High-order Harmonic Generation Research Articles

Effects of polarization direction, amplitude, and photon energy of linearly polarized laser on high order harmonic generation of C60

The study of high-order harmonic generation (HHG) in confined quantum systems is essential for developing a comprehensive physical description of harmonic generation from atoms to bulk solids. Using the time-dependent density-functional theory, we demonstrate how the symmetry of the system modulates the generation of high-order harmonic in fullerene C60 molecules along different orthogonal directions, as well as the effects of amplitude and photon energy of a linearly polarized laser on high-order harmonics generation. We found that the generation of high-order harmonics perpendicular to the laser polarization direction (LPD) is related to the symmetry of molecules along the LPD and the symmetry of molecules perpendicular to the LPD. Within a certain parameter range, the cut-off energy is linearly proportional to the laser amplitude and the laser photon energy.

Efficient angular dispersed high-order harmonic generation by dual laser pulses interacting with a solid target

High-order harmonics emitted from relativistic laser–solid interaction can be used as a bright extreme ultraviolet source. However, such a source usually has mixed frequencies along the emission direction. Through theoretical and numerical studies, we propose a scheme to realize monochromatic harmonic emission along individual directions by using dual laser pulses with orthogonal polarizations, where a relativistic P-polarized laser is used as a pump laser in combination with a moderate S-polarized laser as a seed laser. We find that harmonics of the S-polarized laser can be efficiently generated with several orders of magnitude enhancement and spontaneous angular dispersion depending on the harmonic order. Our scheme may be beneficial to future applications requiring monochromatic radiation along a specific direction or multi-chromatic radiations in different directions.

Tunable spectral continuous shift of high-order harmonic generation in atoms by a plasmon-assisted shaping pulse

We delve into the phenomenon of high-order harmonic generation within a helium atom under the influence of a plasmon-assisted shaping pulse. Our findings reveal an intriguing manipulation of the frequency peak position in the harmonic emission by adjusting the absolute phase parameter within the frequency domain of the shaping pulse. This phenomenon holds potential significance for experimental setups necessitating precisely tuned single harmonics. Notably, we observe a modulated shift in the created harmonic photon energy, spanning an impressive range of 1.2 eV. This frequency peak shift is rooted in the asymmetry exhibited by the rising and falling edges of the laser pulse, directly influencing the position of the peak frequency emission. Our study quantifies the dependence of this tuning range and the asymmetry of the laser pulse, offering valuable insights into the underlying mechanisms driving this phenomenon. Furthermore, our investigation uncovers the emergence of semi-integer order harmonics as the phase parameter is altered. We attribute this discovery to the intricate interference between harmonics generated by the primary and secondary return cores. This observation introduces an innovative approach for generating semi-integer order harmonics, thus expanding our understanding of high-order harmonic generation. Ultimately, our work contributes to the broader comprehension of complex phenomena in laser-matter interactions and provides a foundation for harnessing these effects in various applications, particularly those involving precise spectral control and the generation of unique harmonic patterns.

Time-resolving state-specific molecular dissociation with XUV broadband absorption spectroscopy.

The electronic and nuclear dynamics inside molecules are essential for chemical reactions, where different pathways typically unfold on ultrafast timescales. Extreme ultraviolet (XUV) light pulses generated by free-electron lasers (FELs) allow atomic-site and electronic-state selectivity, triggering specific molecular dynamics while providing femtosecond resolution. Yet, time-resolved experiments are either blind to neutral fragments or limited by the spectral bandwidth of FEL pulses. Here, we combine a broadband XUV probe pulse from high-order harmonic generation with an FEL pump pulse to observe dissociation pathways leading to fragments in different quantum states. We temporally resolve the dissociation of a specific O2+ state into two competing channels by measuring the resonances of ionic and neutral fragments. This scheme can be applied to investigate convoluted dynamics in larger molecules relevant to diverse science fields.

Tailoring polarisation of attosecond pulses via co-rotating bicircular laser fields

The present work introduces a robust way to generate attosecond pulses with tunable ellipticity via high-order harmonic generation by co-rotating ω−2ω bicircular laser fields. The total electric field of the laser fields exhibits an absence of rotational symmetry, which leads to the generation of high harmonics of the same helicity across a broad range of spectral bandwidth. High-harmonics with the same helicity offer the opportunity to synthesize attosecond pulses with tunable ellipticity. The polarisation properties of the generated harmonics are robust against the variations in driving fields' parameters, such as wavelength, intensity ratio, and the sub-cycle phase between ω−2ω fields. Our work opens an avenue to study chiral-sensitive light-matter ultrafast processes on their intrinsic timescale.

Error-diffusion-kernel parameters for binary pattern in 1-bit fringe projection profilometry.

In fringe projection profilometry, 1-bit processing of 8-bit raster patterns is a common method to suppress nonlinear errors in commercial projectors and realize high-speed projection in industrial projectors. In the process of generating 1-bit fringes from sinusoidal fringes, the generation of high-order harmonics is inevitable; choosing to introduce fewer high-order harmonics of the algorithm is conducive to defocus to obtain a better sinusoidal pattern. This paper proposes a method to expand the error-diffusion kernel of the conventional Floyd-Steinberg diffusion dithering algorithm from 2×3 to 3×5, which can reduce the grayscale change of surrounding pixels and generate 1-bit fringes with fewer high-order harmonics. Meanwhile, this paper optimizes the parameters of the 3×5 error-diffusion kernel and proposes the optimal parameters for this kind of diffusion kernel. The simulation results show that the fringes generated by the proposed 3×5 error-diffusion-kernel algorithms are closer to sinusoidal fringes after Gaussian low-pass filtering. The experimental results show that the accuracy of the 3×5 diffusion kernel algorithms is higher.

Progress in analytical solutions for high order harmonic generation in semiconductor superlattice multipliers

Progress in analytical solutions for high order harmonic generation in semiconductor superlattice multipliers

Role of nuclear dynamics in high harmonic generation redshift of H2 +

The detailed spectral and temporal structures of high-order harmonic generation (HHG) have provided us with a wealth of information about the highly nonlinear response of atoms, molecules, and electronic structures to intense low-frequency laser fields. In this study, we aim to investigate the underlying physics behind the molecular high harmonic spectra redshift beyond the Born–Oppenheimer approximation for and its isotopes with numerical simulations of the time-dependent Schrödinger equation. One widely recognized phenomenon is the occurrence of a spectral redshift at the trailing edge of a laser pulse. However, our findings reveal that even when driven by a sinusoidal laser pulse without a falling edge, the HHG redshift appears and highlights that the observed spectral redshift is not solely due to the declining intensity of the laser pulse. We show that it is a direct consequence of the decrease in ionization energy during the transition from recombination time to ionization time within wave packets at short internuclear distances. Interestingly, our results also demonstrate how a sinusoidal laser pulse without a rising part can disrupt the standard picture of redshift in literatures in the past. This finding suggests that there are additional factors influencing the redshift mechanism beyond just the trailing edge of the laser pulse. These phenomena are elucidated through the analysis of the dynamics of the nuclear wave packet. Our study provides valuable insights into the complex dynamics of HHG processes and sheds light on how different laser pulse characteristics can influence spectral redshifts and harmonic generation in molecular systems.

Molecular orbital tomography of HOMO and HOMO-1 of the nonlinear molecule H2O: The study on multi-orbital effects

Molecular orbital tomography (MOT) through high-order harmonic generation (HHG) is a crucial method for probing individual molecular orbitals. Previous studies mainly focused on linear molecules such as N2, and CO, where valence orbitals were imaged by detecting harmonic emission at various alignments. In this study, we investigate the HHG from the water molecules, with the aim of exploring MOT for nonlinear molecules. By employing the time-dependent density functional theory, we obtain HHG spectra for different angles between the laser polarization and molecular symmetry axis. By manipulating the scanning planes (planes perpendicular to the laser propagation direction and contain the field polarization direction), specific orbitals can be selectively imaged. Particularly, a well-reconstructed highest occupied molecular orbital (HOMO) is obtained when the laser scanning plane approximately aligns with the nodal plane of HOMO-1. However, when the laser polarization deviates from the nodal plane, multiple orbitals contribute to the HHG process, and we visualize the orbital distortions resulting from such effects. Furthermore, HOMO-1, can be reconstructed when the laser scanning plane aligns with the nodal plane of HOMO. This research significantly advances the development of MOT and opens up intriguing possibilities for reconstructing orbitals of more complex molecules.

Relativistic calculation of nondipole effects in high-order harmonic generation

Relativistic calculation of nondipole effects in high-order harmonic generation

Chirp compensation for generating ultrashort attosecond pulses with 800-nm few-cycle pulses

Abstract We show that it is feasible to generate sub-40-attosecond pulses with near-infrared few-cycle pulses centered at 800 nm. With proper gating technique, super-broadband continuum spectrum extending from 50 eV to above 200 eV can be obtained, and the intrinsic atto-chirp can be satisfactorily compensated with C filter, producing isolated attosecond pulses with duration of 33 as. According to the wavelength scaling law of high-order harmonic generation, the proposed scheme is of great significance to develop high-flux ultrashort attosecond sources.

Observation of chromatic effects in high-order harmonic generation

Observation of chromatic effects in high-order harmonic generation

Circularly polarized attosecond light generation from OCS molecules irradiated by the combination of linear polarized infrared and orthogonal terahertz fields.

Researching ultrafast dynamics and creating coherent light sources will both benefit significantly from the establishment of polarization control in high-order harmonic generation (HHG). By employing the time-dependent density functional theory method, we investigate HHG of carbonyl sulfide molecules using a combination of a linear polarized infrared (IR) laser and a weaker orthogonal Terahertz (THz) field. Our findings show that by adjusting the amplitude of the THz field, the movement scale of electrons in the THz direction can be tuned, thereby one can control the harmonic intensity in the IR laser direction. This method allows for the creation of near-circularly polarized attosecond pulses. Furthermore, the ellipticity of the attosecond pulse may be changed by modifying the carrier-envelope phase of the IR laser pulse.

Modifying the Electron Dynamics in High-Order Harmonic Generation via a Two-Color Laser Field

We investigate the harmonic emission from bichromatic periodic potential by numerically solving the time-dependent Schrödinger equation in the velocity gauge. The results show that the harmonic minimum is sensitive to the wavelength. Moreover, distinct crystal momentum states contribute differently to harmonic generation. In momentum space, the electron dynamics reveal a close relationship between the spectral minimum and the electron distribution in higher conduction bands. Additionally, by introducing an ultraviolet pulse to the fundamental laser field, the suppression of the harmonic minimum occurs as a result of heightened electron populations in higher conduction bands. This work sheds light on the harmonic emission originating from a solid with a two-atom basis.

Real-Time Extension of TAO-DFT.

Thermally assisted occupation density functional theory (TAO-DFT) has been an efficient electronic structure method for studying the ground-state properties of large electronic systems with multi-reference character over the past few years. To explore the time-dependent (TD) properties of electronic systems (e.g., subject to an intense laser pulse), in this work, we propose a real-time (RT) extension of TAO-DFT, denoted as RT-TAO-DFT. Moreover, we employ RT-TAO-DFT to study the high-order harmonic generation (HHG) spectra and related TD properties of molecular hydrogen H2 at the equilibrium and stretched geometries, aligned along the polarization of an intense linearly polarized laser pulse. The TD properties obtained with RT-TAO-DFT are compared with those obtained with the widely used time-dependent Kohn-Sham (TDKS) method. In addition, issues related to the possible spin-symmetry breaking effects in the TD properties are discussed.

Long-range correlation-induced effects at high-order harmonic generation on graphene quantum dots

Long-range correlation-induced effects at high-order harmonic generation on graphene quantum dots

Tailoring OAM spectrum of high-order harmonic generation driven by two mixed Laguerre–Gaussian beams with nonzero radial nodes

The extreme ultraviolet (XUV) light beam carrying orbital angular momentum (OAM) can be produced via high-order harmonic generation (HHG) due to the interaction of an intense vortex infrared laser and a gas medium. Here we show that the OAM spectrum of vortex HHG can be readily tailored by varying the radial node (from 0 to 2) in the driving laser consisting of two mixed Laguerre–Gaussian (LG) beams. We find that due to the change in spatial profile of HHG, the distribution range of the OAM spectrum can be broadened and its shape can be modified by increasing the radial node. We also show that the OAM mode range becomes much wider and its distribution shape becomes more symmetric when the harmonic order is increased from the plateau to the cutoff when the driving laser has the nonzero radial nodes. Through the map of coherence length and the evolution of harmonic field in the medium, we reveal that the favorable off-axis phase-matching conditions are greatly modified due to the change of intensity and phase distributions of driving laser with the radial node. We anticipate this work to stimulate some interests in generating the XUV vortex beam with tunable OAM spectrum through the gaseous HHG process achieved by manipulating the mode properties of the driving laser beam.

Control of Spatiotemporal Localization of Infrared Pulses in Gas-Filled Capillaries Using Weak Ultraviolet Pulses

Manipulation of intense pulse propagation in gas-filled capillaries is desirable for various high-field applications. Tuning the parameters of the driving laser pulse and the working gas is the conventional approach, and it provides limited capability of control. Here we demonstrate through numerical simulations a practical scheme to control the propagation of intense pulses. A weak ultraviolet pulse is launched into a capillary with a negative delay with respect to a main infrared pulse. The pulses begin to temporally overlap due to dispersion. As the main pulse self-compresses, the control pulse is strongly red-shifted due to cross-phase modulation. The frequency shifts of the two pulses mitigate pulse walk-off and allow an efficient coupling, substantially extending the effective interaction length. This interesting phenomenon may benefit applications such as high-order harmonic generation.

Coherent enhancement of a frequency comb modulated by a terahertz laser field in high-order harmonic generation

Coherent enhancement of a frequency comb modulated by a terahertz laser field in high-order harmonic generation

High-order harmonic generation, attosecond pulse, and non-sequential double ionization in the helium atom under high-intensity femtosecond laser pulses

High-order harmonic generation (HHG), attosecond pulse train (APT), isolated attosecond pulse (IAP), and non-sequential double ionization (NSDI) in the Helium atom under intense femtosecond laser pulses are computed using the time-dependent Schrodinger equation (TDSE) in one dimension (1D). By taking into account the electron–electron and electron-nucleus interactions, as well as determining the Helium atom’s ground state wave function through the imaginary time propagation (ITP) method, we are able to observe the widely recognized ‘knee structure’ in the ionization probability of the Helium atom as a function of intensity within an ionization boundary condition model. The results are in good agreement with the experimental data reported by (Walker et al (1994) Phys. Rev. Lett. 73, 1227).