Molecular Harmonic Generation Research Articles

Electron‐Nuclear Dynamics in Molecular Harmonic Generation Driven by a Plasmonic Nonhomogeneous Field

Electron (z)‐nuclear (R) dynamics in the molecular high‐order harmonic generation (MHHG) from H2+ driven by the plasmonic nonhomogeneous field, generated by the surface plasmon polaritons in the bowtie‐shaped nanostructure, have been theoretically investigated through solving the two dimensional time‐dependent Schrödinger equation with the Non‐Bohn‐Oppenheimer approximation. It is found that (i) due to the plasmonic enhancement of the laser intensity, the harmonic cutoff can be extended when the spatial position of H2+ is away from the gap center of the nanostructure. However, due to the limit of the gap size, the threshold value of the harmonic cutoff can be obtained at a given position of H2+. (ii) Due to the asymmetric enhancement of the laser intensity in space, the extended higher harmonics are respectively from E(t) > 0 a.u. or E(t) < 0 a.u. for the cases of the positive and the negative spatial position of H2+. As a result, the intensities of the extended higher harmonics are different and can be controlled by changing the carrier‐envelope phase and the pulse duration of the laser field. (iii) In the few‐cycle pulse duration, the MHHG mainly comes from the multi‐photon resonance ionization (MPRI), while as the pulse duration increases, the MPRI, the charge‐resonance enhanced ionization (CREI) and even the dissociative ionization (DI) are contributed to the MHHG. Moreover, as the spatial position of H2+ moves, the contributions of the MHHG from the MPRI, the CERI and the DI can be controlled. (iv) The contributions of the MHHG from the two‐H nuclei have been investigated and found that when E(t) > 0 a.u., the intensities of the harmonics from the negative‐H is higher than those from the positive‐H; while when E(t) < 0 a.u., the intensities of the harmonics from the positive‐H plays the main role in the MHHG. Moreover, the multi‐minima, caused by the two‐center interference can also be found. (v) Finally, by superposing a properly selected harmonics, a single isolated attosecond pulse (SIAP) with the full width at half maximum (FWHM) of 34 as can be obtained.

Chirp control on molecular harmonic generation and distribution in H2+

ABSTRACTChirp control on the molecular harmonic emission and distribution in H2+ has been theoretically investigated. The results show that (i) with the introduction of the up-chirped pulse, the intensities of the higher harmonics are decreased; while with the introduction of the down-chirped pulse, the intensities of the higher harmonics can be enhanced. When E(t) < 0.0, the harmonic emission events (HEEs) from the positive-H are higher than those from the negative-H; while when E(t) > 0.0, the HEEs from the negative-H are higher than those from the positive-H. As a result, when the higher harmonics are produced from E(t) < 0.0 or E(t) > 0.0, the positive-H or the negative-H plays the main role in the harmonic spectra. (ii) The distribution of the higher harmonics from the two-H nuclei can be controlled with the introduction of the chirps and the carrier-envelope-phases of the laser field. (iii) Some minima on the harmonic spectra can be obtained, which is attributed to the coupling of the two-center interference and the electron-nuclear dynamics. (iv) By properly superposing the harmonics from the down-chirped pulse, an isolated attosecond pulse (IAP) with the duration of 45 as can be obtained, which is nearly 1 order of magnitude enhancement in pulse intensity compared with the chirp- free case.

Molecular harmonic generation in bowtie-shaped nanostructure

Molecular high-order harmonic generation (MHHG) from in the bowtie-shaped nanostructure has been investigated. The results show that (i) due to the surface plasmon polaritons in the bowtie-shaped nanostructure, the laser intensity can be enhanced and present the nonhomogeneous effect in space. As a result, the extension of the harmonic cutoff can be achieved when the position of is injected away from the gap center of the nanostructure. However, due to the limited gap size of the nanostructure, the inherent threshold value of the harmonic cutoff can be found. (ii) Due to the asymmetric enhancement of the laser intensity in space, the extended higher harmonics come from E(t) > 0 or E(t) < 0 for the cases of the positive or the negative injected positions of , respectively. (iii) In the few-cycle pulse, the extended higher harmonics mainly comes from the multi-photon resonance ionization (MPRI) around R = 4.0 and R = 4.5 but from only one harmonic emission event (HEE), thus leading to the intensity difference of the extended higher harmonics from the positive and the negative positions of . In the multi-cycle pulse, the extended higher harmonics are also attributed to the MPRI but from R = 3.5 to R = 6.0 and there are three HEEs contributed to the extended higher harmonics, thus leading to the similar intensity of the extended higher harmonics from the positive and the negative positions of . (iv) Due to the slower nuclear motion of the heavy nuclei, the intensities of the harmonics from are lower than those from . (v) The contributions of the MHHG from the two-H nuclei show that when E(t) > 0 or E(t) < 0, the left-H or the right-H plays the dominating role in the MHHG. Moreover, as moves away from the gap center, the intensity difference of the higher harmonics from the two-H nuclei can be enhanced. But, it can be decreased as the pulse duration increases.

Chirp control of multi-photon resonance ionization and charge-resonance enhanced ionization on molecular harmonic generation

The effects of the multi-photon resonance ionization (MPRI) and the charge-resonance enhanced ionization (CREI) on the molecular high-order harmonic generation (MHHG) from H2+ have been investigated by using the chirped pulses. It is found that the MHHG only comes from the MPRI in the shorter pulse duration. As the pulse duration increases, both the MPRI and the CREI contribute to the MHHG. But the MPRI plays the main role in the generations of the above-threshold harmonics and the CREI mainly contributes to the below-threshold harmonics. With the introductions of the up-chirped and the down-chirped pulses, the contributions of the MHHG from the CREI and the MPRI can be enhanced, respectively. Finally, the isotopic investigation (e.g. T2+) shows that due to the slower nuclear motion of the heavy nuclei, the contributions of MHHG from the CERI can be suppressed in the heavy nuclei.

Spatial distribution of molecular harmonic generation from HeH 2

Spatial distribution of molecular harmonic generation from HeH 2

Internuclear distance effect on asymmetric molecular harmonic generation in the present of spatial inhomogeneous field

Internuclear distance effect on asymmetric molecular harmonic generation in the present of spatial inhomogeneous field

Theoretical exploration of asymmetric molecular harmonic emission and attosecond pulse generation in the presence of spatially inhomogeneous plasmon-enhanced field

ABSTRACTAsymmetric molecular harmonic generation from HeH2+ ion in the presence of the spatially inhomogeneous plasmon-enhanced field has been theoretically investigated by solving the two-dimensional non-Born–Oppenheimer time-dependent Schrödinger equation (both the electron and nuclear motions are considered only along the laser polarisation axis). It shows that (1) for the normal homogeneous field, the harmonic cut-off from the asymmetric molecule is beyond the classical harmonic cut-off energy from the atom (Ip + 3.17 Up). Further analyses show that the multi-channels ionisation–recombination process is responsible for the harmonic extension. (2) For the spatially inhomogeneous plasmon-enhanced field, the harmonic cut-off can be further enhanced, and an optimal 3.0 dB enhanced field with a 482 eV supercontinuum has been obtained. Quantum time-frequency harmonic analyses have been shown to explain the harmonic characteristics and the harmonic extension process. (3) Initial vibrational state and isotopic effects show that intense harmonics can be generated from higher initial vibrational state and the heavier molecule. Finally, by properly superposing the harmonics, a series of sub-30 as attosecond pulses can be obtained.

The effect carrier-envelope phase on the cut-off of molecular harmonic generation

We investigated the high-order harmonic generation from H+2 ion radiated by a few cycle infrared laser field. Our numerical simulations show that there exists a highly efficient plateau structure in the molecular harmonic spectrum. The carrier envelope phase effect on the cut-off of this plateau is investigated.

Gauge problem in molecular high-order harmonic generation

The problem that the strong-field approximation (SFA) in the length gauge (LG) cannot give the correct molecular harmonic generation spectrum when the internuclear distance is large is studied. By introducing the first excited state in addition to the ground state in the SFA and a procedure to resum translation invariance, the problem is resolved and the superiority of the LG to the velocity gauge in this case is discussed.

High-order harmonic generation by molecules of discrete rotational symmetry interacting with circularly polarized laser field

The dynamics of harmonic generation by a molecule of discrete rotational symmetry oriented in the polarization plane of a circularly polarized laser field is discussed. A simple model system is presented and the corresponding high-order harmonic generation spectrum is calculated analytically as a sum of the bound-bound and the bound-continuum contributions. It is shown that, contrary to the case of rare gas atoms interacting with linearly polarized radiation, the dominant contribution to high-order harmonic generation by the studied class of systems comes from the bound-bound transitions. As a consequence, the mechanism of the process is different from the well-known rescattering mechanism due to Corkum and Kulander. At intensities high enough the molecular harmonic generation spectra reproduce the main features of the atomic ones, i.e., the plateau and the cutoff. Unlike the cutoff in the atomic case, the molecular cutoff position depends linearly on the electric field strength and the molecular dimensions. This should allow one to reach higher harmonic orders by employing larger molecular targets. DOI: 10.1103/PhysRevA.64.033411