Sándor Varró

e-e scattering in the presence of an external field

A nonrelativistic treatment is given of electron-electron scattering in the presence of a laser field. The field is accounted for by the external field approximation and is represented by a circularly polarised monochromatic plane-wave field. A simple analytic expression is derived for the transition amplitude, which is shown to exhibit internal resonances as well as intensity-dependent shifts. The former is the nonrelativistic limit of the resonant Moller scattering predicted previously by Oleinik (1967). The latter, however, appears in a higher order of v/c and is consequently negligible for very slow electrons. The differential cross section of the scattering is also given where the effect of the spin and symmetry is teken into account explicitly. The width of resonances is introduced phenomenologically but its connection with previous methods is established. Consideration is also given to the experimental conditions under which the effects may become observable.

Attosecond electron pulses from interference of above-threshold de Broglie waves

It is shown that the above-threshold electron de Broglie waves, generated by an intense laser pulse at a metal surface are interfering to yield attosecond electron pulses. This interference of the de Broglie waves is an analog on of the superposition of high harmonics generated from rare gas atoms, resulting in trains of attosecond light pulses. Our model is based on the Floquet analysis of the inelastic electron scattering on the oscillating double-layer potential, generated by the incoming laser field of long duration at the metal surface. 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. The clean attosecond structure of the current at the immediate vicinity of the metal surface is largely degraded due to the propagation, but it partially recovers at certain distances from the surface. Accordingly, above the metal surface, there exist “collapse bands,” where the electron current is erratic or noise-like, and there exist “revival layers,” where the electron current consist of ultrashort pulses of about 250 attosecond durations in the parameter range we considered. The maximum value of the current densities of such ultrashort electron pulses has been estimated to be on order of couple of tenth of mA /cm 2 . The attosecond structure of the electron photocurrent can perhaps be used for monitoring ultrafast relaxation processes in single atoms or in condensed matter.

New exact solutions of the Dirac equation of a charged particle interacting with an electromagnetic plane wave in a medium

Exact solutions are presented of the Dirac equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction nm < 1. The found solutions are expressed in terms of new complex trigonometric polynomials, which form a doubly infinite set labelled by two integer quantum numbers. These quantum numbers represent quantized spectra of the energy–momentum components of the charged particle along the polarization vector and along the propagation direction of the applied electromagnetic plane wave field (which is considered as a laser field of arbitrarily high intensity propagating in an underdense plasma). The found solutions may serve as a basis for the description of possible quantum features of mechanisms for the acceleration of electrons by high-intensity laser fields.

Linear and nonlinear absolute phase effects in interactions of ulrashort laser pulses with a metal nano-layer or with a thin plasma layer

It has been shown that in the scattered radiation, generated by an ultrashort laser pulse impinging on a metal nano-layer, non-oscillatory wakefields appears with a definite sign. The magnitude of these wakefields is proportional to the incoming field strength, and the definite sign of them is governed by the cosine of the carrier-envelope phase difference of the incoming pulse. When we let such a Wakefield excite the electrons of a secondary target (say an electron beam, a metal surface or a gas jet), we can obtain 100 percent modulation in the electron signal in a given direction. This scheme can serve as a basis for the construction of a robust linear carrier-envelope phase difference meter. At relativistic laser intensities, the target is considered as a plasma layer in vacuum produced from a thin foil by a prepulse, which is followed by the main high-intensity laser pulse. The nonlinearities stemming from the relativistic kinematics lead to the appearance of higher-order harmonics in the scattered spectra. In general, the harmonic peaks are downshifted due to the presence of an intensity-dependent factor. This phenomenon is analogous to the famous intensity-dependent frequency shift in the nonlinear Thomson scattering on a single electron. In our analysis, an attention has also been paid to the role of the carrier-envelope phase difference of the incoming few-cycle laser pulse. It is also shown that the spectrum has a long tail where the heights of the peaks vary practically within one order of magnitude forming a quasi-continuum. Fourier synthesizing the components from this plateau region attosecond pulses has obtained.

A new class of exact solutions of the Klein–Gordon equation of a charged particle interacting with an electromagnetic plane wave in a medium

Exact solutions are presented of the Klein–Gordon equation of a charged particle moving in a transverse monochromatic plasmon wave of arbitrary high amplitude, which propagates in an underdense plasma. These solutions are expressed in terms of Ince polynomials, forming a doubly infinite set, parametrized by discrete momentum components of the charged particles de Broglie wave along the polarization vector and along the propagation direction of the plasmon radiation. The envelope of the exact wavefunctions describes a high-contrast periodic structure of the particle density on the plasma length scale, which may have relevance in novel particle acceleration mechanisms.

Quantum metal optics

Experimental and theoretical studies of the statistical properties of surface plasmon polaritons (SPOs) are described. Both classical and non-classical properties of surface plasmons are analysed. The temporal statistical behaviour at low excitation level, as measured by detecting the SPO emitted photon statistics as expressed by the correlation function and the temporal photon count distribution, show that the SPOs preserve the photon statistics of the laser. In the spatial distribution of the plasmon field as measured by an STM, squeezing, i.e. non-classical properties, were found. Independent simple model calculations confirmed the existence of both enhanced EM fields of surface plasmons and their squeezed character.

Optically induced band structure of free electrons in an external plane wave field

The motion of a non-relativistic free charged particle in a classical electromagnetic plane wave field is investigated. By introducing the ansatz of a modulated plane wave for the wavefunction, the problem is reduced to the solution of the general Mathieu equation for a circularly polarised field and to the solution of the Hill equation for a linearly polarised field. The corresponding eigenvalue equations show that physical values of the energy are separated into bands. The relationship with earlier methods is also discussed.

Entangled states and entropy remnants of a photon–electron system

In the present paper, an example of entanglement between two different kinds of interacting particles, photons and electrons is analysed. The initial-value problem of the Schrodinger equation is solved non-perturbatively for the system of a free electron interacting with a quantized mode of electromagnetic radiation. Wave packets of the dressed states so obtained are constructed in order to describe the spatio-temporal separation of the subsystems before and after interaction. The joint probability amplitudes are calculated for the detection of the electron at some space–time location and the detection of a definite number of photons. The analytical study of the time evolution of entanglement between the initially separated electron wave packet and the radiation mode leads to the conclusion that in general there are non-vanishing entropy remnants in the subsystems after the interaction. On the basis of the simple model to be presented here, the calculated values of the entropy remnants crucially depend on the character of the assumed switching-on and -off of the interaction.

New exact solutions of the Dirac and Klein–Gordon equations of a charged particle propagating in a strong laser field in an underdense plasma

Abstract Exact solutions are presented of the Dirac and Klein–Gordon equations of a charged particle propagating in a classical monochromatic electromagnetic plane wave in a medium of index of refraction n m

Nonlinear photoelectron emission from metal surfaces induced by short laser pulses: the effects of field enhancement by surface plasmons

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 high 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 surface near-field effects, gives a reasonably good explanation and qualitative agreement in the whole intensity range.