<i>R</i>-matrix-Floquet theory of multiphoton processes

Burke, P. G.; Francken, Philippe; Joachain, Charles

doi:10.1088/0953-4075/24/4/005

Cited by 207 publications

(151 citation statements)

References 49 publications

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“…In the figure we make a comparison with the time-dependent R-matrix calculation by [42] which was found to be almost identical to the earlier Floquet R-matrix results by Burke et al [24]. Our data show certain trend to deviate from those obtained in Burke and Burke [42] and Burke et al [24] for smaller field intensities, around F = 0.02 a.u. This deviation could probably be attributed to difficulties of numerical character which are due to the necessity to manipulate the divergent integrals.…”

Section: The Partial Contribution Of Various Open Channels To the Totsupporting

confidence: 87%

“…Since the work of Shirley [37], it is known that if one neglects spontaneous processes in the quantum description of the interaction of laser light and atom, then the quantum picture and the Floquet method of solving the time-dependent Schrodinger equation become equiavalent. Therefore, the present approach and the ones based on the Floquet anzats (such as [24], for example) are completely equivalent. However, recasting the MPI description in the form presented below may have some practical advantages, especially if we have good means of representing the field-free atomic states for complex atomic systems.…”

Section: Introductionmentioning

confidence: 91%

“…It is this model system that was considered by Burke et al [24] in their seminal paper which gave rise to the spectacular success of the R-matrix Floquet theory. We consider here an electron bound initially in a square well potential V = −2.5 a.u.…”

Section: Nonperturbative Framework For the Description Of The Mpimentioning

confidence: 99%

See 2 more Smart Citations

Lippmann-Schwinger description of multiphoton ionization

Ivanov

Kheifets

2005

Phys. Rev. A

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We outline a formalism and develop a computational procedure to treat the process of multiphoton ionization (MPI) of atomic targets in strong laser fields. We treat the MPI process nonperturbatively as a decay phenomenon by solving a coupled set of the integral Lippmann-Schwinger equations. As basic building blocks of the theory we use a complete set of field-free atomic states, discrete and continuous. This approach should enable us to provide both the total and differential cross-sections of MPI of atoms with one or two electrons. As an illustration, we apply the proposed procedure to a simple model of MPI from a square well potential and to the hydrogen atom.

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Section: The Partial Contribution Of Various Open Channels To the Totsupporting

confidence: 87%

Section: Introductionmentioning

confidence: 91%

See 1 more Smart Citation

Lippmann-Schwinger description of multiphoton ionization

Ivanov

Kheifets

2005

Phys. Rev. A

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“…The configuration space is divided into two regions, inside and outside a sphere of radius r 0 , where r 0 is such that outside the sphere only the Coulomb force is assumed to act between the ionized electron and its parent ion. These assumptions are equivalent to those of R-matrix theory [34] and can be realized in the acceleration gauge provided r 0 > α 0 [39,40], where α 0 = √ I /ω 2 is the amplitude of electron quiver motion in the laser field.…”

Section: Near-threshold Behavior Of Multiphoton Ionization Ratesmentioning

confidence: 99%

Threshold effects in strong-field ionization: Energy shifts and Rydberg structures

2012

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The behavior of strong-field ionization rates of neutral atoms in the vicinity of multiphoton ionization thresholds is analyzed using formal collision theory. Our approach, which accounts nonperturbatively for effects of an intense laser field, shows that the ionization rates have a nearly constant behavior below and above each multiphoton threshold and that between such thresholds there are an apparently finite number of rapid oscillations due to resonances with laser-field-modified Rydberg states. This pattern is typical for any atomic target, as we illustrate specifically for hydrogen and neon atoms. The flat behavior of the ionization yield near multiphoton thresholds gives the appearance of an energy shift of the ionization thresholds, which have been postulated in a number of recent studies concerning diverse aspects of above-threshold ionization and high-harmonic generation of atoms. The flat behaviors of the rates near threshold exhibit only a rather weak dependence on the laser-field intensity. Other aspects of the near-threshold behavior of ionization rates and their dependence on the laser-field parameters are also discussed.

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“…Within the last decade, in response to technological and experimental advances, variants of time-dependent implementations utilizing the Rmatrix computational framework have appeared which have been applied to specific atomic systems, namely the time-dependent R-matrix (TDRM) method [26,27], the time-dependent B-splines R-matrix (TDBSR) method [12,28] and the present RMT method [14,29,30]. An earlier application of the R-matrix theory to multiphoton processes appeared in the form of a Floquet expansion (RMF) of the driven time-dependent wavefunction [31]. The RMF approach, although it is capable of treating the field non-perturbatively, cannot be considered as fully following the TDSE solution methodology since it is only suited to laser pulses containing many cycles.…”

Section: Introductionmentioning

confidence: 99%

R-matrix-incorporating-time method forH2+in short and intense laser fields

Broin

Nikolopoulos

2015

Phys. Rev. A

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In this work we develop an approach for a molecular hydrogen ion (H + 2 ) in the Born-Oppenheimer approximation while exposed to intense short-pulse radiation. Our starting point is the R-Matrix incorporating Time (RMT) formulation for atomic hydrogen [L. A.A. Nikolopoulos et al, Phys. Rev. A 78, 063420 (2008)] which has proven to be successful at treating multi-electron atomic systems efficiently and to high accuracy [LR Moore et al J. of Mod. Opt. 58,1132]. The present study on H + 2 has been performed with a similar objective of developing an ab initio method for solving the Time-dependent Schrödinger Equation (TDSE) for multi-electron diatomic molecules exposed to an external time-dependent potential field. The theoretical formulation is developed in detail for the molecular hydrogen ion where all the multi-electron and inter-nuclei complications are absent. As in the atomic case, the configuration space of the electron's coordinates are separated artificially over two regions; the inner (I) and outer (II) regions. In the region I the time-dependent wavefunction is expanded on the eigenstate basis corresponding to the molecule's Hamiltonian augmented by Bloch operators, while in region II a grid representation is used. We demonstrate the independence of our results on the introduced artificial boundary-surface by calculating observables that are directly accessed experimentally and also by showing gauge-dependent quantities are also invariant with the region I box size. We also compare with other theoretical works and emphasize cases where basis-set approaches are currently very computationally expensive or intractable in terms of computational resources.

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R-matrix-Floquet theory of multiphoton processes

Abstract: We propose a unified R-matrix-FLoquct method which can he used to analyse both the multiphoton ionization of a t o m and laser-assisted electron-atom collisions. Our treatment is nompertwhative and can be applied to an arbitrary LII"'II.

Cited by 207 publications

References 49 publications

Lippmann-Schwinger description of multiphoton ionization

Lippmann-Schwinger description of multiphoton ionization

Threshold effects in strong-field ionization: Energy shifts and Rydberg structures

R-matrix-incorporating-time method forH2+in short and intense laser fields

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