recently characterized as a finite size effect in other models, such as the discrete non-linear Schrödinger equation, in the low temperature phase of the glassy random laser appears to be robust in the limit of large size.
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Jahan, Sharmin, Rubaiya Khondoker Shikha, Abdul Mannan, and A. A. Mamun. "Modulational Instability of Ion-Acoustic Waves in Pair-Ion Plasma." Plasma 5, no. 1 (2021): 1–11. http://dx.doi.org/10.3390/plasma5010001.
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The modulational instability (MI) of ion-acoustic waves (IAWs) is examined theoretically in a four-component plasma system containing inertialess electrons featuring a non-thermal, non-extensive distribution, iso-thermal positrons, and positively as well as negatively charged inertial ions. In this connection, a non-linear Schrödinger equation (NLSE), which dominates the conditions for MI associated with IAWs, is obtained by using the reductive perturbation method. The numerical analysis of the NLSE reveals that the increment in non-thermality leads to a more unstable state, whereas the enhancement in non-extensivity introduces a less unstable state. It also signifies the bright (dark) ion-acoustic (IA) envelope solitons mode in the unstable (stable) domain. The conditions for MI and its growth rate in the unstable regime of the IAWs are vigorously modified by the different plasma parameters (viz., non-thermal, non-extensive q-distributed electron, iso-thermal positron, the ion charge state, the mass of the ion and positron, non-thermal parameter α, the temperature of electron and positron, etc.). Our findings may supplement and add to prior research in non-thermal, non-extensive electrons and iso-thermal positrons that can co-exist with positive as well as negative inertial ions.
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Odegov, N. A., and I. S. Baleyev. "A NUMERICAL-ANALYTICAL METHOD FOR THE SYNTHESIS OF OPTIMAL IRREGULAR DWDM FREQUENCY PLANS." Proceedings of the O.S. Popov ОNAT 1, no. 2 (2020): 70–81. http://dx.doi.org/10.33243/2518-7139-2020-1-2-70-81.
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The possibilities of increasing the throughput of fiber-optic transmission systems by using an uneven frequency grid are investigated. In this case, the bandwidth of each channel is selected so that the transmission rate is the same for all channels. In this work, both linear and some nonlinear effects are taken into account, leading to the distortion of the optical pulse. Simulation of nonlinear effects is based on a model in the form of a generalized nonlinear Schrödinger equation. The developed program provides modeling of linear and nonlinear distortions for the DWDM range (from 1460 to 1625 nm). The characteristics of different types of optical fiber are also provided. Non-linear effects are investigated for NZ DSF-type dispersion-shifted fiber. Differential equations are solved by the method of splitting according to physical factors. It is shown that for this type of fiber at distances of 100 km and more, a soliton transmission mode appears. In this case, the frequency band of the soliton regime can reach significant values (up to 5 THz) at typical lengths of the regeneration sections of the order of 100-300 km. A method for calculating the bandwidth of uneven frequency plans is proposed. This method has been tested for a 15 THz band. A specific example of calculations is given for the comparison base in the form of a uniform frequency plan with a single channel bandwidth of 50 GHz. It is shown that optimal non-uniform frequency plans can significantly increase the throughput of DWDM systems: in the given example, approximately 3 times. At the same time, the complexity of the equipment increases slightly.
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REZNIK, G. M., V. ZEITLIN, and M. BEN JELLOUL. "Nonlinear theory of geostrophic adjustment. Part 1. Rotating shallow-water model." Journal of Fluid Mechanics 445 (October 16, 2001): 93–120. http://dx.doi.org/10.1017/s002211200100550x.
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We develop a theory of nonlinear geostrophic adjustment of arbitrary localized (i.e. finite-energy) disturbances in the framework of the non-dissipative rotating shallow-water dynamics. The only assumptions made are the well-defined scale of disturbance and the smallness of the Rossby number Ro. By systematically using the multi-time-scale perturbation expansions in Rossby number it is shown that the resulting field is split in a unique way into slow and fast components evolving with characteristic time scales f−10 and (f0Ro)−1 respectively, where f0 is the Coriolis parameter. The slow component is not influenced by the fast one and remains close to the geostrophic balance. The algorithm of its initialization readily follows by construction.The scenario of adjustment depends on the characteristic scale and/or initial relative elevation of the free surface ΔH/H0, where ΔH and H0 are typical values of the initial elevation and the mean depth, respectively. For small relative elevations (ΔH/H0 = O(Ro)) the evolution of the slow motion is governed by the well-known quasi-geostrophic potential vorticity equation for times t [les ] (f0Ro)−1. We find modifications to this equation for longer times t [les ] (f0Ro2)−1. The fast component consists mainly of linear inertia–gravity waves rapidly propagating outward from the initial disturbance.For large relative elevations (ΔH/H0 [Gt ] Ro) the slow field is governed by the frontal geostrophic dynamics equation. The fast component in this case is a spatially localized packet of inertial oscillations coupled to the slow component of the flow. Its envelope experiences slow modulation and obeys a Schrödinger-type modulation equation describing advection and dispersion of the packet. A case of intermediate elevation is also considered.
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Muhammad, Zahid, Ubaid Ullah Khalil, Anees Khan, Tanweer Ahmed, Waqas Khan, and Samra Naz. "Design Optimization of Fiber Laser for Generation of Femtosecond Optical Pulses." Scholars Journal of Physics, Mathematics and Statistics 11, no. 08 (2024): 89–100. http://dx.doi.org/10.36347/sjpms.2024.v11i08.002.
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The precise coordination of dispersion management, temperature control, mode-locking mechanisms, and gain medium qualities are required in the design and optimization of fiber laser cavities for the generation of femtosecond pulses. The performance and capacities of femtosecond fiber lasers are being enhanced by developments in these fields, opening up new uses for them. The main focus of this research work was to design a lasing cavity for the generation of femtosecond optical pulses. So, we designed a laser cavity having six segments with a total length of 5.4 meters. The first segment is a 100-centimeter-long single mode fiber (SMF), the second one is an active fiber (Yb doped fiber) which is 40-centimeter long, and the third segment is a 70-centimeter-long SMF.A 130 cm free space region(cavity) makes up the fourth segment, which include a collimator, mirror, grating, half wave plate, quarter wave plate, isolator, and polarized beam splitter (PBS). Single-mode fibers of 80 cm and 120 cm in length comprises the fifth and sixth sections respectively. The calculated repetition rate of the laser cavity is 37.06 MHz.. We used the software "Ultrafast Pulse Propagator Version 3.0.0", created by Bilkent University in Ankara, Turkey, to accomplished this task. This application was initially created to examine fiber links, mode-locking, and fiber amplification. The physics of the code is based on the generalized non-linear Schrödinger equation, which includes high order dispersion, bandwidth, gain with restriction, saturation loss, and saturation absorption. For data visualization, this software uses FORTRAN code and MATLAB algorithms. The pulse width increased linearly from 1.2809 to 1.3227 Ps and the spectral width decreased linearly from 2.3841 to 2.2561 nm when the Yb doped fiber's length were changed between 5 and 50 cm. 94729 fs2 is the total dispersion from the 5.4 m long lasing cavity. In the end, we determined the pulses' repetition rate, which came out to be 37.0