Below-threshold Harmonic Generation Research Articles

Below-threshold harmonic generation in gas-jets for Th-229 nuclear spectroscopy.

The generation of below-threshold harmonics in gas-jets constitutes a promising path towards optical frequency combs in the vacuum ultra-violet (VUV) spectral range. Of particular interest is the 150 nm range, which can be exploited to probe the nuclear isomeric transition of the Thorium-229 isotope. Using widely available high-power, high-repetition-rate Ytterbium-based laser sources, VUV frequency combs can be generated through the process of below-threshold harmonic generation, in particular 7th harmonic generation of 1030 nm. Knowledge about the achievable efficiencies of the harmonic generation process is crucial for the development of suitable VUV sources. In this work, we measure the total output pulse energies and conversion efficiencies of below-threshold harmonics in gas-jets in a phase-mismatched generation scheme using Argon and Krypton as nonlinear media. Using a 220 fs, 1030 nm source, we reach a maximum conversion efficiency of 1.1 × 10-5 for the 7th harmonic (147 nm) and 0.78 × 10-4 for the 5th harmonic (206 nm). In addition, we characterize the 3rd harmonic of a 178 fs, 515 nm source with a maximum efficiency of 0.3%.

Carrier-envelope-phase-dependent below-threshold harmonic generation in few-cycle mid-infrared laser fields.

We theoretically study the dependence of below-threshold harmonic generation (BTHG) of atoms on the carrier-envelope phase (CEP) driven by few-cycle mid-infrared laser pulses. The BTHG spectra can be accurately and efficiently calculated by solving the three-dimensional time-dependent Schrödinger equation using the time-dependent generalized pseudospectral method. We present the BTHG spectra as a function of the laser-field CEP. CEP-dependent enhancement or suppression occurred at low laser field intensities owing to the changes in the resonant effects associated with multiple quantum trajectories. However, the BTHG of atoms driven by high laser intensities is insensitive to the CEP. The synchrosqueezing time-frequency transform of the BTHG and extended semiclassical analysis are performed to elucidate the underlying physical mechanism.

Rabi-flopping signatures in below-threshold harmonic generation from the stretched H2 and N2 molecules in intense laser fields

We theoretically study the spectral and temporal fine subpeak structures in the below-threshold harmonic (BTH) spectra of the stretched H2 and N2 molecules by solving the one-electron time-dependent Schrödinger equation (TDSE) in conjunction with the wavelet time-frequency analysis. We identify such fine subpeaks come from the Rabi-flopping between the ground state and the first excited state using the simple two-state model. We also confirm that these subpeak structures in BTH spectra are common for molecules at large internuclear distances if two molecular states are strongly coupled. Furthermore, the spacing between the adjacent subpeaks in BTH spectra can be determined approximately by analyzing the induced dipole moment in the time domain.

Multichannel-resolved dynamics in resonance-enhanced below-threshold harmonic generation of H2+ molecular ions

Recently the study of the resonance-enhanced below-threshold harmonic generation (BTHG) of atoms and molecules has received considerable attention. BTHG, with spatially coherent and high conversion efficiency, can provide a potential way to produce powerful vacuum-ultraviolet light sources. However, the resonance effects associated with molecular BTHG have become more complex to study due to the presence of the extra internuclear degree of freedom. Here we perform an ab initio study and demonstrate the multichannel-resolved dynamics in resonance-enhanced BTHG of ${\mathrm{H}}_{2}^{+}$ molecular ions by combining a synchrosqueezing time-frequency transform with an extended semiclassical simulation. We find that BTHG of ${\mathrm{H}}_{2}^{+}$ on resonance is enabled only near the zero-laser field region and the multichannel interference is responsible for enhanced BTHG. The time-frequency spectra in the vicinity of the resonance exhibit a periodic split structure with oscillating laser pulses and can be explained by the individual dynamical behavior of multiple channels in BTHG.

Role of nuclear symmetry in below-threshold harmonic generation of molecules

Below-threshold harmonic generation (BTHG) is one of few potential methods for the generation of novel vacuum-ultraviolet (VUV) light sources. However, most previous studies have focused on the atomic BTHG; a comprehensive understanding of the molecular BTHG is valuable for the advancement of this field. Here, we present an ab initio study of the role of nuclear symmetry on BTHG of both homonuclear and heteronuclear diatomic molecules. We reveal very distinctive electronic dynamical behaviors in molecular BTHG by identifying subtle multiple-channel contributions. In particular, it is found that the channels associated with the electron-nuclear coupling from light nuclear core to heavy nuclear core of the asymmetric molecules play an important role in the constructive interference of the harmonic emission, leading to a significant enhancement of the BTHG. Our results suggest that asymmetric molecular systems can be used for substantial improvement of the molecular BTHG-based VUV light sources.

Mechanism of laser intensity-dependent below-threshold harmonic generation

<sec> High-order-harmonic generation (HHG) is a fundamental atomic and molecular process in strong laser fields and plays a crucial role in the development of ultrafast science and technology. The essential features in HHG, such as the above-threshold harmonic plateau and cutoffs, can be well understood by the semiclassical three-step model. The HHG cutoff occurs approximately at the energy <inline-formula><tex-math id="M1">\begin{document}$3.17{U_{\rm p}} + {I_{\rm p}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M1.png"/></alternatives></inline-formula>, where <inline-formula><tex-math id="M2">\begin{document}${I_{\rm p}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M2.png"/></alternatives></inline-formula> is the atomic ionization potential, and <inline-formula><tex-math id="M3">\begin{document}${U_{\rm p}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M3.png"/></alternatives></inline-formula> is the ponderomotive potential.</sec><sec> In the past, most studies focused on the HHG above the ionization threshold, and the general pattern of the HHG spectrum can be qualitatively explained by means of the strong field approximation (SFA) and the quantum treatment of three-dimensional time-dependent Schr?dinger equation (TDSE). However, the SFA results in inadequate description for the process in the harmonic generation below the ionization threshold since it neglects the Coulomb potential and the detailed electronic structure of atoms. Recently, as a promising method to produce vacuum-ultraviolet frequency comb, the HHG in the near- and below-ionization threshold has been increased considerably. However, the dynamical origin of in these lower harmonics is less understood and largely unexplored.</sec><sec> Here we perform an ab initio quantum study of the near- and below-threshold harmonic generation of hydrogen atom by means of the time-dependent generalized pseudospectral method. We study the intensity dependence of the harmonic spectra below the ionization threshold of hydrogen atom in the intense laser field. The high-order harmonic spectra are calculated by the Fourier transform of the atom induced dipole moment in the laser field. The below-threshold harmonic spectra yield is scaled as a function of the laser peak intensity. We find that the spectra yield in below-threshold harmonic generation (BTHG) dependents on the light intensity in the multiphoton ionization regime. And the laser intensity plays an important role in the channel selection process for BTHG. There are mainly two kinds of quantum channels to be responsible for the BTHG. Namely, the generalized short trajectories and the long trajectories, in which the long trajectories are more sensitive to the laser field intensity. Combining with wavelet time-frequency transform, semiclassical trajectories simulation, and quantum channel analysis associated with the laser intensity, the dynamical origin of the BTHG is uncovered.</sec>

Dynamical origin of below-threshold harmonic generation of diatomic molecules

SynopsisWe present an ab initio quantum study of below-threshold harmonic generation (BTHG) from H2 + molecules in the presence of an intense laser field by solving the time-dependent Schrödinger equation accurately in space and time. We find that multiple channels contribute to BTHG of H2 + molecules, which are related to the electron driven initially at specific time of the laser pulse from one nuclear core to another nuclear core or back to the parent core itself. The distinct contributions of these channels are distinguished by using a novel synchro squeezing time-frequency analysis.

Role of the dressed and bound states on below-threshold harmonic generation of He atom**Project supported by the National Natural Science Foundation of China (Grant Nos. 11674268, 11764038, and 11765018) and the Scientific Research Foundation of Physics of CPEE–NWNU and NWNU-LKQN-17-1, China.

High-order harmonic generation below ionization threshold of He atom in the laser field is investigated by solving the three-dimensional time-dependent Schrödinger equation. An angular momentum-dependent model potential of He atom was used for getting the accurate energy levels of singlet states. The satellite-peak structures of the below-threshold harmonic generation (BTHG) of He are observed. We analyze the emission properties of the BTHG by employing a synchrosqueezing transform technique. We find that the satellite-peak structures have two types related to two kinds of transitions. One is the transition of the dressed states of the excited states, the other is the transition between the excited states and the ground state in the field-free case. Furthermore, our results show that the maximum Stark shift of the 2p state is about (penderomotive energy), and that of the 4p state is about . It indicates that the energy difference between some satellite- and main-peaks of the BTHG can be used to measure the maximum Stark shift of the excited states of He atom in the laser field.

Efficient enhancement of below-threshold harmonic generation by laser-driven excited states of Cs atom

We propose an efficient method for the enhancement of below-threshold harmonic generation (BTHG) by mid-infrared laser-driven excited states of a Cs atom. The BTHG is calculated by solving three-dimensional time-dependent Schrödinger equation accurately and efficiently using the time-dependent generalized pseudospectral method. We adopt an excited state as the initial state of a Cs atom. As a result, the BTHG is significantly enhanced by two orders of magnitude compared with the case of the initial ground state. Furthermore, we find that a single vacuum-ultraviolet pulse can be generated by mid-infrared laser-driven excited states by superposing several below-threshold harmonics of a Cs atom. Our finding suggests that the generation of below-threshold harmonics by laser-driven excited states of an atom can provide a powerful methodology for the production of intense vacuum-ultraviolet pulses.

Below-threshold harmonic generation from strong non-uniform fields

Strong-field photoemission below the ionization threshold is a rich/complex region where atomic emission and harmonic generation may coexist. We studied the mechanism of below-threshold harmonics (BTH) from spatially non-uniform local fields near the metallic nanostructures. Discrete harmonics are generated due to the broken inversion symmetry, suggesting enriched coherent emission in the vuv frequency range. Through the numerical solution of the time-dependent Schrödinger equation, we investigate wavelength and intensity dependence of BTH. Wavelength dependence identifies counter-regular resonances; individual contributions from the multi-photon emission and channel-closing effects due to quantum path interferences. In order to understand the underlying mechanism of BTH, we devised a generalized semi-classical model, including the influence of Coulomb and non-uniform field interactions. As in uniform fields, Coulomb potential in non-uniform fields is the determinant of BTH; we observed that the generation of BTH are due to returning trajectories with negative energies. Due to large distance effectiveness of the non-uniformity, only long trajectories are noticeably affected.

Dynamical origin of near- and below-threshold harmonic generation of Cs in an intense mid-infrared laser field.

Near- and below-threshold harmonic generation provides a potential approach to generate vacuum-ultraviolet frequency comb. However, the dynamical origin of in these lower harmonics is less understood and largely unexplored. Here we perform an ab initio quantum study of the near- and below-threshold harmonic generation of caesium (Cs) atoms in an intense 3,600-nm mid-infrared laser field. Combining with a synchrosqueezing transform of the quantum time-frequency spectrum and an extended semiclassical analysis, the roles of multiphoton and multiple rescattering trajectories on the near- and below-threshold harmonic generation processes are clarified. We find that the multiphoton-dominated trajectories only involve the electrons scattered off the higher part of the combined atom-field potential followed by the absorption of many photons in near- and below-threshold regime. Furthermore, only the near-resonant below-threshold harmonic is exclusive to exhibit phase locked features. Our results shed light on the dynamic origin of the near- and below-threshold harmonic generation.

Quantum path interference in the wavelength-dependent below-threshold harmonic generation

We have theoretically investigated the wavelength-dependent below-threshold harmonic (BTH) generation in different laser intensity regimes. Based on the simulations of the time-dependent Schr\"odinger equation, we find a periodic fluctuation in the wavelength-dependent BTH yields with laser intensities in the magnitude of ${10}^{13}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$. This result shows significant differences from the resonance peak structures in the recent study with intensities about ${10}^{12}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$ [Xiong et al., Phys. Rev. Lett. 112, 233001 (2014)]. By performing both the quantum path analysis and time-frequency transform of the harmonic spectra, we demonstrate that the difference in the wavelength-dependent BTH yields is due to the complicated quantum path distributions of BTHs with the intensities in the magnitude of ${10}^{13}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$. And the periodic fluctuation is further demonstrated to originate from the interference between the two quantum paths that dominate the harmonic generation.

Role of laser-driven electron-multirescattering in resonance-enhanced below-threshold harmonic generation in He atoms

We present an ab initio investigation of the below-threshold harmonic generation of helium (He) atoms in few-cycle infrared laser fields by accurately solving the time-dependent Schr\odinger equation and Maxwell's equation simultaneously. We find that the enhancement of the below-threshold harmonic generation only occurs to near the resonance structure of He, for which this mechanism is in agreement with the recent experimental study [M. Chini et al., Nat. Photonics 8, 437 (2014)]. Moreover, we perform the quantum and semiclassical trajectories analysis, including both the atomic potential and the laser field, as well as the synchrosqueezed transform of the harmonic spectra. Our results reveal that several multirescattering trajectories contribute to the resonance-enhanced below-threshold harmonic generation.

Mechanisms of Below-Threshold Harmonic Generation in Atoms

Most previous studies have focused on high-order harmonic generation beyond the ionization threshold; mechanisms of below-threshold harmonics are less understood. We schematically study the harmonic emission process in this region by numerically solving the time-dependent Schrödinger equation of an atom in laser fields. We show that, besides the quantum path interference mechanism recently identified, the effects induced by the Coulomb potential also have a critical impact on these harmonics. These mechanisms can be distinguished in the structure of harmonic spectra by changing the laser wavelength and peak intensity. We find that the long quantum orbits can influence lower-order harmonics at a higher laser intensity. In addition, we show that the intensity-dependent steps of harmonic yield can disappear for certain harmonic orders, due to the trapping in the Rydberg states before recombination, which can explain recent experimental observations.

Coherent phase-matched VUV generation by field-controlled bound states

Little attention has been devoted to development and characterization of below-threshold harmonic sources, which are critical for extending time-resolved photoemission spectroscopy to megahertz repetition rates and for developing high-average-power vacuum-ultraviolet sources. Now, a new regime of below-threshold harmonic generation accompanied by the bright, coherent emission of vacuum-ultraviolet lines is reported.

Semiclassical approaches to below-threshold harmonics

We study the generation of below-threshold harmonics in a model atom by extending the three-step semiclassical model of harmonic generation to include effects of the atomic potential. We explore the generalization of semiclassical trajectories of the electron in the presence of the combined laser-atom potential and calculate the intensity-dependent dipole phase associated with these trajectories. Our results are in good agreement with fully quantum mechanical calculations, as well as with recent experimental observations. We show that the so-called long trajectory readily generalizes to below-threshold harmonic generation and is relatively insensitive to the choice of initial conditions. We also find that the short trajectory can only lead to low-energy harmonics for electrons that have been released close to the ion core in a process that is closer to multiphoton than to tunnel ionization.