Strong-field approximation for harmonic generation in diatomic molecules

Chirilă, C. C.; Lein, Manfred

doi:10.1103/physreva.73.023410

Cited by 105 publications

(98 citation statements)

References 41 publications

(83 reference statements)

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“…The length and velocity gauges, where the interaction terms are given by E · r and A · p, respectively, are both widely used in the literature. For extended systems, we note here that the length gauge results in a nonphysical origin dependence of the spectra with no upper limit of the cutoff frequency as the maximum distance between two site atoms becomes increasingly large [26,27]. We therefore describe the ionization in the velocity gauge, which, in contrast, gives a cutoff behavior for two atoms with increasing internuclear distance R, in agreement with exact calculations.…”

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confidence: 70%

High-order harmonic generation from graphene: Strong attosecond pulses with arbitrary polarization

2013

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We explore high-order harmonic generation (HHG) from a graphene sheet exposed to intense femtosecond laser pulses based on the Lewenstein model. It is demonstrated that the HHG cutoff frequency increases with graphene size up to the classical limit for distant diatomic systems. In contrast to two-center systems, the cutoff frequency remains constant with increasing power of the harmonics as the graphene diameter extends beyond maximal electron excursion. It is shown that the extended nature of the graphene sheet allows for strong HHG signals at maximum cutoff for linearly as well as circularly polarized laser pulses, the latter opening for generation of strong circularly polarized attosecond pulses. High-order harmonic generation (HHG) refers to the nonlinear process of creation of very high overtones of an intense laser pulse with central frequency ω 0 , which interacts with a dilute gas of atoms or molecules. The realization of laser intensities beyond 10 14 W/cm 2 paved the way for theoretical studies [1,2] and experiments [3][4][5] on HHG from a gas of atoms in the early 1990s. Now, after about 20 years of intense HHG research, the three-step model [6] describing HHG within a single-atom picture is well established: The atom (i) ionizes, (ii) gains energy when accelerated by the electric field in the continuum, and (iii) eventually recombines with the ion emitting a photon at odd multiples of the driving-field frequency. Since a single excursion and recombination of an electron takes place within one-half optical cycle, the generated HHG photons define a coherent attosecond highfrequency laser pulse which is a unique tool for probing and imaging of ultrafast dynamics [7][8][9]. In laser-based imaging the HHG spectra have been used for tomographic reconstruction of molecular orbitals withångström spatial resolution [10][11][12].In recent years HHG following interaction with molecules has received particular attention. First, it has been shown that ionization at one molecular center and recombination at another allows for larger maximum harmonic frequencies [13,14]. Second, the two-center structure allows for the generation of attosecond pulses with elliptical polarization as well as even harmonics if the inversion symmetry is broken [15,16]. It has been shown theoretically that a preprepared molecular medium can be used to produce controlled secondary attosecond pulses, when exposed to a seed attosecond XUV pulse [17]. In addition, the study of HHG has been advancing towards molecules of increasing complexity such as benzene rings [18], fullerenes [19], and carbon nanotubes [20], including the investigation of symmetry properties essential for the selective generation of high-order harmonics.The realization of graphene [21], a two-dimensional monolayer of carbon atoms, has received explosive interest in the last decade due to its extraordinary physical properties such * stian.sorngard@ift.uib.no † sigrid.simonsen@ift.uib.no as its superior strength and electronic conductivity. What was for years believed to b...

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confidence: 70%

High-order harmonic generation from graphene: Strong attosecond pulses with arbitrary polarization

2013

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“…This approach will be called either "Lewenstein model" or "SFA" interchangeably in this thesis. SFA has also been applied to study the characteristics of HHG from molecular targets [85][86][87][88][89][90][91][92]. In the following we derive the Lewenstein model for an atomic target in detail, and then it is extended for a molecular target straightforwardly.…”

Section: Strong-field Approximationmentioning

confidence: 99%

Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium

Jin

2013

Springer Theses

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In this thesis, we establish the theoretical tools to investigate high-order harmonic generation (HHG) by intense infrared lasers in a gaseous medium. The macroscopic propagation of both the fundamental and the harmonic fields is taken into account by solving Maxwell's wave equations, while the single-atom (or single-molecule) response is obtained by quantitative rescattering theory. The initial spatial mode of the fundamental laser is assumed either a Gaussian or a truncated Bessel beam. On the examples of Ar, N 2 and CO 2 , we demonstrate that the available experimental HHG spectra with isotropic and aligned target media can be accurately reproduced theoretically even though the HHG spectra are sensitive to the experimental conditions. We show that the macroscopic HHG can be expressed as a product of a macroscopic wave packet and a photorecombination cross section, where the former depends on laser and experimental conditions while the latter is the property of the target only. The factorization makes it possible to retrieve the single-atom or single-molecule structure information from experimental HHG spectra. As for the multiple molecular orbital contribution in HHG, it causes the disappearance of the minimum in the HHG spectrum of aligned N 2 with the increase of laser intensity, and the position of minimum in HHG spectrum of aligned CO 2 depending on many factors is also attributed to it, which could explain why the minima observed in different laboratories may differ. For an important application of HHG as ultrashort light source, we show that measured continuous harmonic spectrum of Xe due to the reshaping of the fundamental laser field can be used to produce an isolated attosecond pulse by spectral and spatial filtering in the far field. For on-going application of using HHG to ionize aligned molecules, we present the photoelectron angular distribution from aligned N 2 and CO 2 in the laboratory frame, which can be compared directly with future experiments. demonstrate that the available experimental HHG spectra with isotropic and aligned target media can be accurately reproduced theoretically even though the HHG spectra are sensitive to the experimental conditions. We show that the macroscopic HHG can be expressed as a product of a macroscopic wave packet and a photorecombination cross section, where the former depends on laser and experimental conditions while the latter is the property of the target only. The factorization makes it possible to retrieve the single-atom or single-molecule structure information from experimental HHG spectra. As for the multiple molecular orbital contribution in HHG, it causes the disappearance of the minimum in the HHG spectrum of aligned N 2 with the increase of laser intensity, and the position of minimum in HHG spectrum of aligned CO 2 depending on many factors is also attributed to it, which could explain why the minima observed in different laboratories may differ. For an important application of HHG as ultrashort light source, we show that measured continu...

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“…(8), the term related to the lack of orthogonality between bound state and continuum states that occurs in the SFA has been removed by hand. This is a widely used procedure, and it is related to the fact that this term blurs the two-center interference condition (see [28,29,35] for discussions).…”

Section: A Transition Amplitudementioning

confidence: 99%

“…The SFA, however, has serious limitations. Apart from the gauge dependence and its influence on the structural interference [28,29,35], different forms of recombination dipole matrix element affect this condition [31,36,37]. The most appropriate form to be used has raised considerable debate in the context of the tomographical reconstruction of molecular orbitals [38][39][40] If the field however is orthogonally polarized, the electron's angle of return is effectively incorporated in the two-center interference condition.…”

Section: Introductionmentioning

confidence: 99%

“…A particularly good method for assessing this type of interference is the strong-field approximation (SFA), which allows an intuitive interpretation of the problem in terms of electron orbits. For that reason, it has been widely employed in the study of molecules [25][26][27][28][29][30][31][32][33][34]). The SFA, however, has serious limitations.…”

Section: Introductionmentioning

confidence: 99%

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Shifting nodal-plane suppressions in high-order-harmonic spectra from diatomic molecules in orthogonally polarized driving fields

Das¹,

Faria²

2016

Phys. Rev. A

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We analyze the imprint of nodal planes in high-order harmonic spectra from aligned diatomic molecules in intense laser fields whose components exhibit orthogonal polarizations. We show that the typical suppression in the spectra associated to nodal planes is distorted, and that this distortion can be employed to map the electron's angle of return to its parent ion. This investigation is performed semi-analytically at the single-molecule response and single-active orbital level, using the strong-field approximation and the steepest descent method. We show that the velocity form of the dipole operator is superior to the length form in providing information about this distortion. However, both forms introduce artifacts that are absent in the actual momentum-space wavefunction. Furthermore, elliptically polarized fields lead to larger distortions in comparison to two-color orthogonally polarized fields. These features are investigated in detail for O2, whose highest occupied molecular orbital provides two orthogonal nodal planes.

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Strong-field approximation for harmonic generation in diatomic molecules

Cited by 105 publications

References 41 publications

High-order harmonic generation from graphene: Strong attosecond pulses with arbitrary polarization

High-order harmonic generation from graphene: Strong attosecond pulses with arbitrary polarization

Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium

Shifting nodal-plane suppressions in high-order-harmonic spectra from diatomic molecules in orthogonally polarized driving fields

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