Mathematical and Computer Simulation of Pulses Interaction (original) (raw)
Quantum interactions with pulses of radiation
Physical Review A, 2020
This article presents a general master equation formalism for the interaction between travelling pulses of quantum radiation and localized quantum systems. Traveling fields populate a continuum of free space radiation modes and the Jaynes-Cummings model, valid for a discrete eigenmode of a cavity, does not apply. We develop a complete input-output theory to describe the driving of quantum systems by arbitrary incident pulses of radiation and the quantum state of the field emitted into any desired outgoing temporal mode. Our theory is applicable to the transformation and interaction of pulses of radiation by their coupling to a wide class of material quantum systems. We discuss the most essential differences between quantum interactions with pulses and with discrete radiative eigenmodes and present examples relevant to quantum information protocols with optical, microwave and acoustic waves.
The Integrated Pulse Profiles of Fast Radio Bursts
arXiv: High Energy Astrophysical Phenomena, 2019
Multi-peaked features appear on the integrated pulse profiles of fast radio burst observed below 2.5 GHz and the instantaneous spectrum of many bursts observed between 4 and 8 GHz. The mechanism of pulse or spectrum shaping has attracted little attention. Here we show that these interference-like pulse profiles are mostly the instantaneous spectra near the source regions of fast radio bursts. The corresponding instantaneous spectra are coincident to the spectrum from a single electron passing through a tapered undulator. The multi-peaked spectrum observed between 4 and 8 GHz can also be explained consistently by this type of spectrum. The spectrum is invisible unless the particles in the radiation beam are bunched. The bunching effect is probably due to the acceleration of particles in the plasma wakefield.
Interference effects in the reradiation of ultrashort electromagnetic pulses
arXiv: Atomic Physics, 2012
Reradiation of a spatially non-uniform ultrashort electromagnetic pulse interacting with the linear chain of multielectron atoms is studied in the framework of sudden perturbation approximation. Angular distributions of the reradiation spectrum for arbitrary number of atoms are obtained. It is shown that interference effects for the photon radiation amplitudes lead to appearing of "diffraction" maximums. The obtained results can be extended to the case of two- and three-dimensional crystal lattices and atomic chains. The approach developed allows also to take into account thermal vibrations of the lattice atoms.
Optics and Spectroscopy, 2008
The calculation of the energy of the ground state of atoms is the criterion for the correctness of compact analytical atomic wave functions. However, such a test is in fact static. We studied the degree of taking into account electron correlations in various simple analytical wave functions in the dynamic process of reemission by the helium atom of ultrashort pulses of an electromagnetic field. Direct guidelines are given on the use of particular analytical wave functions, which can be helpful in simple calculations and estimations of dynamic processes.
Interaction of pulses in the nonlinear Schrödinger model
Physical Review E, 2003
The interaction of two rectangular pulses in the nonlinear Schrödinger model is studied by solving the appropriate Zakharov-Shabat system. It is shown that two real pulses may result in an appearance of moving solitons. Different limiting cases, such as a single pulse with a phase jump, a single chirped pulse, in-phase and out-of-phase pulses, and pulses with frequency separation, are analyzed. The thresholds of creation of new solitons and multisoliton states are found.
On the interaction of NLS-described modulating pulses with different carrier waves
Mathematical Methods in the Applied Sciences, 2007
We give a detailed analysis of the interaction of two modulating pulse solutions of a nonlinear wave equation. These solutions consist of pulse-like envelopes satisfying approximately a nonlinear Schrödinger equation, advancing in the laboratory frame, and modulating underlying wave trains. We improve the bound for the possible shift of the envelopes caused by the interaction of two well-prepared pulses from order O(1) to order O(ε). Thus, we manifest the statement that there is almost no interaction of pulses with different carrier waves.
An Approximation of Gaussian Pulses
usv.ro
A new technique for generating an approximate replica of Gaussian pulses with good accuracy is proposed and investigated. The Gaussian function is approximated with a waveform that results from the convolution of two triangles. The proposed pulse performs better than other previously reported pulse. The results show good agreement not only for the Gaussian pulse but also for its first and second derivatives. As the triangular pulse generator is standard and widely used, the proposed technique needs besides it an appropriate filter.
Propagation of Electromagnetic Pulses
wlovinformatica.no-ip.info
This paper begins with a brief historical description of how electromagnetic waves were discovered, first theoretically and then experimentally, and how they were originally utilized for radio transmission. It addresses the relation between wireless and transmission line propagation and the approximations involved in the mathematical description of the propagation process. Since pulse transmission at faster rates have become a necessity in all communication and digital data systems, the problems associated with the propagation of such signals need to be addressed. The paper includes a brief description of the Linear Filter approach developed by the author to evaluate both quantitatively and qualitatively dispersion effects in optical and superconductive lines. Nonlinear effects are briefly described as difficult to analyze, but promising in terms of new applications. Power line surges, including nonlinear effects, are also described to include contributions from the author. More recent issues of interest include the potential problems associated with electromagnetic pulses produced by nuclear detonations and solar activity. Finally, the challenges posed by the Smart Grid are briefly addressed, including a novel application of transients to monitor energy consumption in the "Smart House". References were chosen with the intent of emphasizing the contribution of Brazilian researchers and, whenever possible, giving preference to publications easily available on the web.
Profile alterations of a symmetrical light pulse coming through a quantum well
2000
The theory of a response of a two-energy-level system, irradiated by symmetrical light pulses, has been developed.(Suchlike electronic system approximates under the definite conditions a single ideal quantum well (QW) in a strong magnetic field {\bf H}, directed perpendicularly to the QW's plane, or in magnetic field absence.) The general formulae for the time-dependence of non-dimensional reflection {\cal R}(t), absorption {\cal A}(t) and transmission {\cal T}(t) of a symmetrical light pulse have been obtained. It has been shown that the singularities of three types exist on the dependencies {\cal R}(t), {\cal A}(t), {\cal T}(t). The oscillating time dependence of {\cal R}(t), {\cal A}(t), {\cal T}(t) on the detuning frequency \Delta\omega=\omega_l-\omega_0 takes place. The oscillations are more easily observable when \Delta\omega\simeq\gamma_l. The positions of the total absorption, reflection and transparency singularities are examined when the frequency \omega_l is detuned.
Experimental Observation of Carrier-Envelope Phase Effects in MultiCycle Pulses
Physical Review A, 2011
Using intense RF pulses interacting with the magnetic Zeeman sub-levels of Rubidium (Rb) atoms, we have experimentally and theoretically shown the CEP effects in the population transfer between two bound atomic states interacting with pulses consisting of many cycles (up to 15 cycles) of the field. It opens several exciting applications and interesting possibilities that can be easily transfer to
Experimental observation of carrier-envelope-phase effects by multicycle pulses
Physical Review A, 2011
We present an experimental and theoretical study of carrier-envelope phase (CEP) effects on the population transfer between two bound atomic states interacting with pulses consisting of many cycles. Using intense radio-frequency pulse with Rabi frequency of the order of the atomic transition frequency, we investigated the influence of CEP on the control of phase dependent multi-photon transitions between the Zeeman sub-levels of the ground state of 87 Rb. Our scheme has no limitation on the duration of the pulses. Extending the CEP control to longer pulses creates interesting possibilities to generate pulses with accuracy that is better than the period of optical oscillations.
Spectra induced by interactions of atoms with ultrashort electromagnetic pulses
Optics and Spectroscopy, 2009
An ultrashort pulse of an electromagnetic field incident on an atom shakes the atom and gives rise to various electron transitions in it. These processes are accompanied by the reemission of the incident ultrashort pulse. This paper studies the relation between the spectra of reemitted photons of an ultrashort pulse and the transitions of atomic electrons into particular states. The obtained partial reemission spectra can allow one to relate direction patterns to the probability of the excitation of an atom into different states.
Application Value of Slow Decay Behavior of Energy Density Excited by Electromagnetic Pulses
International Journal of Infrared and Millimeter Waves, 1999
By comparing the radiated energy densities excited by the continuous wave (CW), the sinusoidal pulse, the Gaussian pulse and the rectangular pulse respectively with the same energy, it is shown that the pulses are not more efficient than CW in the energy transmission. For the sinusoidal pulse and the CW, the radiated energy densities are the same in far zone. The radiated energy density of the Gaussian pulse is equal to the one of CW in far zone when the pulse width equals 1/2π of the CW′s period T0. The energy transmission of pulse is more efficient only in the case of τ <T0/2π. For the rectangular pulse, the radiated energy density is equal to the one of CW in far zone when the maximum of frequency spectrum is 10f0 (f0=1/T0) and the pulse width is T0. The numerical results and theoretical analysis in this paper show that the application value of the slow decay behavior of the energy density excited by electromagnetic pulses is limited.
Effect of Interactions on Ultrashort Pulses Transmission
2013
Optical fiber communication has great advantages over the conventional cable communication system. The most important advantage is the availability of enormous communication bandwidth which is a measure of the information carrying capacity. Ultrashort pulses (solitons) refer to a situation where light beam propagates through a nonlinear optical medium without any change in its shape and velocity. Optical ultrashort pulses are formed due to the balance between the group velocity dispersion and self phase modulation. Depending upon the individual pulse width, inter pulse spacing and loss in the fiber, co-propagating ultrashort pulses do interact and share energy. Generating ultrashort pulses with the appropriate parameters is just the first step in successful ultrashort pulses communication systems. Ultrashort pulses must also be able to propagate through an optical fiber while maintaining these parameters. Incorporating the mathematical model based on the Nonlinear Schrodinger (NLS) ...
Pulsed processes during the interaction between an electron beam and a surface electromagnetic wave
2000
We study features of nonlinear pulsed microwave processes in a periodic wave-guide with electron beam. The transition from one or a few pulses to a long-term oscillation mode is considered. Features of this mode in the relativistic os-cillator of surface wave are analyzed for the beam and field synchronism at frequencies near the transparency band boundary corresponding to π-type oscillations.
Nonlinear wave interactions between short pulses of different spatio-temporal extents OPEN
We study the nonlinear wave interactions between short pulses of different spatio-temporal extents. Unlike the well-understood mixing of quasi-monochromatic waves, this configuration is highly non-intuitive due to the complex coupling between the spatial and temporal degrees of freedom of the interacting pulses. We illustrate the process intuitively with transitions between different branches of the dispersion curves and interpret it in terms of spectral exchange between the interacting pulses. We verify our interpretation with an example whereby a spectrally-narrow pulse " inherits " the wide spectrum of a pump pulse centered at a different wavelength, using exact numerical simulations, as well as a simplified coupled mode analysis and an asymptotic analytical solution. The latter also provides a simple and intuitive quantitative interpretation. The complex wave mixing process studied here may enable flexible spatio-temporal shaping of short pulses and is the starting point of the study of more complicated systems. Wave mixing is one of the most basic nonlinear optical processes. In the vast majority of cases, it is studied for one or more interacting quasi-monochromatic waves, for which all temporal and spatial scales are similar and much larger than the period(s) and wavelength(s), respectively 1. In contrast, there are very few studies of the mixing of wave packets having different spectral widths, and temporal and spatial profiles 1,2. Indeed, these configurations involve a rather complicated and non-intuitive wave mixing process such that it is difficult to assess, a priory, what would be the final spatial length, temporal duration and spectral width of the pulses generated by the interaction. In this Article, we present a systematic way to predict and interpret the complex wave interactions in such scenarios in terms of exchange of spectral and spatial Fourier components between the interacting pulses. Specifically, we study the case where a short pulse (e.g., femtosecond or picosecond long) is extracted from a much longer pulse. Such a process is enabled by a wave-mixing interaction we denote as spectral inheritance-a temporally long (and spectrally-narrow) pulse propagating in a material with an intensity-dependent refractive index " inherits " the wide spectrum of an intense, temporally short (spectrally-broad) pump pulse centered at a different wavelength. We focus on a case where the (short) pump pulse is periodically-patterned such that it induces a transient Bragg grating (TBG) whose stop gap matches the frequency of an incoming (long) signal pulse. TBGs have been studied extensively 3,4 mostly in the context of measuring fundamental material properties such as diffusion coefficients and free-carrier recombination time. Almost no attention was given, however, to the possibility of using TBGs for spectral and spatio-temporal shaping of pulses, as well as for using them for telecom applications such as all-optical switching. Indeed, this configuration offers great flexibility in determining the duration and intensity of the reflected pulse and can be adapted to any incoming wavelength by a simple adjustment of the spatial period of the TBG. Intuitively, the TBG will cause signal photons captured within it to be reflected during its " lifetime ". It is insightful to interpret the wave mixing process induced by the TBG using dispersion curves and transitions between them, see Fig. 1. In general, the TBG causes a (forward propagating) signal photon, characterized by a longitudinal momentum k f > 0 and ω f to be converted into a new (backward propagating) photon, characterized by k b < 0 and ω b. The relation between these quantities is determined by the spatio-temporal spectral content introduced by the perturbation of the optical properties of the waveguide material, = n n r t (,). Indeed, a pertur