Harmonic generation in keldysh-type models

Ehlotzky, F.

doi:10.1007/bf02457041

Cited by 17 publications

(13 citation statements)

References 15 publications

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“…Here, we discuss an alternative method to calculate photoelectron spectra from atomic systems by analytically solving the TDSE under the so-called Strong Field Approximation. This approach dates back to Keldysh [41], and has since been employed by many other authors [27][28][29][42][43][44][45][46]. It is worth noted that SFA provides a quantum framework and extension of the, so called, "simple man's" or "three step" or "re-collision" model, usually attributed to P.…”

Section: Tudesmentioning

confidence: 99%

Above-threshold ionization and photoelectron spectra in atomic systems driven by strong laser fields

et al. 2015

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Above-threshold ionization (ATI) results from strong field laser-matter interaction and it is one of the fundamental processes that may be used to extract electron structural and dynamical information about the atomic or molecular target. Moreover, it can also be used to characterize the laser field itself. Here, we develop an analytical description of ATI, which extends the theoretical Strong Field Approximation (SFA), for both the direct and re-scattering transition amplitudes in atoms. From a non-local, but separable potential, the bound-free dipole and the re-scattering transition matrix elements are analytically computed. In comparison with the standard approaches to the ATI process, our analytical derivation of the re-scattering matrix elements allows us to study directly how the re-scattering process depends on the atomic target and laser pulse features -we can turn on and off contributions having different physical origins or corresponding to different physical mechanisms. We compare SFA results with the full numerical solutions of the time-dependent Schrödinger equation (TDSE) within the few-cycle pulse regime. Good agreement between our SFA and TDSE model is found for the ATI spectrum. Our model captures also the strong dependence of the photoelectron spectra on the carrier envelope phase of the laser field.

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Section: Tudesmentioning

confidence: 99%

Above-threshold ionization and photoelectron spectra in atomic systems driven by strong laser fields

et al. 2015

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“…It is a generalization of the Keldysh-Faisal-Reiss approximation [71,56,129], applied to the problem of harmonic generation. It was for the first time formulated in the context of harmonics by Ehlotzky [52]; it is also strongly related to the, so called, Becker model of an atom with a zero range pseudo-potential interacting with the laser field (see below).…”

Section: A Single Atom Theoriesmentioning

confidence: 99%

Study of The Spatial and Temporal Coherence of High-Order Harmonics

Salières

L’Huillier

Antoine

et al. 1999

Advances in Atomic, Molecular, and Optical Physics

318

147

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We apply the theory of high-order harmonic generation by low-frequency laser fields in the strong field approximation to the study of the spatial and temporal coherence properties of the harmonics. We discuss the role of dynamically induced phases of the atomic polarization in determining the optimal phase matching conditions and angular distributions of harmonics. We demonstrate that the phase matching and the spatial coherence can be controlled by changing the focusing parameters of the fundamental laser beam. Then we present a detailed study of the temporal and spectral properties of harmonics. We discuss how the focusing conditions influence the individual harmonic spectra and time profiles, and how the intensity dependence of the dynamically induced phase leads to a chirp of the harmonic frequency. This phase modulation can be used to control the temporal and spectral properties of the harmonic radiation. Temporally, the harmonic chirped pulse can be recompressed to very small durations. Spectrally, chirping of the fundamental beam may be employed to compensate for the dynamically induced chirp and to control the individual harmonic spectrum. Finally, we discuss the short pulse effects, in particular nonadiabatic phenomena and the possibility of generating attosecond pulses.

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“…The semiconductor Bloch equations (101,102) are too complex to solve directly other than numerically but, as in the atomic case, they are subject to the Keldysh approximation [33] which allows us to give an approximate expression for the current,…”

Section: Sfa For Solidsmentioning

confidence: 99%

Symphony on strong field approximation

et al. 2019

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In the last three decades, we have witnessed incredible advances in laser technology and in the understanding of nonlinear laser-matter interactions, crowned recently by the award of the Nobel prize to Gérard Mourou and Donna Strickland [1,2]. It is now routinely possible to produce few-cycle femtosecond (1 fs = 10 −15 s) laser pulses in the visible and mid-infrared regimes [3,4]. By focusing such ultrashort laser pulses on gas or solid targets, possibly in a presence of nano-structures [5], the targets are subjected to an ultra-intense electric field, with peak field strengths approaching the binding field inside the atoms themselves. Such fields permit the exploration of the interaction between strong electromagnetic coherent radiation and an atomic or molecular system with unprecedented spatial and temporal resolution [6]. On one hand, HHG nowadays can be used to generate attosecond pulses in the extreme ultraviolet [7,8], or even in the soft X-ray regime [9]. Such pulses themselves may be used for dynamical spectroscopy of matter; despite carrying modest pulse energies, they exhibit excellent coherence properties [10,11]. Combined with femtosecond pulses they can also be used to extract information about the laser pulse electric field itself [12]. HHG sources therefore offer an important alternative to other sources of XUV and X-ray radiation: synchrotrons, free electron lasers, X-ray lasers, and laser plasma sources. Moreover, HHG pulses can provide information about the structure of the target atom, molecule or solid [13][14][15]. Of course, to decode such information from a highly nonlinear HHG signal is a challenge, and that is why a possibly perfect, and possibly "as analytical as possible" theoretical understanding of these processes is in high demand. Here is the first instance where SFA offers its basic services.Since electronic motion is governed by the waveform of the laser electric field, an important quantity to describe the electric field shape is the so-called absolute phase or carrier-envelope phase (CEP). Control over the CEP is paramount for extracting information about electron dynamics, and to retrieve structural information from atoms and molecules [13,16,17]. For instance, in HHG an electron is liberated from an atom or molecule through ionization, which occurs close to the maximum of the electric field. Within the oscillating field, the electron can thus accelerate along oscillating trajectories, which may result in recollision with the parent ion, roughly when the laser field approaches a zero value. Control over the CEP is particularly important for HHG, when targets are driven by laser pulses comprising only one or two optical cycles. In that situation the CEP determines the relevant electron trajectories, i.e. the CEP determines whether emission results in a single or in multiple attosecond bursts of radiation [16,18].The influence of the CEP on electron emission is also extremely important. It was demonstrated for instance in an anti-correlation experiment, in which the number of AT...

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Harmonic generation in keldysh-type models

Cited by 17 publications

References 15 publications

Above-threshold ionization and photoelectron spectra in atomic systems driven by strong laser fields

Above-threshold ionization and photoelectron spectra in atomic systems driven by strong laser fields

Study of The Spatial and Temporal Coherence of High-Order Harmonics

Symphony on strong field approximation

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