Showing papers on "High harmonic generation published in 2013"
TL;DR: In this paper, the nonlinear optical and optoelectronic properties of graphene with the emphasis on the processes of harmonic generation, frequency mixing, photon drag and photogalvanic effects as well as generation of photocurrents due to coherent interference effects are reviewed.
Abstract: The nonlinear optical and optoelectronic properties of graphene with the emphasis on the processes of harmonic generation, frequency mixing, photon drag and photogalvanic effects as well as generation of photocurrents due to coherent interference effects, are reviewed. The article presents the state-of-the-art of this subject, including both recent advances and well-established results. Various physical mechanisms controlling transport are described in depth including phenomenological description based on symmetry arguments, models visualizing physics of nonlinear responses, and microscopic theory of individual effects.
330 citations
TL;DR: In this article, the authors demonstrate that the ionization-limited attainable intracavity peak intensity increases with decreasing pulse duration, which can be used for high-order harmonic generation in a gas, with repetition rates around 100 MHz.
Abstract: Coherently enhancing laser pulses in a passive cavity provides ideal conditions for high-order harmonic generation in a gas, with repetition rates around 100 MHz (refs 1,2,3). Recently, extreme-ultraviolet radiation with photon energies of up to 30 eV was obtained, which is sufficiently bright for direct frequency-comb spectroscopy at 20 eV (ref. 4). Here, we identify a route to scaling these radiation sources to higher photon energies. We demonstrate that the ionization-limited attainable intracavity peak intensity increases with decreasing pulse duration. By enhancing nonlinearly compressed pulses of an Yb-based laser and coupling out the harmonics through a pierced cavity mirror, we generate spatially coherent 108 eV (11.45 nm) radiation at 78 MHz. Exploiting the full potential of the demonstrated techniques will afford high-photon-flux ultrashort-pulsed extreme-ultraviolet sources for a number of applications in science and technology, including photoelectron spectroscopy, coincidence spectroscopy with femtosecond to attosecond resolution5,6 and characterization of components and materials for nanolithography7. Spatially coherent 11.45 nm radiation is produced by outcoupling the harmonics of cavity-enhanced nonlinearly compressed pulses from a Yb-based laser through a pierced cavity mirror. This technique may lead to high-photon-flux ultrashort-pulse extreme-ultraviolet sources for use in a wide range of applications.
172 citations
TL;DR: A theoretical study of high-order harmonic generation (HHG) and propagation driven by an infrared field carrying orbital angular momentum (OAM) and the possibility of combining OAM and HHG phase locking to produce attosecond pulses with helical pulse structure is shown.
Abstract: We present a theoretical study of high-order harmonic generation (HHG) and propagation driven by an infrared field carrying orbital angular momentum (OAM). Our calculations unveil the following relevant phenomena: extreme-ultraviolet harmonic vortices are generated and survive to the propagation effects, vortices transport high-OAM multiples of the corresponding OAM of the driving field and, finally, the different harmonic vortices are emitted with similar divergence. We also show the possibility of combining OAM and HHG phase locking to produce attosecond pulses with helical pulse structure.
155 citations
TL;DR: The generation of two-colour extreme ultraviolet pulses of controlled wavelengths, intensity and timing by seeding of high-gain harmonic generation free-electron laser with multiple independent laser pulses is reported.
Abstract: Exploring the dynamics of matter driven to extreme non-equilibrium states by an intense ultrashort X-ray pulse is becoming reality, thanks to the advent of free-electron laser technology that allows development of different schemes for probing the response at variable time delay with a second pulse. Here we report the generation of two-colour extreme ultraviolet pulses of controlled wavelengths, intensity and timing by seeding of high-gain harmonic generation free-electron laser with multiple independent laser pulses. The potential of this new scheme is demonstrated by the time evolution of a titanium-grating diffraction pattern, tuning the two coherent pulses to the titanium M-resonance and varying their intensities. This reveals that an intense pulse induces abrupt pattern changes on a time scale shorter than hydrodynamic expansion and ablation. This result exemplifies the essential capabilities of the jitter-free multiple-colour free-electron laser pulse sequences to study evolving states of matter with element sensitivity.
147 citations
TL;DR: In this paper, an all-optical photonic streaking measurement is demonstrated that provides direct experimental access to individual attosecond pulses, and the effects of non-adiabatic electron dynamics and plasma formation on the generated attoscond pulse train are directly observed when the pulse train is applied to harmonic generation in gases.
Abstract: An all-optical photonic streaking measurement is demonstrated that provides direct experimental access to individual attosecond pulses. The effects of non-adiabatic electron dynamics and plasma formation on the generated attosecond pulse train are directly observed when the pulse train is applied to harmonic generation in gases.
140 citations
TL;DR: This work demonstrates experimentally the key influence of the steepness of the plasma-vacuum interface on the interaction, by measuring the spectral and spatial properties of harmonics generated on a plasma mirror whose initial density gradient scale length L is continuously varied.
Abstract: High-order harmonics and attosecond pulses of light can be generated when ultraintense, ultrashort laser pulses reflect off a solid-density plasma with a sharp vacuum interface, i.e., a plasma mirror. We demonstrate experimentally the key influence of the steepness of the plasma-vacuum interface on the interaction, by measuring the spectral and spatial properties of harmonics generated on a plasma mirror whose initial density gradient scale length L is continuously varied. Time-resolved interferometry is used to separately measure this scale length.
137 citations
TL;DR: The TD-RASSCF (Time-dependent restricted-active-space self-consistent field) as discussed by the authors was proposed as a framework for the time-dependent many-electron problem.
Abstract: We present the time-dependent restricted-active-space self-consistent-field (TD-RASSCF) theory as a framework for the time-dependent many-electron problem. The theory generalizes the multiconfigurational time-dependent Hartree-Fock (MCTDHF) theory by incorporating the restricted-active-space scheme well known in time-independent quantum chemistry. Optimization of the orbitals as well as the expansion coefficients at each time step makes it possible to construct the wave function accurately while using only a relatively small number of electronic configurations. In numerical calculations of high-order harmonic generation spectra of a one-dimensional model of atomic beryllium interacting with a strong laser pulse, the TD-RASSCF method is reasonably accurate while largely reducing the computational complexity. The TD-RASSCF method has the potential to treat large atoms and molecules beyond the capability of the MCTDHF method.
127 citations
TL;DR: A novel scheme based on using below-threshold harmonics, generated in a “seeding cell”, to boost the HHG process in a "generation cell" placed further downstream in the focused laser beam, enhances the conversion efficiency of HHG, opening the path for the realization of robust intense attosecond XUV sources.
Abstract: High-order harmonic generation (HHG) in gases has been established as an important technique for the generation of coherent extreme ultraviolet (XUV) pulses at ultrashort time scales Its main drawback, however, is the low conversion efficiency, setting limits for many applications, such as ultrafast coherent imaging, nonlinear processes in the XUV range, or seeded free electron lasers Here we introduce a novel scheme based on using below-threshold harmonics, generated in a "seeding cell", to boost the HHG process in a "generation cell", placed further downstream in the focused laser beam By modifying the fundamental driving field, these low-order harmonics alter the ionization step of the nonlinear HHG process Our dual-cell scheme enhances the conversion efficiency of HHG, opening the path for the realization of robust intense attosecond XUV sources
99 citations
TL;DR: Numerical simulations of high-order harmonic generation in helium using a temporally synthesized and spatially nonhomogeneous strong laser field based on the convergence of three complementary approaches: resolution of the three dimensional time dependent Schrödinger equation, time-frequency analysis of the resulting dipole moment, and classical trajectory extraction.
Abstract: We present numerical simulations of high-order harmonic generation in helium using a temporally synthesized and spatially nonhomogeneous strong laser field. The combination of temporal and spatial laser field synthesis results in a dramatic cutoff extension far beyond the usual semiclassical limit. Our predictions are based on the convergence of three complementary approaches: resolution of the three dimensional time dependent Schrodinger equation, time-frequency analysis of the resulting dipole moment, and classical trajectory extraction. A laser field synthesized both spatially and temporally has been proven capable of generating coherent extreme ultraviolet photons beyond the carbon K edge, an energy region of high interest as it can be used to initiate inner-shell dynamics and study time-resolved intramolecular attosecond spectroscopy.
92 citations
TL;DR: A semiconductor saturable absorber mirror (SESAM) mode-locked thin disk laser (TDL) based on Yb:CaGdAlO(4) (Yb:CALGO) generating 62 fs pulses, which is the shortest pulse duration achieved from mode- Locked TDLs to date.
Abstract: We present a semiconductor saturable absorber mirror (SESAM) mode-locked thin disk laser (TDL) based on Yb:CaGdAlO(4) (Yb:CALGO) generating 62 fs pulses, which is the shortest pulse duration achieved from mode-locked TDLs to date. The oscillator operates at a repetition rate of 65 MHz and delivers 5.1 W of average output power. The short pulse duration of our TDL in combination with the high intracavity peak power of 44 MW makes this oscillator attractive for intracavity table-top extreme nonlinear optics applications such as high harmonic generation and vacuum ultraviolet frequency comb generation. The current average power was limited by the quality of the Yb:CALGO disk. However, power scaling of Yb:CALGO TDLs to the multi-10-W range with short pulse durations (<100 fs) appears feasible in the near future by using thinner disks of better quality and further optimized SESAMs.
91 citations
TL;DR: A robust scheme to select a single high-order harmonic among the harmonic comb by using a driving laser field with subcycle waveform control, which is synthesized by the fundamental 800 nm laser pulse and two controlling laser pulses at 400 and 267 nm with perpendicular polarizations is experimentally demonstrated.
Abstract: We experimentally demonstrate a robust scheme to select a single high-order harmonic among the harmonic comb by using a driving laser field with subcycle waveform control, which is synthesized by the fundamental 800 nm laser pulse and two controlling laser pulses at 400 and 267 nm with perpendicular polarizations. By controlling the relative phase among the pulses of different colors, a single high-order harmonic is selectively enhanced while the adjacent harmonics are greatly suppressed with the intensity contrast increased by more than 1 order of magnitude and the peak intensity enhanced simultaneously by more than 2 orders of magnitude compared to the case by using only the fundamental 800 nm laser pulse. Such phenomena can be mainly attributed to the intra-atomic phase matching realized with the sub-cycle waveform controlled field.
TL;DR: A table top setup for time- and angle-resolved photoelectron spectroscopy is presented to investigate band structure dynamics of correlated materials driven far from equilibrium by femtosecond laser pulse excitation.
Abstract: We present a table top setup for time- and angle-resolved photoelectron spectroscopy to investigate band structure dynamics of correlated materials driven far from equilibrium by femtosecond laser pulse excitation. With the electron-phonon equilibration time being in the order of 1–2 ps it is necessary to achieve sub-picosecond time resolution. Few techniques provide both the necessary time and energy resolution to map non-equilibrium states of the band structure. Laser-driven high-order harmonic generation is such a technique. In our experiment, a grating monochromator delivers tunable photon energies up to 40 eV. A photon energy bandwidth of 150 meV and a pulse duration of 100 fs FWHM allow us to cover the k-space necessary to map valence bands at different kz and detect outer core states.
TL;DR: A method is described for cooling the electron beam energy spread by off-resonance seed laser modulation, through the use of a transversely dispersed electron beam and a modulator undulator with an appropriate transverse field gradient.
Abstract: To improve temporal coherence in electron beam based light sources, various techniques employ frequency up conversion of external seed sources via electron beam density modulation; however, the energy spread of the beam may hinder the harmonic generation efficiency. In this Letter, a method is described for cooling the electron beam energy spread by off-resonance seed laser modulation, through the use of a transversely dispersed electron beam and a modulator undulator with an appropriate transverse field gradient. With this novel mechanism, it is shown that the frequency up-conversion efficiency can be significantly enhanced. We present theoretical analysis and numerical simulations for seeded soft x-ray free-electron laser and storage ring based coherent harmonic generation in the extreme ultraviolet spectral region.
TL;DR: An experimental strategy for the generation of high- energy high-order harmonics in gases for studies of nonlinear processes in the soft x-ray region and the macroscopic conditions for absorption-limited conversion efficiency and optimization of the HHG pulse energy for high-energy laser systems are theoretically examined.
Abstract: We develop and implement an experimental strategy for the generation of high-energy high-order harmonics (HHG) in gases for studies of nonlinear processes in the soft x-ray region. We generate high-order harmonics by focusing a high energy Ti:Sapphire laser into a gas cell filled with argon or neon. The energy per pulse is optimized by an automated control of the multiple parameters that influence the generation process. This optimization procedure allows us to obtain energies per pulse and harmonic order as high as 200 nJ in argon and 20 nJ in neon, with good spatial properties, using a loose focusing geometry (f#≈400) and a 20 mm long medium. We also theoretically examine the macroscopic conditions for absorption-limited conversion efficiency and optimization of the HHG pulse energy for high-energy laser systems.
TL;DR: It is shown that the carrier-envelope phase of laser pulses that contain huge numbers of cycles can cause profound effects, similar to high-order harmonic generation in atoms or molecules.
Abstract: We analyze the features of the output field of a generic optomechanical system that is driven by a control field and a nanosecond driven pulse, and find a robust high-order sideband generation in optomechanical systems. The typical spectral structure, plateau and cutoff, confirms the nonperturbative nature of the effect, which is similar to high-order harmonic generation in atoms or molecules. Based on the phenomenon, we show that the carrier-envelope phase of laser pulses that contain huge numbers of cycles can cause profound effects.
TL;DR: In this paper, the authors investigate electronic and structural material changes in the type I to type II transition via coherent and incoherent secondary light emission reflecting free carrier behavior and post-irradiation material relaxation in the index change patterns.
Abstract: Ultrashort laser pulses can modify the inner structure of fused silica, generating refractive index changes varying from soft positive (type I) light guiding forms to negative (type II) values with void presence and anisotropic sub-wavelength modulation. We investigate electronic and structural material changes in the type I to type II transition via coherent and incoherent secondary light emission reflecting free carrier behavior and post-irradiation material relaxation in the index change patterns. Using phase contrast microscopy, photoluminescence, and Raman spectroscopy, we determine in a space-resolved manner defect formation, redistribution and spatial segregation, and glass network reorganization paths in conditions marking the changeover between type I and type II photoinscription regimes. We first show characteristic patterns of second harmonic generation in type I and type II traces, indicating the collective involvement of free carriers and polarization memory. Second, incoherent photoemission ...
TL;DR: In this paper, a photonic crystal L3 cavity was used for second harmonic generation in a thin self-suspended lithium niobate membrane with a quality factor of around 500.
Abstract: We report on second harmonic generation in a photonic crystal L3 cavity drilled in a thin self-suspended lithium niobate membrane. The cavity, resonant for the pump beam in the telecom wavelength range, exhibits a quality factor of around 500. Second harmonic generation has been measured with a low power continuous laser. A conversion efficiency of 6.4×10−9 has been estimated with an input coupled power of 53 μW.
TL;DR: In this article, the authors investigated the response of multi-layer epitaxial graphene and chemical vapor deposition (CVD)-grown single-layer graphene to strong terahertz (THz) fields.
Abstract: We investigate the response of multi-layer epitaxial graphene and chemical vapor deposition (CVD)-grown single-layer graphene to strong terahertz (THz) fields. Contrary to theoretical predictions of strong nonlinear response, the transmitted fields exhibit no harmonic generation, indicating that the nonlinear response is limited by fast electron thermalization due to carrier-carrier scattering. The fast electron heating gives rise to large THz transmission enhancement (>15%) in single-layer CVD graphene at high THz fields (ETHz > 10kVcm 1 ). The nonlinear effects exhibit non-Drude behavior in the THz conductivity, where THz fields induce extreme non-equilibrium electron distributions.
TL;DR: In this paper, the authors present an experimental realization of cycle-shaped waveforms and demonstrate control of the HHG process on the single-atom quantum level via attosecond steering of the electron trajectories.
Abstract: Quasi-free field-driven electron trajectories are a key element of strong-field dynamics. Upon recollision with the parent ion, the energy transferred from the field to the electron may be released as attosecond duration XUV emission in the process of high harmonic generation (HHG). The conventional sinusoidal driver fields set limitations on the maximum value of this energy transfer, and it has been predicted that this limit can be significantly exceeded by an appropriately ramped-up cycleshape. Here, we present an experimental realization of such cycle-shaped waveforms and demonstrate control of the HHG process on the single-atom quantum level via attosecond steering of the electron trajectories. With our optimized optical cycles, we boost the field-ionization launching the electron trajectories, increase the subsequent field-to-electron energy transfer, and reduce the trajectory duration. We demonstrate, in realistic experimental conditions, two orders of magnitude enhancement of the generated XUV flux together with an increased spectral cutoff. This application, which is only one example of what can be achieved with cycle-shaped high-field light-waves, has farreaching implications for attosecond spectroscopy and molecular self-probing.
TL;DR: Nonlinear generation of higher harmonics leading to the emission of caustic spin-wave beams in a low-damping microstructured Co(2)Mn(0.6)Fe( 0.4)Si Heusler waveguide is reported.
Abstract: Magnetic Heusler materials with very low Gilbert damping are expected to show novel magnonic transport phenomena. We report nonlinear generation of higher harmonics leading to the emission of caustic spin-wave beams in a low-damping microstructured ${\mathrm{Co}}_{2}{\mathrm{Mn}}_{0.6}{\mathrm{Fe}}_{0.4}\mathrm{Si}$ Heusler waveguide. The source for the higher harmonic generation is a localized edge mode formed by the strongly inhomogeneous field distribution at the edges of the spin-wave waveguide. The radiation characteristics of the propagating caustic waves observed at twice and three times the excitation frequency are described by an analytical calculation based on the anisotropic dispersion of spin waves in a magnetic thin film.
TL;DR: In this article, the authors present theoretical investigations of high-order-harmonic generation (HHG) resulting from the interaction of noble gases with localized surface plasmons and demonstrate that the strong nonhomogeneity of this laser field plays an important role in the HHG process and leads to a significant increase of the harmonic-cutoff energy.
Abstract: We present theoretical investigations of high-order-harmonic generation (HHG) resulting from the interaction of noble gases with localized surface plasmons. These plasmonic near-fields are produced when a metal nanoparticle is subject to a few-cycle laser pulse. The enhanced field, which largely depends on the geometrical shape of the metallic nanostructure, has a strong spatial dependency. We demonstrate that the strong nonhomogeneity of this laser field plays an important role in the HHG process and leads to a significant increase of the harmonic-cutoff energy. In order to understand and characterize this feature, we include the functional form of the laser electric field obtained from recent attosecond streaking experiments [F. S\"u\ss{}mann and M. F. Kling, Proc. SPIE 8096, 80961C (2011)] in the time-dependent Schr\"odinger equation. By performing classical simulations of the HHG process we show consistency between them and the quantum-mechanical predictions. These allow us to understand the origin of the extended harmonic spectra as a selection of particular trajectory sets. The use of metal nanoparticles is an alternate way of generating coherent XUV light with a laser field whose characteristics can be synthesized locally.
TL;DR: In this paper, the authors report on the generation of extreme ultraviolet radiation utilizing the plasmonic field enhancement in arrays of bow-tie gold optical antennae, and their suitability to support high-order harmonic generation is examined by means of finite-difference time-domain calculations and experiments.
Abstract: We report on the generation of extreme ultraviolet radiation utilizing the plasmonic field enhancement in arrays of bow-tie gold optical antennae. Furthermore, their suitability to support high-order harmonic generation is examined by means of finite-difference time-domain calculations and experiments. Particular emphasis is paid to the thermal properties, which become significant at the employed peak intensities. A damage threshold depending on the antenna length is predicted and confirmed by our experimental findings. Moreover, the gas density in the vicinity of the antennae is characterized experimentally to determine the number of atoms contributing to the measured radiation, which is almost an order of magnitude larger than previously reported.
TL;DR: In this paper, the authors theoretically investigate high-order harmonic generation in a spatially inhomogeneous field with mid-infrared driving wavelength and few-cycle duration, and they show that this spatiotemporally synthesized electric field is powerful to control the quantum path; as a result an ultra-broadband supercontinuum with bandwidth over 300 eV can be obtained successfully.
Abstract: We theoretically investigate high-order harmonic generation in a spatially inhomogeneous field with mid-infrared driving wavelength and few-cycle duration. It is found that this spatiotemporally synthesized electric field is powerful to control the quantum path; as a result an ultra-broadband supercontinuum with bandwidth over 300 eV can be obtained successfully. Important characteristics of the attosecond pulse generation, including temporal envelope, harmonic chirp and carrier–envelope phase (CEP) dependence are further discussed. The results show that close-to-Fourier-limit 27 as isolated pulses are straightforwardly filtered from the supercontinuum. Moreover, such short isolated attosecond pulses can be supported by nearly all the CEPs of the laser electric field. This would open a way to obtain broadband isolated attosecond pulses with no need of CEP stabilization of the laser field.
TL;DR: In this article, the second and third harmonic generation (SHG/THG) of Bi2ZnOB2O6 crystals were investigated by the SHG/HG Maker fringes technique.
Abstract: Bi2ZnOB2O6 nonlinear optical single crystals were grown by means of the Kyropoulos method from stoichiometric melt. The second and third harmonic generation (SHG/THG) of Bi2ZnOB2O6 crystals were investigated by the SHG/THG Maker fringes technique. Moreover, SHG microscopy studies were carried out providing two-dimensional SHG images as a function of the incident laser polarization. The high nonlinear optical efficiency combined with the possibility to grow high quality crystals make Bi2ZnOB2O6 an excellent candidate for photonic applications.
TL;DR: In this paper, the effects of elastic and inelastic scattering, varying pulse characteristics and the inclusion of material-specific parameters through a realistic band structure are considered. And the authors find that the harmonic spectra are fairly robust against elastic and INELastic scattering.
Abstract: We consider several aspects of high-order harmonic generation in solids: the effects of elastic and inelastic scattering, varying pulse characteristics and inclusion of material-specific parameters through a realistic band structure. We reproduce many observed characteristics of high harmonic generation experiments in solids including the formation of only odd harmonics in inversion-symmetric materials, and the nonlinear formation of high harmonics with increasing field. We find that the harmonic spectra are fairly robust against elastic and inelastic scattering. Furthermore, we find that the pulse characteristics can play an important role in determining the harmonic spectra.
TL;DR: In this paper, the authors performed the first temporal characterization of the attosecond emission from a tin plasma under near-resonant conditions for two different resonance detunings.
Abstract: Resonant enhancement of high harmonic generation can be obtained in plasmas containing ions with strong radiative transitions resonant with harmonic orders. The mechanism for this enhancement is still debated. We perform the first temporal characterization of the attosecond emission from a tin plasma under near-resonant conditions for two different resonance detunings. We show that the resonance considerably changes the relative phase of neighboring harmonics. For very small detunings, their phase locking may even be lost, evidencing strong phase distortions in the emission process and a modified attosecond structure. These features are well reproduced by our simulations, allowing their interpretation in terms of the phase of the recombination dipole moment.
TL;DR: In this paper, the authors performed a spectrally and spatially resolved study in a controlled mixture of clusters and monomers, and they were able to isolate a region of the spectrum where the emission purely originates from clusters.
Abstract: High order harmonic generation from clusters is a controversial topic: conflicting theories exist, with different explanations for similar experimental observations. From an experimental point of view, separating the contributions from monomers and clusters is challenging. By performing a spectrally and spatially resolved study in a controlled mixture of clusters and monomers, we are able to isolate a region of the spectrum where the emission purely originates from clusters. Surprisingly, the emission from clusters is depolarized, which is the signature of statistical inhomogeneous emission from a low-density source. The harmonic response to laser ellipticity shows that this generation is produced by a new recollisional mechanism, which opens the way to future theoretical studies.
TL;DR: This work obtains the times of ionization and return of the laser-driven electron in high-order harmonic generation by probing the dynamics with a second harmonic field polarized orthogonal to the fundamental field and observing the harmonic emission in dependence on the two-color delay.
Abstract: From the numerical solution of the time-dependent Schr\"odinger equation, we obtain the times of ionization and return of the laser-driven electron in high-order harmonic generation by probing the dynamics with a second harmonic field polarized orthogonal to the fundamental field and observing the harmonic emission in dependence on the two-color delay. Our retrieval method using complex-time evolution gives ionization and return times in excellent agreement with the quantum-orbit model, while a retrieval based on real-time classical dynamics can introduce substantial errors. Because of the imaginary parts, the harmonic signal polarized along the probe field is nonzero for any two-color delay. The tunneling time can be retrieved under an assumption for the return time.
TL;DR: In this paper, the atomic nonlinear polarization induced by high-intensity ultrashort laser pulses in hydrogen was modeled by numerically solving the time-dependent Schrodinger equation.
Abstract: Motivated by the ongoing controversy over the origin of the nonlinear index saturation and subsequent intensity clamping in femtosecond filaments, we study the atomic nonlinear polarization induced by high-intensity ultrashort laser pulses in hydrogen by numerically solving the time-dependent Schr\"odinger equation. Special emphasis is given to the efficient modeling of the nonlinear polarization at a central laser frequency corresponding to a wavelength of 800 nm. Here, the recently proposed model of the higher-order Kerr effect (HOKE) and two versions of the standard model for femtosecond filamentation, including either a multiphoton or tunnel ionization rate, are compared. We find that around the clamping intensity the instantaneous HOKE model does not reproduce the temporal structure of the nonlinear response obtained from the quantum-mechanical results. In contrast, the noninstantaneous charge contributions included in the standard models ensure a reasonable quantitative agreement. Therefore, the physical origin for the observed saturation of the overall electron response is confirmed to mainly result from contributions of free or nearly-free electrons.
TL;DR: In this article, the subcycle rate for transitions of electrons between two bands of a sinusoidal band structure is derived and a simple closed-form expression for the rate is derived.
Abstract: In this paper a method is presented for calculating the subcycle rate for transitions of electrons between two bands of a sinusoidal band structure. A simple closed-form expression for the rate is derived. We show that transition dynamics are sensitive to the shape of the band structure away from the minima of the conduction band. A model of high-order-harmonic generation in periodic solids that incorporates the subcycle dynamics of transitions across the band gap is described. Harmonic emission is found to be highly sensitive to the temporal shape of the transition rate. Destructive interference of electron currents in the conduction band due to subcycle transition dynamics is described.