Harmonic Generation Spectra Research Articles

Effect of material properties on the accuracy of antiresonant approximation: Linear and second-order optical responses

Many ab initio calculations, in particular in solid state physics, rely on the antiresonant approximation. In this paper we discuss the derivation, the validity, and the accuracy of this approximation, analyzing how the optical properties of several bulk semiconducting materials and surfaces can be affected. We present accurate results for different spectroscopic quantities in the linear and nonlinear responses and we analyze the discrepancies between approximated and exact formulas. An investigation is made of the effect of the approximation on absorption spectra for different materials, showing the reliability of the approximation even in the presence of local field and excitonic effects. The energy loss is shown to be drastically affected. The effect of the band gap of materials on the quality of the approximation is also discussed. Finally, we report on the influence of the antiresonant approximation on second harmonic generation spectra.

High-order harmonic generation by H in super-intense xuv ultrashort laser pulses

Dynamics of the two-dimensional H under 30- and 40-cycle xuv (45 and 90 nm) laser pulses is investigated by numerical solution of the time-dependent Schrödinger equation beyond the dipole and Born–Oppenheimer approximations for two orientations (θ = 0° and θ = 90° referenced to the molecular axis) of the laser polarization. Dynamics of the electron and nuclei are treated in quantum and classical approaches, respectively. The ground, first and second excited states of H are considered as initial states for different laser field intensities in the range of (4 × 1016 – 4 × 1019 W cm−2). For parallel orientation (θ = 0°), a negligibly small difference is seen for high-order harmonic generation (HOHG) spectra obtained with the dipole and non-dipole Hamiltonians for all three electronic states. While, for the perpendicular orientation (θ = 90°), non-dipole forces attenuate the HOHG spectra for the initial ground and the second excited states. For the initial first excited state and orientation θ = 90°, the motion of nuclei considerably increases the HOHG yield within the dipole approximation, but decreases it partially beyond dipole approximation. It is shown that contribution of the motion of nuclei to the HOHG yield depends on the extent of the increase in the separation between nuclei.

Time-dependent restricted-active-space self-consistent-field singles method for many-electron dynamics

The time-dependent restricted-active-space self-consistent-field singles (TD-RASSCF-S) method is presented for investigating TD many-electron dynamics in atoms and molecules. Adopting the SCF notion from the muticonfigurational TD Hartree-Fock (MCTDHF) method and the RAS scheme (single-orbital excitation concept) from the TD configuration-interaction singles (TDCIS) method, the TD-RASSCF-S method can be regarded as a hybrid of them. We prove that, for closed-shell Ne-electron systems, the TD-RASSCF-S wave function can be fully converged using only Ne/2 + 1 ⩽ M ⩽ Ne spatial orbitals. Importantly, based on the TD variational principle, the converged TD-RASSCF-S wave function with M = Ne is more accurate than the TDCIS wave function. The accuracy of the TD-RASSCF-S approach over the TDCIS is illustrated by the calculation of high-order harmonic generation spectra for one-dimensional models of atomic helium, beryllium, and carbon in an intense laser pulse. The electronic dynamics during the process is investigated by analyzing the behavior of electron density and orbitals. The TD-RASSCF-S method is accurate, numerically tractable, and applicable for large systems beyond the capability of the MCTDHF method.

Theoretical exploration of control factors for the high-order harmonic generation (HHG) spectrum in two-color field

In this work, the laser-parameter effects on the high-order harmonic generation (HHG) spectrum and attosecond trains by mixing two-color laser field, a visible light field of 800nm and a mid-infrared (mid-IR) laser pulses of 2400nm, are theoretically demonstrated for the first time. Different schemes are applied to discuss the function of intensity, carrier-envelope phase (CEP) and pulse duration on the generation of an isolated attosecond pulse. As a consequence, an isolated 16as pulse is obtained by Fourier transforming an ultrabroad XUV continuum of 208eV with the fundamental field of duration of 6fs, 9×1014W/cm2 of intensity, the duration of 12fs, the CEPs of the two driving pulses of −π and the relative strength ratio R=0.2.

Electronic states at polar/nonpolar interfaces grown on SrTiO3studied by optical second harmonic generation

Optical second harmonic generation (SHG) spectra of LaAlO${}_{3}$/SrTiO${}_{3}$, LaGaO${}_{3}$/SrTiO${}_{3}$, and NdGaO${}_{3}$/SrTiO${}_{3}$ interfaces with SrTiO${}_{3}$ substrates have been measured up to 4.2 eV as a function of film thickness and temperature. This spectral range is characterized by two-photon transitions from the valence to conduction bands of SrTiO${}_{3}$ which are classified with a model based on symmetry, selection rules, and atomic orbital overlaps. This model is further confirmed in spectral measurements as a function of film thickness, material overlayer, and temperature. SHG enhancement at low temperature indicates an increase of the interfacial polarity with decreasing temperature. This confirms the relation between SHG and the spatial translation of Ti ions which are more prone to move at lower temperatures because of the quantum-paraelectric nature of SrTiO${}_{3}$. We finally show that SHG spectroscopy captures structural details of the interfaces. In particular, we find evidence for proximity effects such as LaAlO${}_{3}$-induced distortions of the TiO${}_{6}$ octahedra or bond buckling. We also observe a correlation between SHG and the in-plane lattice mismatch between the SrTiO${}_{3}$ substrate and the LaAlO${}_{3}$, LaGaO${}_{3}$, and NdGaO${}_{3}$ overlayers.

Evaluation of domain randomness in periodically poled lithium niobate by diffraction noise measurement

Random duty-cycle errors (RDE) in ferroelectric quasi-phase-matching (QPM) devices not only affect the frequency conversion efficiency, but also generate non-phase-matched parasitic noise that can be detrimental to some applications. We demonstrate an accurate but simple method for measuring the RDE in periodically poled lithium niobate. Due to the equivalence between the undepleted harmonic generation spectrum and the diffraction pattern from the QPM grating, we employed linear diffraction measurement which is much simpler than tunable harmonic generation experiments [J. S. Pelc, et al., Opt. Lett.36, 864-866 (2011)]. As a result, we could relate the RDE for the QPM device to the relative noise intensity between the diffraction orders.

High harmonic generation in H2 + and HD + by two-colour femtosecond laser pulses

We have theoretically investigated the high harmonic generation (HHG) spectra of H2 + and HD + using a time-dependent wave packet approach for the nuclear motion with combined two-colour (1ωL–3ωL) pulsed lasers for ωL corresponding to wavelengths 1064 nm and 800 nm. The 1ωL and 3ωL lasers have peak intensities of I10 = 5.0×1013 W/cm2 and I20 = 2.0×1014 W/cm2, respectively. We have taken the pulse duration of T = 50 fs for both the fields, and the molecular initial vibrational level v0 = 0. We have argued that for these combinations, the harmonic generation due to transitions in the electronic continuum by tunnelling or multiphoton ionization may be neglected and only the electronic transitions within the two lowest electronic states would be important. Thus, the characteristic features of HHG spectra in the two-colour field are determined, in our model, by the nuclear motions on the two lowest field-coupled electronic states between which interelectronic and intraelectronic (due to the intrinsic dipole moments in case of HD + ) radiative transitions can take place. We have studied the role of relative phase (φ) of the two fields on the HHG spectra of the molecular ions. In case of HD + , the effect of nonadiabatic (NA) nonradiative interaction between the two lowest Born-Oppenheimer (BO) electronic states (1sσg, 2pσu) has been taken into account. Our calculations give realistic HHG spectra which are reasonably efficient and extended for both H2 + and HD + in the mixed two-colour field without involving the electronic continuum. The use of two-colour (1ωL–3ωL) field enables us to generate high harmonics beyond that achievable with a single 1ωL or 3ωL field of the corresponding intensity, frequency and pulse time.

The role of Rydberg and continuum levels in computing high harmonic generation spectra of the hydrogen atom using time-dependent configuration interaction

We study the role of Rydberg bound-states and continuum levels in the field-induced electronic dynamics associated with the High-Harmonic Generation (HHG) spectroscopy of the hydrogen atom. Time-dependent configuration-interaction (TD-CI) is used with very large atomic orbital (AO) expansions (up to L = 4 with sextuple augmentation and off-center functions) to describe the bound Rydberg levels, and some continuum levels. To address the lack of ionization losses in TD-CI with finite AO basis sets, we employed a heuristic lifetime for energy levels above the ionization potential. The heuristic lifetime model is compared against the conventional atomic orbital treatment (infinite lifetimes), and a third approximation which is TD-CI using only the bound levels (continuum lifetimes go to zero). The results suggest that spectra calculated using conventional TD-CI do not converge with increasing AO basis set size, while the zero lifetime and heuristic lifetime models converge to qualitatively similar spectra, with implications for how best to apply bound state electronic structure methods to simulate HHG. The origin of HHG spectral features including the cutoff and extent of interference between peaks is uncovered by separating field-induced coupling between different types of levels (ground state, bound Rydberg levels, and continuum) in the simulated electronic dynamics. Thus the origin of deviations between the predictions of the semi-classical three step model and the full simulation can be associated with particular physical contributions, which helps to explain both the successes and the limitations of the three step model.

The influence of the quantum nature of nuclei in high harmonic generation from H+2-like molecular ions

We study the full quantum dynamics of a simple molecular ion driven by an intense laser field. In particular we show that the quantum nature of the nuclear dynamics affects the emitted high harmonic generation (HHG) spectra, strongly reshaping the plateau region. In fact, it is evident that the characteristic flat trend is transformed into a descending trend, with the lower harmonics being two orders of magnitude more intense than the higher harmonics. We show that this effect is more pronounced in the lighter isotopic species of H2+ molecular ions and we also demonstrate that in this case the contribution to HHG from the antibonding electronic energetic surface is of the same order of magnitude as that from the bonding state.

Structural and nonlinear optical properties of as-grown and annealed metallophthalocyanine thin films

The paper presents the Third Harmonic Generation investigation of four metallophtalocyanine (MPc, M=Cu, Co, Mg and Zn) thin films. The investigated films were fabricated by Physical Vapor Deposition in high vacuum onto quartz substrates. MPc thin films were annealed after fabrication in ambient atmosphere for 12h at the temperature equal to 150°C or 250°C. The Third Harmonic Generation spectra were measured to investigate the nonlinear optical properties and their dependence on the structure of the thin film after the annealing process. This approach allowed us to determine the electronic contribution of the third-order nonlinear optical susceptibility χ<3>elec of these MPc films and to investigate two theoretical models for explanation of the observed results. We find that the annealing process significantly changes the optical and structural properties of MPc thin films.

Time-dependent restricted-active-space self-consistent-field theory for laser-driven many-electron dynamics

We present the time-dependent restricted-active-space self-consistent field (TD-RASSCF) theory as a new 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.

High harmonic generation in $\textbf{H}_{{2}}^{{+}} $ and HD + by intense femtosecond laser pulses: A wave packet approach with nonadiabatic interaction in HD +

We have theoretically investigated the high harmonic generation (HHG) spectra of \(\textrm{H}_2^+ \) and HD + using a time-dependent wave packet approach for the nuclear motion with pulsed lasers of peak intensities (I0) of 3.5 ×1014 and 4.5 ×1014 W/cm2, wavelengths (λL) of 800 and 1064 nm, and pulse durations (T) of 40 and 50 fs, for initial vibrational levels v0 = 0 and 1. We have argued that for these conditions the harmonic generation due to the transitions in the electronic continuum by tunnelling or multiphoton ionization will not be important. Thus, the characteristic features of HHG spectra in our model arise only due to the nuclear motions on the two lowest field-coupled electronic states between which both interelectronic and intraelectronic (due to intrinsic dipole moments, for HD + ) radiative transitions can take place. For HD + , the effect of nonadiabatic (NA) interaction between the two lowest Born–Oppenheimer (BO) electronic states has been taken into account and comparison has been made with the HHG spectra of HD + obtained in the BO approximation. Even harmonics and a second plateau in the HHG spectra of HD + with the NA interaction and hyper-Raman lines in the spectra of both \(\textrm{H}_2^+ \) and HD + for v0 = 1 have been observed for higher value of I0 or λL. Our calculations indicate reasonable efficiencies of harmonic generation even without involving the electronic continuum.

Application of smooth exterior scaling method to calculate the high harmonic generation spectra

We have calculated the high harmonic generation spectra from Xe atom by imposing different kinds of absorbing potentials. Owing to the center of inversion of the model system, one should get odd harmonics only. However, using negative imaginary potentials as an absorbing boundary condition, we have also got even order harmonics along with the odd order harmonics. These non-odd order harmonics are generated due to the spurious reflections occurring at the grid boundary. On the contrary, when smooth exterior scaling methods are used as an absorbing boundary condition, only odd order harmonics are obtained. Hence, smooth exterior scaling methods impose proper absorbing boundary condition.

Carrier envelope phase retrieval of a multi-cycle pulse by heterodyne mixing of a pulse containing a few cycles

We present a theoretical routine for carrier envelope phase (CEP) retrieval of a multi-cycle femtosecond pulse by heterodyne mixing with a CEP-known few-cycle pulse using the time-dependent wavepacket quantum dynamics method. Our study is based on the CEP measuring technique and the dependence of high-order harmonic generation (HHG) spectra on CEP. After heterodyne mixing, half-cycle cutoffs (HCOs) in HHG spectra become distinct when the CEPs of multi-cycle and few-cycle pulses are well matched. The well-matched CEP of the heterodyne mixing field has a significant effect on the HHG spectra. Moreover, both quantum analysis and classical calculations are performed to demonstrate our theoretical results. The extension of CEP measurement from few-cycle pulses to multi-cycle pulses strengthens the controllability of laser parameters for femtosecond pulses.

Analysis on the cutoff frequency of high order harmonic generation in the crystal

By numerically solving the time-dependent Schrödinger equation with the interaction between one-dimensional multi-well potential and the mid-infrared few-cycle femtosecond pulses, we theoretically investigate the high-order harmonic generation spectra in a crystal, further find the cutoff frequency formula under the new condition. Our results clearly show that the high order harmonic generation in the crystal is fundamentally different from that in the atomic case, owing to the high density and periodic structure. The harmonics spectrum shows a cutoff position that scales linearly with the peak amplitude of electric field of the drive laser and the lattice parameters. Based on the important role of the three-step model obtained by quasi-calssical mechanics method in gas harmonic generation, in this paper, this method is also well used to verify the cutoff position law in crystal harmonic generation.

Characterization, Optical, and Theoretical Investigation of Arrays of the Metallic Nanowires Fabricated by a Shadow Deposition Method

We have fabricated Au, Cu, and Pt nanowires by using a shadow deposition technique. We have then investigated optical properties of these nanowires by studying the second harmonic generation (SHG) spectra. With experimental and theoretical studies, we have discovered that the surface plasmon resonance was served as an origin of the enhancement of the SH response from the metallic nanowires.

Nonlinear Optical Properties of Controlled Fabrication of Copper Nanowires by a Shadow Deposition

The strongly geometrical shape, high aspect ratios, and nanoscale cross-section of nanowires is expected to affect optical properties through confinement effects. Herein we have investigated optical properties of Cu nanowires with studies of second harmonic generation (SHG) spectra. These optical properties of Cu nanowires will be one of the most important issues when considering the types of materials used in current applications and development of new applications.

Influence of ultrashort pulses on resonantly driven systems

The influence of ultrashort low-frequency laser pulses of different intensities and pulse lengths on the dynamics of a resonantly driven atomic system is investigated theoretically. We demonstrate the periodical dependence of the total ionization rate on the appearance time of a strong few-cycle laser pulse. By depleting the excited state, the intense short pulse not only resets the Rabi oscillations, but also introduces a time shift that is proportional to the pulse length. This time shift can be employed to determine the ultrashort pulse length. In the case of ultrashort pulses with lower intensities, we observe side-bands in the two-photon ionization spectrum, whose intensities vary periodically with the appearance time of the pulse. This can be utilized to measure the period of Rabi oscillations. We have developed an S-matrix theory of two-colour ionization which can explain some of the observations of our numerical calculations. Furthermore, we have studied the high harmonic generation spectra as well as the attosecond pulses generated from the high harmonics. We show that the Rabi oscillation can be used to alter the ionization rate within laser sub-cycles and therefore select different quantum trajectories in the high harmonics generation.

Linear and nonlinear optical response of LiNbO3 calculated from first principles

The dielectric function and second-harmonic generation spectrum of ferroelectric LiNbO(3) are calculated from first principles. The calculations are based on the electronic structure obtained within density functional theory. The use of the GW approach to account for quasiparticle effects and the subsequent solution of the Bethe-Salpeter equation lead to a dielectric function in excellent agreement with measured data. The second harmonic generation spectrum calculated within the independent (quasi) particle approximation predicts strong nonlinear coefficients for photon energies above about 1.5 eV. The comparison with measured data suggests that the inclusion of self-energy effects in the nonlinear response improves the agreement with experiment.

Retrieving Molecular Structural Information and Tracking HNC/HCN Isomerization Process with High Harmonic Generation by Ultrashort Laser Pulses

We investigate the possibility of applying the iterative method,suggested in our previous work, for HCN molecule and its HNCisomer. We found that the high-order harmonic generation (HHG)spectra are quite insensitive to the change of H-C (or H-N) bondlength so that only the inter-nuclear C-N distance can beretrieved from the high-order harmonic spectra using ultrashortintense lasers. Furthermore, by analyzing the HHG spectra emittedby HCN during the chemical reaction path of isomerization weidentify the intensity peaks nearby the stable, meta-stable andtransition states. This finding can be useful for tracking theHNC/HCN isomerization process.