Complicated high-order harmonic generation due to the falling edge of a trapezoidal laser pulse

Ahmadi, Hamed; Vafaee, Mohsen

doi:10.1088/0953-4075/49/3/035602

Cited by 13 publications

(19 citation statements)

References 38 publications

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“…To introduce the third definition of the absolute asymmetry parameter, we first decompose the total wavefunction as [24,46] ψ(z, ρ, R; t) = (9) c g (R; t)ψ g (z, ρ; R) + c u (R; t)ψ u (z, ρ; R) + ψ res (z, ρ, R; t). ψ g (z, ρ; R) and ψ u (z, ρ; R) are ground and first excited electronic wavefunctions, respectively, corresponding to the 1sσ g and 2pσ u states.…”

Section: Methodsmentioning

confidence: 99%

“…They attributed the appearance of even-order harmonics to symmetry breaking of the system due to final electron localization at relatively large internuclear separations. We recently showed that the HHG spectrum gets complex due to the influence of a few-cycle pulse trailing edge [24,25]. These complicated patterns were attributed to the nonadiabatic redshift [24,25] and spatially asymmetric emission [25].…”

Section: Introductionmentioning

confidence: 99%

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Understanding molecular harmonic emission at relatively long intense laser pulses: Beyond the Born-Oppenheimer approximation

Ahmadi

Vafaee

2016

Phys. Rev. A

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The underlying physics behind the molecular harmonic emission in relatively long sin 2 -like laser pulses is investigated. We numerically solved the full-dimensional electronic time-dependent Schrödinger equation beyond the Born-Oppenheimer approximation for simple molecular ion H + 2 . The occurrence and the effect of electron localization, non-adiabatic redshift and spatially asymmetric emission are evaluated to understand better complex patterns appearing in the high-order harmonic generation (HHG) spectrum. Results show that the complex patterns in the HHG spectrum originate mainly from a non-adiabatic response of the molecule to the rapidly changing laser field and also from a spatially asymmetric emission along the polarization direction. The effect of electron localization on the HHG spectrum was not observed as opposed to what is reported in the literature.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Understanding molecular harmonic emission at relatively long intense laser pulses: Beyond the Born-Oppenheimer approximation

Ahmadi

Vafaee

2016

Phys. Rev. A

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“…These differences in the spectrum pattern for the two isotopes are well understood with the consideration of effects of the falling edge of the laser pulse, nuclear motion and ionization probability. We showed recently that even a two-cycle falling part of a trapezoidal laser pulse leads to a significant modulation on the HHG spectrum and violation of the odd harmonic rule [13]. In order to see the contribution of the falling part of the laser pulse in HHG, the Morlet-wavelet time profile of the HHG spectra of Fig.…”

Section: Methodsmentioning

confidence: 99%

“…In fact, the time-dependent ionization of molecules permits the observation of the non-adiabatic redshift. References [12,13] are focused on the non-adiabatic redshift induced by the falling edge of the laser pulse.…”

Section: Introductionmentioning

confidence: 99%

Identifying spatially asymmetric high-order harmonic emission in the falling edge of an intense laser pulse

Vafaee

Ahmadi

2016

J. Phys. B: At. Mol. Opt. Phys.

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Two different induced effects of a laser falling edge on high-order harmonic generation are resolved by solving numerically full-dimensional electronic time-dependent Schrödinger equation beyond the Born-Oppenheimer approximation. The harmonic spectrum of H + 2 and T + 2 isotopes are compared to see the effects of a 4-cycle falling edge of a 800 nm, 15-cycle trapezoidal laser pulse of I =3 ×10 14 Wcm −2 intensity on harmonic emission spectrum. The harmonic emission at the laser falling part is negligible for H + 2 due to ionization suppression, but considerable for T + 2 . The falling edge of the laser pulse induces two effects on the HHG in T + 2 . The first well-known effect is nonadiabatic frequency redshift of generated odd-order harmonics. The second unknown one is spatially asymmetric harmonic emission which appears as even harmonic orders. In order to clarify this new effect, spatial distribution of HHG and resolving HHG into different components are demonstrated. The asymmetric emission would appear for both atoms and molecules as long as harmonic emission of either rising or falling edge of an intense trapezoidal or non-trapezoidal laser pulse is dominant.

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“…HHG in the molecular system arises from evolution of the electronic wavepackets which can be partitioned into different electronic levels, different vibrational levels, different spatial regions (left and right side of the simulation box), or different components of a molecule in a laser field. To obtain the contributions of different vibrational and electronic states to the total HHG spectrum, it is possible to decompose the total wavefunction as a superposition of the several lowest Born-Oppenheimer electronic wavefunctions of the system and the residual part of the wavefunction including the higher excited states and electronic continuum states [20,21]. Total HHG signal can be also decomposed into different localized signals by introducing the electronic wavefunction localized on the right and the left nucleus [22].…”

Section: Introductionmentioning

confidence: 99%

Contribution of the pre-ionized H₂ and the ionized H₂ ⁺ subsystems to the HHG Spectra of H₂ in intense laser fields

Iravani¹,

Sabzyan²,

Vafaee³

et al. 2018

J. Phys. B: At. Mol. Opt. Phys.

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Contributions of the pre-ionized H2 (PI-H2) and ionized H + 2 subsystems of the two-electron H2 system to its high-order harmonic generation in 8-cycle sin 2 -like ultrafast intense laser pulses are calculated and analyzed based on the solution of the time-dependent Schrödinger equation (TDSE) for the one-dimensional two-electronic H2 system with fixed nuclei. The laser pulses have λ = 390 & 532 nm wavelengths and I = 1 × 10 14 , 5×10 14 , 1×10 15 & 5×10 15 Wcm −2 intensities. It is found that at the two lower intensities, the PI-H2 subsystem dominantly produces the HHG spectra. While, at the two higher intensities, both PI-H2 and ionized H + 2 subsystems contribute comparably to the HHG spectra. In the H + 2 subsystem, the symmetry of the populations of H + 2 (I) and H + 2 (II) regions (left and right regions of H + 2 subsystem) is broken by increasing the laser intensity. Complex patterns and even harmonics also appear at these two higher intensities. For instance, at 1 × 10 15 Wcm −2 intensity and λ = 532 nm wavelength, the even harmonics are appeared near cut-off region. Interestingly, at 5 × 10 15 Wcm −2 intensity and λ = 390 nm wavelength, the even harmonics replaced by the odd harmonics with red shift. At λ = 390 & 532 nm wavelengths and I = 1×10 15 intensity, the two-electron cutoffs corresponding to nonsequential double-recombination (NSDR) with maximum return kinetic energy of 4.70Up are detected. The HHG spectra of the whole H2 system obtained with and without nuclear dynamics treated classically are approximately similar. However, at 1 × 10 15 Wcm −2 intensity and λ = 532 nm wavelength, if we take into account nuclear dynamics, the even harmonics which are appeared near cutoff region, replaced by the odd harmonics with blue shift. *

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Complicated high-order harmonic generation due to the falling edge of a trapezoidal laser pulse

Cited by 13 publications

References 38 publications

Understanding molecular harmonic emission at relatively long intense laser pulses: Beyond the Born-Oppenheimer approximation

Understanding molecular harmonic emission at relatively long intense laser pulses: Beyond the Born-Oppenheimer approximation

Identifying spatially asymmetric high-order harmonic emission in the falling edge of an intense laser pulse

Contribution of the pre-ionized H₂ and the ionized H₂ ⁺ subsystems to the HHG Spectra of H₂ in intense laser fields

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Complicated high-order harmonic generation due to the falling edge of a trapezoidal laser pulse

Cited by 13 publications

References 38 publications

Understanding molecular harmonic emission at relatively long intense laser pulses: Beyond the Born-Oppenheimer approximation

Understanding molecular harmonic emission at relatively long intense laser pulses: Beyond the Born-Oppenheimer approximation

Identifying spatially asymmetric high-order harmonic emission in the falling edge of an intense laser pulse

Contribution of the pre-ionized H2 and the ionized H2 + subsystems to the HHG Spectra of H2 in intense laser fields

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Contribution of the pre-ionized H₂ and the ionized H₂ ⁺ subsystems to the HHG Spectra of H₂ in intense laser fields