Generation of isolated attosecond pulses by polarization gating of high-order harmonic emission from $\boldsymbol {\rm H_2^+}$ in intense ultrashort laser fields

Safaei, Nehzat

doi:10.1088/1612-202x/aa9318

Cited by 6 publications

(13 citation statements)

References 29 publications

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“…Having computed x‐ or y‐component of dipole acceleration a x ( y ) via Equation (), the profile of the attosecond pulse for each direction is obtainable superposing different harmonics orders 62

I_{x (y)} (t) = {|\sum a_{x {(y)}_{q}} e^{italiciqωt}|}^{2}

where

a_{x {(y)}_{q}} = \int a_{x ((), y)} ((), t) e^{- italiciqwt} normald t .

The time‐frequency profiles of the high harmonics w ( ω , t ) are also obtained via a Morlet wavelet transform of the time‐dependent dipole acceleration

w ((),, ω, t) = \sqrt{\frac{ω}{π^{\frac{1}{2}} σ}} \int_{- \infty}^{\infty} a ((), t^{'}) e^{- italiciω ((), t^{'} - t)} e^{- \frac{ω^{2} {(t^{'} - t)}^{2}}{2 σ^{2}}} d t^{'}

where we set the Gaussian width σ = 2 π in this work.…”

Section: Resultsmentioning

confidence: 99%

“…and the intensity of I = 3 Â 10 14 W/cm 2 for ϕ = 0 and ϕ = π/2 similar to. 62 In Figure 6, we have illustrated the SAP achieved from SCS approach using polarization gating technique for carrier envelope phase ϕ = 0 (left panel) and ϕ = π/2 (right panel). The simulation results in Figure 6 obtained by averaging the expectation value of the acceleration of the single electron along x and y directions over 40 different random simulations (each contains a total number of 12,000 CSs = 3000 internal CSs + 9000 external CSs).…”

Section: Sap Generationmentioning

confidence: 99%

“…Such a field is the central idea behind the generation of single attosecond pulses (SAP). 61,62 Throughout this paper, atomic units (a.u. ), e = ℏ = m e = 1 are used unless stated otherwise.…”

Section: Introductionmentioning

confidence: 99%

“…Subsequently, as a complementary work and an application of the SCS approach, the

H_{2}^{+}

system is introduced to a 10 cycle circularly polarized laser pulse with a polarization gate. Such a field is the central idea behind the generation of single attosecond pulses (SAP) 61,62 …”

Section: Introductionmentioning

confidence: 99%

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High‐order harmonic generation by static coherent states method in single‐electron atomic and molecular systems

et al. 2021

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We solve the time-dependent Schrodinger equation using the coherent states as basis sets for computing high harmonic generation (HHG) in a full-dimensional singleelectron "realistic" system. We apply the static coherent states (SCS) method to investigate HHG in the hydrogen molecular ion induced by a linearly polarized laser field. We show that SCS gives reasonable agreement compared to the three dimensional unitary split-operator approach. Next, we study isolated attosecond pulse gen-To do so, we employ the well-known polarization gating technique, which combines two delayed counter-rotating circular laser pulses, and opens up a gate at the central portion of the superposed pulse. Our results suggest that the SCS method can be used for full-dimensional quantum simulation of higher dimensional systems such as the hydrogen molecule in the presence of an external laser field.

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I_{x (y)} (t) = {|\sum a_{x {(y)}_{q}} e^{italiciqωt}|}^{2}

where

a_{x {(y)}_{q}} = \int a_{x ((), y)} ((), t) e^{- italiciqwt} normald t .

The time‐frequency profiles of the high harmonics w ( ω , t ) are also obtained via a Morlet wavelet transform of the time‐dependent dipole acceleration

w ((),, ω, t) = \sqrt{\frac{ω}{π^{\frac{1}{2}} σ}} \int_{- \infty}^{\infty} a ((), t^{'}) e^{- italiciω ((), t^{'} - t)} e^{- \frac{ω^{2} {(t^{'} - t)}^{2}}{2 σ^{2}}} d t^{'}

where we set the Gaussian width σ = 2 π in this work.…”

Section: Resultsmentioning

confidence: 99%

Section: Sap Generationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Subsequently, as a complementary work and an application of the SCS approach, the

H_{2}^{+}

system is introduced to a 10 cycle circularly polarized laser pulse with a polarization gate. Such a field is the central idea behind the generation of single attosecond pulses (SAP) 61,62 …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High‐order harmonic generation by static coherent states method in single‐electron atomic and molecular systems

et al. 2021

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show abstract

“…This approach is implementable for simulating systems with a limited number of particles in a limited region of momentum or coordinate space. There are different TDSE approaches for simulating the electron dynamics in an atomic or molecular laser-induced system in one, two, or three (full) coordinate (or momentum) dimensions [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Some of the TDSE approaches treat the nuclei in the laser-induced system dynamically using classical or quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Static Coherent States Method: One- and Two-Electron Laser-Induced Systems with Classical Nuclear Dynamics

2018

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Featured Application: We present a new computational method that can be used to investigate the quantum dynamics of one-or two-electron systems during interaction with an ultrashort laser pulse, including nuclear dynamics. The inclusion of both electronic and nuclear degrees of freedom allows for a description of a wide range of processes, including charge migration during the nuclear dissociation process. Abstract:In this report, we introduce the static coherent states (SCS) method for investigating quantum electron dynamics in a one-or two-electron laser-induced system. The SCS method solves the time-dependent Schrödinger equation (TDSE) both in imaginary and real times on the basis of a static grid of coherent states (CSs). Moreover, we consider classical dynamics for the nuclei by solving their Newtonian equations of motion. By implementing classical nuclear dynamics, we compute the electronic-state potential energy curves of H + 2 in the absence and presence of an ultra-short intense laser field. We used this method to investigate charge migration in H + 2 . In particular, we found that the charge migration time increased exponentially with inter-nuclear distance. We also observed substantial charge localization for sufficiently long molecular bonds.

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High-order harmonic generation of CO and N₂ molecules under linearly- and bi circularly-polarized laser pulses by TD-DFT

et al. 2018

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We present a method for high-order harmonics generation of N 2 and CO molecules under two-color circularly polarized counter-rotating laser pulses at frequencies of ω 0 and 2ω 0 . Pulse envelope in this investigation is sin-squared and the intensity of each laser beam is 2 × 10 14 W • cm −2 with ten-optical cycle (o.c.). We show that an isolated pulse with a pulse duration shorter than 20 attosecond from the superposition of several harmonics can be generated. Both two-color linearly-and bicircularly-polarized laser pulses are considered. Our results have also been compared with the outcomes of the previous theoretical works as well as experiment observations. It is found that for CO molecule, the bicircularly-polarized laser pulses are superior and more efficient, and it can generate narrower attosecond pulses than the linearly-polarized pulses. While for N 2 molecule, the two-color linearly-polarized pulses are more efficient, and it can generate narrower attosecond pulses than the bicircularlypolarized pulses. Furthermore, in order to demonstrate the origin of red-and blue-shifts in high-harmonic spectra, the effect of pulse duration on the high-order harmonics spectra is investigated. In addition, to obtain imaging on the temporal dependence of the electron densities, the time dependent electron localization function is used. Moreover, in order to study of the quantum trajectory of electrons, time-frequency analysis is utilized.

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Generation of isolated attosecond pulses by polarization gating of high-order harmonic emission from $\boldsymbol {\rm H_2^+}$ in intense ultrashort laser fields

Cited by 6 publications

References 29 publications

High‐order harmonic generation by static coherent states method in single‐electron atomic and molecular systems

High‐order harmonic generation by static coherent states method in single‐electron atomic and molecular systems

Static Coherent States Method: One- and Two-Electron Laser-Induced Systems with Classical Nuclear Dynamics

High-order harmonic generation of CO and N₂ molecules under linearly- and bi circularly-polarized laser pulses by TD-DFT

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Generation of isolated attosecond pulses by polarization gating of high-order harmonic emission from $\boldsymbol {\rm H_2^+}$ in intense ultrashort laser fields

Cited by 6 publications

References 29 publications

High‐order harmonic generation by static coherent states method in single‐electron atomic and molecular systems

High‐order harmonic generation by static coherent states method in single‐electron atomic and molecular systems

Static Coherent States Method: One- and Two-Electron Laser-Induced Systems with Classical Nuclear Dynamics

High-order harmonic generation of CO and N2 molecules under linearly- and bi circularly-polarized laser pulses by TD-DFT

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Product

Resources

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High-order harmonic generation of CO and N₂ molecules under linearly- and bi circularly-polarized laser pulses by TD-DFT