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Diatomic molecule in a strong infrared laser field: level-shifts and bond-length change due to laser-dressed Morse potential
Authors:
Sándor Varró,
Szabolcs Hack,
Gábor Paragi,
Péter Földi,
Imre F. Barna,
Attila Czirják
Abstract:
We present a general mathematical procedure to handle interactions described by a Morse potential in the presence of a strong harmonic excitation. We account for permanent and field-induced terms and their gradients in the dipole moment function, and we derive analytic formulae for the bond-length change and for the shifted energy eigenvalues of the vibrations, by using the Kramers-Henneberger fra…
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We present a general mathematical procedure to handle interactions described by a Morse potential in the presence of a strong harmonic excitation. We account for permanent and field-induced terms and their gradients in the dipole moment function, and we derive analytic formulae for the bond-length change and for the shifted energy eigenvalues of the vibrations, by using the Kramers-Henneberger frame. We apply these results to the important cases of $\mathrm{H}_{2}$ and $\mathrm{LiH}$, driven by a near- or mid-infrared laser in the $10^{13}$ $\mathrm{ W/cm^2}$ intensity range.
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Submitted 28 June, 2023; v1 submitted 8 March, 2023;
originally announced March 2023.
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Quantum interference in strong-field ionization by a linearly polarized laser pulse, and its relevance to tunnel exit time and momentum
Authors:
Szabolcs Hack,
Szilárd Majorosi,
Mihály G. Benedict,
Sándor Varró,
Attila Czirják
Abstract:
We investigate the liberation of an atomic electron by a linearly polarized single-cycle near-infrared laser pulse having a peak intensity that ensures tunneling. Based on phase space analysis and energy distribution in the instantaneous potential, we reveal the importance of quantum interference between tunneling and over-the-barrier pathways of escape. Tunneling is blurred both in space and time…
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We investigate the liberation of an atomic electron by a linearly polarized single-cycle near-infrared laser pulse having a peak intensity that ensures tunneling. Based on phase space analysis and energy distribution in the instantaneous potential, we reveal the importance of quantum interference between tunneling and over-the-barrier pathways of escape. Tunneling is blurred both in space and time, and the contribution of tunneling at the mean energy is almost negligible. We suggest and justify improved initial conditions for a classical particle approximation of strong-field ionization, based on the quantum momentum function, and we show how to reconstruct them from the detected momentum of an escaped electron.
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Submitted 10 September, 2021; v1 submitted 23 March, 2021;
originally announced March 2021.
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High-order harmonics as induced by a quantized field:a phase-space picture
Authors:
Ákos Gombkötő,
Sándor Varró,
Péter Mati,
Péter Földi
Abstract:
The interaction of matter with a quantized electromagnetic mode is considered. Representing a strong exciting field, the mode is assumed to contain a large number of photons. As a result, the material response is highly nonlinear: the completely quantized description results in generation of high harmonics. In order to understand the essence of the physical processes that are involved, we consider…
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The interaction of matter with a quantized electromagnetic mode is considered. Representing a strong exciting field, the mode is assumed to contain a large number of photons. As a result, the material response is highly nonlinear: the completely quantized description results in generation of high harmonics. In order to understand the essence of the physical processes that are involved, we consider a finite dimensional model for the material system. Using an appropriate description in phase space, this approach leads to a transparent picture showing that the interaction splits the initial, exciting coherent state into parts, and the rapid change of the populations of these parts (that are coherent states themselves) results in the generation of high-order harmonics as secondary radiation. The method we use is an application of the discrete lattice of coherent states that was introduced by J. von Neumann.
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Submitted 15 January, 2020; v1 submitted 22 October, 2019;
originally announced October 2019.
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The role of the time delay in the reflection and transmission of ultrashort electromagnetic pulses on a system of parallel current sheets
Authors:
M. Polner,
S. Varró,
A. Vörös-Kiss
Abstract:
The reflection and transmission of a few-cycle laser pulse impinging on two parallel thin metal layers have been analyzed. The two layers, with a thickness much smaller than the skin depth of the incoming radiation field, are represented by current sheets embedded in three dielectrics, all with different index of refraction. The dynamics of the surface currents and the scattered radiation field ar…
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The reflection and transmission of a few-cycle laser pulse impinging on two parallel thin metal layers have been analyzed. The two layers, with a thickness much smaller than the skin depth of the incoming radiation field, are represented by current sheets embedded in three dielectrics, all with different index of refraction. The dynamics of the surface currents and the scattered radiation field are described by the coupled system of Maxwell-Lorentz equations. When applying the plane wave modeling assumptions, these reduce to a hybrid system of two delay differential equations for the electron motion in the layers and a recurrence relation for the scattered field. The solution is given as the limit of a singularly perturbed system and the effects of the time delay on the dynamics is analyzed.
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Submitted 7 December, 2018;
originally announced December 2018.
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Sub-cycle quantum electrodynamics in strongly laser-driven semiconductors
Authors:
N. Tsatrafyllis,
S. Kuhn,
M. Dumergue,
P. Foldi,
S. Kahaly,
E. Cormier,
I. A. Gonoskov,
B. Kiss,
K. Varju,
S. Varro,
P. Tzallas
Abstract:
Electrodynamical processes induced in complex systems like semiconductors by strong electromagnetic fields, have traditionally/conventionally been described using semi-classical approaches. Although these approaches, allowed the investigation of ultrafast dynamics in solids culminating in multi-petahertz electronics, they do not provide any access in the quantum optical nature of the interaction a…
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Electrodynamical processes induced in complex systems like semiconductors by strong electromagnetic fields, have traditionally/conventionally been described using semi-classical approaches. Although these approaches, allowed the investigation of ultrafast dynamics in solids culminating in multi-petahertz electronics, they do not provide any access in the quantum optical nature of the interaction as they treat the driving-field classically and unaffected by the interaction. Here, using a full quantum-optical approach, we demonstrate that the sub-cycle electronic response in a strongly driven semiconductor crystal is imprinted in the quantum-state of the driving-field resulting in non-classical light-states carrying the information of the interaction. This vital step towards strong-field ultrafast quantum electrodynamics unravels information inaccessible by conventional approaches and leads to the development of a new class non-classical light sources.
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Submitted 30 October, 2018;
originally announced October 2018.
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Carrier-envelope phase controlled isolated attosecond pulses in the nm wavelength range, based on superradiant nonlinear Thomson-backscattering
Authors:
Szabolcs Hack,
Sándor Varró,
Attila Czirják
Abstract:
A proposal for a novel source of isolated attosecond XUV -- soft X-ray pulses with a well controlled carrier-envelope phase difference (CEP) is presented in the framework of nonlinear Thomson-backscattering. Based on the analytic solution of the Newton-Lorentz equations, the motion of a relativistic electron is calculated explicitly, for head-on collision with an intense fs laser pulse. By using t…
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A proposal for a novel source of isolated attosecond XUV -- soft X-ray pulses with a well controlled carrier-envelope phase difference (CEP) is presented in the framework of nonlinear Thomson-backscattering. Based on the analytic solution of the Newton-Lorentz equations, the motion of a relativistic electron is calculated explicitly, for head-on collision with an intense fs laser pulse. By using the received formulae, the collective spectrum and the corresponding temporal shape of the radiation emitted by a mono-energetic electron bunch can be easily computed. For certain suitable and realistic parameters, single-cycle isolated pulses of ca. 20 as length are predicted in the XUV -- soft X-ray spectral range, including the 2.33-4.37 nm water window. According to our analysis, the generated almost linearly polarized beam is extremely well collimated around the initial velocity of the electron bunch, with considerable intensity and with its CEP locked to that of the fs laser pulse.
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Submitted 18 December, 2017; v1 submitted 7 September, 2017;
originally announced September 2017.
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A quantum optical model for the dynamics of high harmonic generation
Authors:
Ákos Gombkötő,
Attila Czirják,
Sándor Varró,
Péter Földi
Abstract:
We investigate a two-level atom in the field of a strong laser pulse. The resulting time-dependent polarization is the source of a radiation the frequency components of which are essentially harmonics of the driving field's carrier frequency. The time evolution of this secondary radiation is analyzed in terms of the expectation values of the photon number operators for a large number of electromag…
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We investigate a two-level atom in the field of a strong laser pulse. The resulting time-dependent polarization is the source of a radiation the frequency components of which are essentially harmonics of the driving field's carrier frequency. The time evolution of this secondary radiation is analyzed in terms of the expectation values of the photon number operators for a large number of electromagnetic modes that are initially in the vacuum state. Our method is based on a multimode version of the Jaynes-Cummings-Paul model and can be generalized to different radiating systems as well. We show, that after the exciting pulse, the final distribution of the photon numbers is close to the conventional (Fourier transform-based) power spectrum of the secondary radiation. The details of the high harmonic spectra are also analyzed, for many-cycle excitations a clear physical interpretation can be given in terms of the Floquet quasi-energies. A first step towards the determination of the photon statistics of the HHG modes reveals states with slightly super-Poissonian distribution.
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Submitted 12 September, 2016; v1 submitted 3 May, 2016;
originally announced May 2016.
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Electron Acceleration by a Bichromatic Chirped Laser Pulse in Underdense Plasmas
Authors:
Mihály András Pocsai,
Imre Ferenc Barna,
Sándor Varró
Abstract:
A theoretical study of laser and plasma based electron acceleration is presented. An effective model has been used, in which the presence of an underdense plasma has been taken account via its index of refraction $n_{m}$. In the confines of this model, the basic phenomena can be studied by numerically solving the classical relativistic equations of motion. The key idea of this paper is the applica…
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A theoretical study of laser and plasma based electron acceleration is presented. An effective model has been used, in which the presence of an underdense plasma has been taken account via its index of refraction $n_{m}$. In the confines of this model, the basic phenomena can be studied by numerically solving the classical relativistic equations of motion. The key idea of this paper is the application of chirped, bichromatic laser fields. We investigated the advantages and disadvantages of mixing the second harmonic to the original $λ= 800 \, \mathrm{nm}$ wavelength pulse. We performed calculations both for plane wave and Gaussian pulses.
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Submitted 13 October, 2015; v1 submitted 8 July, 2015;
originally announced July 2015.
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Electron Acceleration in Underdense Plasmas Described with a Classical Effective Theory
Authors:
Mihály András Pocsai,
Imre Ferenc Barna,
Sándor Varró
Abstract:
An effective theory of laser--plasma based particle acceleration is presented. Here we treated the plasma as a continuous medium with an index of refraction $n_{m}$ in which a single electron propagates. Because of the simplicity of this model, we did not need to perform PIC simulations in order to study the properties of the electron acceleration. We studied the properties of the electron motion…
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An effective theory of laser--plasma based particle acceleration is presented. Here we treated the plasma as a continuous medium with an index of refraction $n_{m}$ in which a single electron propagates. Because of the simplicity of this model, we did not need to perform PIC simulations in order to study the properties of the electron acceleration. We studied the properties of the electron motion due to the Lorentz force and the relativistic equations of motion were numerically solved and analysed. We compared our results to PIC simulations and experimental data.
Keywords: Underdense plasma; Electron acceleration; Classical electrodynamics; Relativistic equation of motion; Ultrashort laser pulses
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Submitted 19 February, 2015; v1 submitted 4 November, 2014;
originally announced November 2014.
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Surface plasmon assisted magnetic anomalies on room temperature gold films in high-intensity laser fields
Authors:
N. Kroó,
P. Rácz,
S. Varró
Abstract:
Supplementing our STM and electron emission studies investigations, concluding in electron pairing in strong laser fields [1], further time-of-flight electron emission studies were carried out, changing the angle of polarization of the incident light, exciting surface plasmon oscillations. It has been found, that those parts of the electron spectrum which have been attributed to electron pairing h…
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Supplementing our STM and electron emission studies investigations, concluding in electron pairing in strong laser fields [1], further time-of-flight electron emission studies were carried out, changing the angle of polarization of the incident light, exciting surface plasmon oscillations. It has been found, that those parts of the electron spectrum which have been attributed to electron pairing have a significantly different angular dependence around 80 GW/cm2 where the pairing effect has been found than outside this region (e.g. 120 GW/cm2). These results have been interpreted as the appearance of ideal or partly ideal diamagnetism on the one hand and as anomaly in the magneto-optical effect (rotation) on the other, in the same laser intensity region where the pairing effect has been found.
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Submitted 1 June, 2015; v1 submitted 26 September, 2014;
originally announced September 2014.
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Pre-Excitation Studies for Rubidium-Plasma Generation
Authors:
M. Aladi,
J. S. Bakos,
I. F. Barna,
A. Czitrovszky,
G. P. Djotyan,
P. Dombi,
D. Dzsotjan,
I. B. Földes,
G. Hamar,
P. N. Ignácz,
M. Kedves,
A. Kerekes,
P. Lévai,
I. Márton,
A. Nagy,
D. Oszetzky,
M. A. Pócsai,
P. Rácz,
B. Ráczkevi,
J. Szigeti,
Zs. Sörlei,
R. Szipőcs,
D. Varga,
K. Varga-Umbrich,
S. Varró
, et al. (2 additional authors not shown)
Abstract:
The key element in the Proton-Driven-Plasma-Wake-Field-Accelerator (AWAKE) project is the generation of highly uniform plasma from Rubidium vapor. The standard way to achieve full ionization is to use high power laser which can assure the over-barrier-ionization (OBI) along the 10 meters long active region. The Wigner-team in Budapest is investigating an alternative way of uniform plasma generatio…
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The key element in the Proton-Driven-Plasma-Wake-Field-Accelerator (AWAKE) project is the generation of highly uniform plasma from Rubidium vapor. The standard way to achieve full ionization is to use high power laser which can assure the over-barrier-ionization (OBI) along the 10 meters long active region. The Wigner-team in Budapest is investigating an alternative way of uniform plasma generation. The proposed Resonance Enhanced Multi Photon Ionization (REMPI) scheme probably can be realized by much less laser power. In the following the resonant pre-excitations of the Rb atoms are investigated, theoretically and the status report about the preparatory work on the experiment are presented.
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Submitted 10 September, 2013;
originally announced September 2013.
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Hysteresis phenomena in electron tunneling, induced by surface plasmons
Authors:
Norbert Kroo,
Sandor Varro,
Peter Racz
Abstract:
A high spatial resolution surface plasmon near field scanning tunneling microscope (STM) has been used to study the properties of localized surface plasmons (SPO) in so-called hot spots on a gold surface, where the local electromagnetic field is extremely high. A CW semiconductor laser and a femtosecond Ti:Sa laser were used to excite the plasmons and the SPO excited tunnel current was used as the…
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A high spatial resolution surface plasmon near field scanning tunneling microscope (STM) has been used to study the properties of localized surface plasmons (SPO) in so-called hot spots on a gold surface, where the local electromagnetic field is extremely high. A CW semiconductor laser and a femtosecond Ti:Sa laser were used to excite the plasmons and the SPO excited tunnel current was used as the detector. When scanning the STM from negative to positive bias and reversed, hysteresis in the tunnel signal was found, excluding (or rather minimizing) the role of the presence of a Casimir effect in the process. It was found, however, that a multiple image charge induced double well potential may explain our experimental findings. The stepwise behaviour of the area of the observed hysteresis loops is a new, additional indication of the non-classical properties of the SPOs.
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Submitted 9 February, 2013;
originally announced February 2013.
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Generation of rectangular optical waves by relativistic clipping
Authors:
Sandor Varro
Abstract:
Theoretical results are reported, concerning the reflection and transmission of few-cycle laser pulses on a very thin conducting layer, which may represent the surface current density of the massless charges of graphene. It is shown that the pulse may undergo violent distortions, even at moderate intensities, to that extent, that the scattered radiation contains rectangular trains, which are appro…
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Theoretical results are reported, concerning the reflection and transmission of few-cycle laser pulses on a very thin conducting layer, which may represent the surface current density of the massless charges of graphene. It is shown that the pulse may undergo violent distortions, even at moderate intensities, to that extent, that the scattered radiation contains rectangular trains, which are approximate realizations of Rademacher functions in the optical or terahertz regime.
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Submitted 25 January, 2013;
originally announced January 2013.
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Hanbury Brown - Twiss type correlations with surface plasmon light
Authors:
Sandor Varro,
Norbert Kroo,
Daniel Oszetzky,
Attila Nagy,
Aladar Czitrovszky
Abstract:
Intensity-intensity correlations are studied for light signals stemming from the spontaneous decay of surface plasmon oscillations, generated in the Kretschmann geometry. Non-classical photon statistics and the the transition from antibunching to bunching of the electron counts have been found experimentally and analysed on a new theoretical basis.
Intensity-intensity correlations are studied for light signals stemming from the spontaneous decay of surface plasmon oscillations, generated in the Kretschmann geometry. Non-classical photon statistics and the the transition from antibunching to bunching of the electron counts have been found experimentally and analysed on a new theoretical basis.
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Submitted 9 January, 2013;
originally announced January 2013.
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Nonlinear photoemission from metal surfaces induced by short laser pulses: the effect of field enhancement by surface plasmons
Authors:
Sandor Varro,
Norbert Kroo
Abstract:
Nonlinear electron emission processes induced by surface plasmon oscillations have been studied both experimentally and theoretically. The measured above-threshold electron spectra extend up to energies whose appearance cannot be explained solely by standard non-perturbative methods, which predict photon energy separated discrete energy line spectra with the known fast fall - plateau - cutoff enve…
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Nonlinear electron emission processes induced by surface plasmon oscillations have been studied both experimentally and theoretically. The measured above-threshold electron spectra extend up to energies whose appearance cannot be explained solely by standard non-perturbative methods, which predict photon energy separated discrete energy line spectra with the known fast fall - plateau - cutoff envelope shape, even when taking the large field enhancement into account. The theoretical analysis of our data, based on the concept of plasmon-induced near-field effects, gives reasonably good explanation and qualitative agreement in the whole intensity range.
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Submitted 9 January, 2013;
originally announced January 2013.
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Synchrotron radiation in the presence of a cylindrical mirror. Note on the interference of the direct radiation and the high-order whispering-gallery modes
Authors:
Sandor Varro
Abstract:
Exact solutions are given for the Maxwell equations driven by a gyrating ultrarelativistic electron inside a reflecting cylindrical boundary. The axis of the electrons's trajectory and the axis of the surrounding cylinder are supposed to coincide. It is found that, at certain values of the ratio of the cylinder's and of the trajectory's radii, the field amplitudes diverge as functions of time. The…
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Exact solutions are given for the Maxwell equations driven by a gyrating ultrarelativistic electron inside a reflecting cylindrical boundary. The axis of the electrons's trajectory and the axis of the surrounding cylinder are supposed to coincide. It is found that, at certain values of the ratio of the cylinder's and of the trajectory's radii, the field amplitudes diverge as functions of time. The physical reason for this resonance is the constructive interference between the radiation emitted earlier and fed back by reflection to the actual position of the radiating electron.
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Submitted 30 January, 2011;
originally announced January 2011.
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Spontaneous emission of radiation by metallic electrons in the presence of electromagnetic fields of surface plasmon oscillations
Authors:
Sandor Varro,
Norbert Kroo,
Gyozo Farkas,
Peter Dombi
Abstract:
The spontaneous emission of radiation of metallic electrons embedded in a high-intensity enhanced surface plasmon field is considered analytically. The electrons are described by exact dressed quantum states which contain the interaction with the plasmon field non-perturbatively. Considerable deviations from the pertubative behaviour have been found in the intensity dependence of the emitted fun…
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The spontaneous emission of radiation of metallic electrons embedded in a high-intensity enhanced surface plasmon field is considered analytically. The electrons are described by exact dressed quantum states which contain the interaction with the plasmon field non-perturbatively. Considerable deviations from the pertubative behaviour have been found in the intensity dependence of the emitted fundamental and the second harmonic signals, even at moderate incoming laser intensities. The theoretical predictions deduced from the formalism are in good qualitative agreement with the experimental results.
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Submitted 25 October, 2009; v1 submitted 28 February, 2009;
originally announced March 2009.
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Attosecond electron pulses from interference of above-threshold de Broglie waves
Authors:
Sandor Varro,
Gyozo Farkas
Abstract:
It is shown that the the interference of above-threshold electron de Broglie waves, generated by an intense laser pulse at a metal surface yields attosecond electron pulses. This inerference is an analogon of the superposition of high harmonics generated from rare gas atoms, resulting in trains of attosecond light pulses.Owing to the inherent kinematic dispersion, the propagation of attosecond d…
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It is shown that the the interference of above-threshold electron de Broglie waves, generated by an intense laser pulse at a metal surface yields attosecond electron pulses. This inerference is an analogon of the superposition of high harmonics generated from rare gas atoms, resulting in trains of attosecond light pulses.Owing to the inherent kinematic dispersion, the propagation of attosecond de Broglie waves in vacuum is very different from that of attosecond light pulses, which propagate without changing shape. Above the metal surface there are "collaps bands" and "revival layers" of the electron current even at macroscopic distances. In the range of parameters considered, the maximum value of the current densities of such ultrashort electron pulses has been estimated to be of order of couple of tenths of milliamps per square centimeters.
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Submitted 2 May, 2007;
originally announced May 2007.
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Linear and nonlinear absolute phase effects in interactions of ultrashort laser pulses with a metal nano-layer or with a plasma layer
Authors:
Sandor Varro
Abstract:
It has been shown that in the scattered radiation, generated by an ultrashort laser pulse impinging on a metal nano-layer, non-oscillatory wake-fields appear with a definite sign. The magnitude of these wake-fields is proportional with the incoming field strength, and a sign of them is governed by the cosine of the carrier-envelope phase difference of the incoming pulse. At relativistic laser in…
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It has been shown that in the scattered radiation, generated by an ultrashort laser pulse impinging on a metal nano-layer, non-oscillatory wake-fields appear with a definite sign. The magnitude of these wake-fields is proportional with the incoming field strength, and a sign of them is governed by the cosine of the carrier-envelope phase difference of the incoming pulse. At relativistic laser intensities the target is considered as a plasma layer in vacuum, produced from a thin foil by a pre-pulse, which is followed by the main high-intensity laser pulse. The nonlinearities stemming from the relativistic kinematics of the surface current density (representing the plasma electrons) lead to the appearance of higher-harmonics in the scattered spectra. In general, the harmonic peaks are down-shited due to the presence of an intensity-dependent factor. Certain regions of these spectra are very sensitive to the variation of the carrier-envelope phase difference. The spectra has a long tail where the heigths of the peaks vary practically within one order of magnitude forming a quasi-continuum. By Fourier synthetising the components from this plateau region attosecond pulses have been obtained.
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Submitted 29 October, 2006;
originally announced October 2006.
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Scattering of a few-cycle laser pulse by a plasma layer: the role of the carrier-envelope phase difference at relativistic intensities
Authors:
Sandor Varro
Abstract:
The reflection and transmission of a few-cycle Ti:Sa laser pulse iminging on a thin plasma layer have been analysed on the basis of classical electrodynamics. An approximate analytic solution has been given for the coupled Maxwell-Lorentz equations describing the dynamics of the surface current and the composite radiation field. The nonlinearities stemming from the relativistics kinematics of fr…
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The reflection and transmission of a few-cycle Ti:Sa laser pulse iminging on a thin plasma layer have been analysed on the basis of classical electrodynamics. An approximate analytic solution has been given for the coupled Maxwell-Lorentz equations describing the dynamics of the surface current and the composite radiation field. The nonlinearities stemming from the relativistics kinematics of free electrons lead to the appearance of higher-harmonics in the scattered spectra. In our analysis particular attention has been paid to the effect of the carrier-envelope phase difference of the incoming laser pulse. For the fourth harmonic peak we calculated almost 25 percent modulation. In general, the harmonic peaks are down-shifted due to presence of the intensity-dependent factors by an order of 15-65 percent in case of an incoming field of intensity we have discussed. The spectrum of the high-harmonics has a long tail where the heights of the peaks vary within one order of magnitude forming a quasi-continuum. By Fourier synthetising the field components of this plateau region attosecond pulses have been obtained.
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Submitted 27 October, 2006;
originally announced October 2006.
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Reflection of a few-cycle laser pulse on a metal nano-layer: generation of phase-dependent wake-fields
Authors:
Sandor Varro
Abstract:
The reflection and transmission of a few-cycle femtosecond Ti:Sa laser pulse impinging on a metal nano-layer have been analysed. The thickness of the layer was assumed to be of order of 2-10 nm, and the metallic free electrons were represented by a surface current density distributed at the plane boundary of a dielectric substrate. The target studied this way can be imagined, for instance, as a…
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The reflection and transmission of a few-cycle femtosecond Ti:Sa laser pulse impinging on a metal nano-layer have been analysed. The thickness of the layer was assumed to be of order of 2-10 nm, and the metallic free electrons were represented by a surface current density distributed at the plane boundary of a dielectric substrate. The target studied this way can be imagined, for instance, as a semi-transparent mirror produced by evapotating a thin aluminum layer on the surface of a glass plate. The exact analytic solution has been given for the system of the coupled Maxwell-Lorentz equations decribing the dynamics of the surface current and the scattered radiation fields. It has been shown that in general a non-oscillatoty frozen-in wake-field appears following the main pulse with an exponential decay and with a definite sign of the electric field. The characteristic time of these wake-fields is inversely proportional with the square of the plasma frequency and with the thickness of the metal nano-layer, and can be larger than the original pulse duration. The magnitude of these wake-fields is proportional with the incoming field strength, and the definite sign of them governed by the cosine of the carrier-envelope phase difference of the incoming ultrashort laser pulse. As a consequence, when we let such a wake-field excite the electrons of a secondary target (say an electron beam, a metal plate or a gas jet), we obtain 100 percent modulation in the electron signal in a given direction, as we vary the carrier-envelope phase difference. This scheeme can perhaps serve as a basis for the construction of a robust linear carrier-envelope phase difference meter.
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Submitted 25 October, 2006;
originally announced October 2006.