Publisher's Note: Generation of a broadband xuv continuum in high-order-harmonic generation by spatially inhomogeneous fields [Phys. Rev. A<b>85</b>, 013416 (2012)]

Yavuz, İlhan; Bleda, Erdi A.; Altun, Zikri; Topçu, Türker

doi:10.1103/physreva.85.029905

Cited by 45 publications

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“…These two features are mainly due to the spatial variation at a nanometer scale of the laser electric field along the laser polarization axis (see e.g. [11][12][13][14][15]). …”

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confidence: 99%

Double-electron recombination in high-order-harmonic generation driven by spatially inhomogeneous fields

2016

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We present theoretical studies of high-order harmonic generation (HHG) driven by plasmonic fields in two-electron atomic systems. Comparing the two-active electron and single-active electron approximation models of the negative hydrogen ion atom, we provide strong evidence that a double non-sequential two-electron recombination appears to be the main responsible for the HHG cutoff extension. Our analysis is carried out by means of a reduced one-dimensional numerical integration of the two-electron time-dependent Schrödinger equation (TDSE), and on investigations of the classical electron trajectories resulting from the Newton's equation of motion. Additional comparisons between the negative hydrogen ion and the helium atom suggest that the double recombination process depends distinctly on the atomic target. Our research paves the way to the understanding of strong field processes in multi-electronic systems driven by spatially inhomogeneous fields.PACS numbers: 42.65. Ky, 32.80.Rm, 33.20.Xx, 32.80 Qk, 42.50 Ct The incessant development of ultrafast, femtosecond (10 −15 fs) laser technology in the infrared (IR) regime opened new avenues to study a wide range of strong-field laser matter processes at their natural time scale [1][2][3]. These invaluable experimental and technological tools allowed physicists to address instrumental aspects of one of the most fundamental processes: the tunneling ionization of atoms and molecules [3]. In particular, the application of this laser technology provided a key factor for the understanding of the main mechanisms underlying the emission of coherent radiation from atoms or molecules [2, 4-6].As a matter of fact, one could say the high-order harmonic generation (HHG) process fits within the tunneling ionization regime, when the Keldysh parameter, defined by γ = Ip 2Up , is γ ≤ 1. I p and U p = E 2 0 4ω 2 0 denote here the ionization potential of the atomic target, and the electron ponderomotive potential energy in atomic units, respectively. E 0 is the peak amplitude of the laser electric field and ω 0 the carrier frequency. The so-called three-step or "simple man's" picture describes the underlying physics behind the HHG phenomenon [5]. In the first step, occurring about the maximum of the strong laser electric field, the Coulomb potential is deformed in such a way that a potential barrier is formed. Then, the electron is able to tunnel out throughout this "atomic barrier", and the atom is then ionized. In the second step, or better to say phase, once the electron is in the continuum, the electric field of the laser accelerates it. Naturally, the electron gains energy from the oscillating field, converting it into a kinetic energy. Consequently, when the electric field changes its sign, the electron reverses the direction of its motion and has a certain probability to recombine back to the ground state of the remaining ion-core. In this third step it emits its energy excess as an attosecond burst of coherent radiation, typically in the XUV or EUV spectral range. In partic...

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“…These two features are mainly due to the spatial variation at a nanometer scale of the laser electric field along the laser polarization axis (see e.g. [11][12][13][14][15]). …”

mentioning

confidence: 99%

Double-electron recombination in high-order-harmonic generation driven by spatially inhomogeneous fields

2016

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“…As a consequence, spatially arranged nanostructures open a wide range of possibilities to enhance or shape the spectral and spatial properties of the fundamental laser field and the harmonic field [19]. These two features imply strong modifications in the harmonic spectra which will raise the interest of the strong field community to utilize nanoparticles surrounded by gas atoms or molecules as a new type of target [22][23][24][25]. However, the initial thrill about the utilization of plasmonic fields for HHG in the XUV range, was put in debate by recent findings [26][27][28].…”

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confidence: 99%

High-order-harmonic generation by enhanced plasmonic near-fields in metal nanoparticles

et al. 2013

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We present theoretical investigations of high-order harmonic generation (HHG) resulting from the interaction of noble gases with localized surface plasmons. These plasmonic fields are produced when a metal nanoparticle is subject to a few-cycle laser pulse. The enhanced field, which largely depends on the geometrical shape of the metallic structure, has a strong spatial dependency. We demonstrate that the strong non-homogeneity of this laser field plays an important role in the HHG process and leads to a significant increase of the harmonic cut-off energy. In order to understand and characterize this new feature, we include the functional form of the laser electric field obtained from recent attosecond streaking experiments [F. Süßmann and M. F. Kling, Proc. of SPIE, Vol. 8096, 80961C (2011)] in the time dependent Schrödinger equation (TDSE). By performing classical simulations of the HHG process we show consistency between them and the quantum mechanical predictions. These allow us to understand the origin of the extended harmonic spectra as a selection of particular trajectory sets. The use of metal nanoparticles shall pave a completely new way of generating coherent XUV light with a laser field which characteristics can be synthesized locally. When matter, i.e. atoms or molecules, is exposed to short and intense laser radiation, non-linear phenomena are triggered as a consequence of this interaction. Amongst these phenomena, high-order harmonics generation (HHG) process [1, 2] has attracted considerable interests, since it is one of the most reliable pathways to generate coherent light from the ultraviolet (UV) to extreme ultraviolet (XUV) spectral range. As a result, HHG has proven to be a robust source for the generation of a PHz attosecond pulses train [3], that can be temporally confined to a single XUV attosecond pulse, now with kHz repetition rates [4]. Thanks to its remarkable properties, HHG can be used as well to extract temporal and spatial information with both attosecond and subAngström resolution on the generating system [5]. Hence, HHG represents a considerable tool to enable scrutinizing the atomic world with its natural temporal and spatial scales [6][7][8][9][10][11].The intuitive physical mechanism behind HHG, for a single atom or molecule (referred to as 'single emitter'), has been well established in the so-called three steps or simple man's model [12][13][14]: in the first step, an electronic wave packet is released the continuum by tunnel ionization through the potential barrier as a consequence of the non-perturbative interaction of the single emitter with the laser field. In the second step, the emitted electronic wave packet propagates away from its ionic core in the continuum to be finally driven back when the laser electric field changes its sign. In the final step, upon its return, the electronic wave packet may recombine with the core and the system relaxes the excess kinetic energy acquired by radiating a high-harmonic photon.In order to experimentally control the high harmonic ...

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“…As in the case of homogeneous fields, we include an horizontal line with the value of the semiclassical cutoff and we can observe that the HHG driven by this spatially (linear) nonhomogeneous fields reaches cutoff values of harmonic order far beyond this conventional limit (see e.g. [13,14,15]). …”

Section: The Linear Casementioning

confidence: 99%

“…Starting with the seminal experiment of Kim et al [12], the activity on this field has been constant, lively and not without controversy (see e.g. [13,14,15,16,17,18,21,22,23,24,25,26]). We point out, however, that the discussion about the experimental feasibility of this process falls out of the aim of the present work.…”

Section: High-order Harmonic Generation (Hhg) Driven By Spatial Inhommentioning

confidence: 99%

“…The function named TionTrecLinear allow us to calculate the recombination times t rec as a function of the ionization times t ion by solving numerically the Newton-Lorentz equation of motion for an electron moving in an oscillating and (linear) spatially varying electric field. A new variable, β, is needed in order to perform the classical simulations and it governs the inhomogeneity strength [13,14,15]. A typical example can be obtained by using:…”

Section: The Linear Casementioning

confidence: 99%

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ClassSTRONG: Classical simulations of strong field processes

Ciappina

Pérez-Hernández

Lewenstein

2014

Computer Physics Communications

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A set of Mathematica functions is presented to model classically two of the most important processes in strong field physics, namely high-order harmonic generation (HHG) and above-threshold ionization (ATI). Our approach is based on the numerical solution of the Newton-Lorentz equation of an electron moving on an electric field and takes advantage of the symbolic languages features and graphical power of Mathematica. Similarly as in the Strong Field Approximation (SFA), the effects of atomic potential on the motion of electron in the laser field are neglected. The SFA has proven to be an essential tool in strong field physics in the sense that it is able to predict with great precision the harmonic (in the HHG) and energy (in the ATI) limits. We have extended substantially the conventional classical simulations, where the electric field is only dependent on time, including spatial nonhomogeneous fields and spatial and temporal synthesized fields. Spatial nonhomogeneous fields appear when metal nanosystems interact with strong and short laser pulses and temporal synthesized fields are routinely generated in attosecond laboratories around the world. Temporal and spatial synthesized fields have received special attention nowadays because they would allow to exceed considerably the conventional harmonic and electron energy frontiers. Classical simulations are an invaluable tool to explore exhaustively the parameters domain at a cheap computational cost, before massive quantum mechanical calculations, absolutely indispensable for detailed analysis, are performed. Nature of problem: The Mathematica functions model high-order harmonic generation (HHG) and above-threshold ionization (ATI) using the classical equations of motion of an electron moving in an oscillating electric field. In Strong Field Physics HHG and ATI represent two of the most prominent examples of the nonperturbative interaction between strong laser sources and matter. In HHG an atomic or molecular bound electron is put into the continuum by the external laser electric field. Due to the oscillatory nature of the electromagnetic radiation, the electron is steered back and recombines with the parent ion converting its kinetic energy as high energy photons. For ATI the electron is laser-ionized in the same way as in HHG, but in its return it is elastically rescattered by the parent ion gaining even more kinetic energy. We incorporate functions for different laser pulse envelopes, namely sine-squared, gaussian, trapezoidal and numerically defined by the user. In addition we relax the assumption of spatial homogeneity of the laser electric field, allowing weak spatial variations with different functional forms. Finally we combine spatial and temporal synthesized laser fields to produce HHG and ATI. For all the cases the functions allow the extraction of pre-formatted graphs as well as raw data which can be used to generate plots with other graphical programs. PACSSolution method: The functions employ the numerical solution of the NewtonLorentz equat...

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Publisher's Note: Generation of a broadband xuv continuum in high-order-harmonic generation by spatially inhomogeneous fields [Phys. Rev. A85, 013416 (2012)]

Cited by 45 publications

References 0 publications

Double-electron recombination in high-order-harmonic generation driven by spatially inhomogeneous fields

Double-electron recombination in high-order-harmonic generation driven by spatially inhomogeneous fields

High-order-harmonic generation by enhanced plasmonic near-fields in metal nanoparticles

ClassSTRONG: Classical simulations of strong field processes

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