Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics Letters

High-field harmonic generation in helium

John K. Crane, R. W. Falcone, M. D. Perry, Steve M. Herman

Published Sep 15, 1992• 73 citations
Publisher

Abstract

We observe harmonics of 526-nm laser light up to the 45th order, 11.7 nm, in helium. We discuss the extension of the harmonic plateau with increasing laser intensity. The data suggest that the highest harmonic order produced depends on the highest intensity seen by the atom before photoionization. Harmonics are generated predominantly from neutrals. Harmonic generation from ions is weak owing to poor phase matching between the fundamental and harmonic fields at high electron densities.

DOI
10.1364/ol.17.001256

Related papers

Nonperturbative theory of harmonic generation in helium under a high-intensity laser field: The role of intermediate resonance and of the ion

Huale Xu, Xian Tang, P. Lambropoulos

The time-dependent Schr\"odinger equation for the helium atom with a model potential is solved on a numerical grid. The effects of intermediate-state resonance and of the ionization of the atom upon the harmonic generation are investigated. We also evaluate the contribution of the helium ion when the laser intensity is sufficiently high for most of the atoms to be ionized during the laser pulse. We find that the harmonics with order higher than 13 are due to the ion when the photon energy is 5.0 eV, while for photon energy 2.0 eV the atom produces up to about the 49th harmonic.

Physical Review A•Sep 1, 1992•68 citations

Intensity dependence of the phase of harmonics in one- and two-frequency laser fields

W.-C. Liu, Charles W. Clark

The phase relationship between an induced atomic dipole moment and a driving laser field is an essential aspect of high harmonic generation (HHG) in a dense medium. A ``phase-matching'' criterion must be fulfilled to obtain coherent amplification of harmonic radiation, which is critical for practical HHG. We have performed numerical calculations on model atoms to survey the intensity dependence of the phase in the case of strong one- or two-frequency laser fields. The calculations show that multiphoton resonances significantly affect the yield of harmonic generation and that in the ``plateau'' regime, the phases exhibit only weak dependence upon the intensity of the driving field. \textcopyright{}1996 The American Physical Society.

Physical Review A•May 1, 1996•5 citations

Second-harmonic generation at Lyman-α in atomic hydrogen

L. Marmet, K. Hakuta, Boris Peter Stoicheff

Second-harmonic generation in atomic hydrogen is investigated with and without an applied electric field, by tuning laser radiation at 243.1 nm through the 2 (2)S((1/2))-1(2)S((1/2)) two-photon resonance. Even at zero applied field, secondharmonic radiation at 121.6 nm was observed. The measured intensity is shown to arise from a charge-separation field caused by ions produced in three-photon ionization. calculated value based on the measured ion density.

Optics Letters•Feb 15, 1991•7 citations

Second-harmonic generation in atomic hydrogen at Lyman-α

L. Marmet, K. Hakuta, Boris Peter Stoicheff

We have observed second-harmonic generation in atomic hydrogen in the Lyman-α region, with and without an applied dc electric field, Ea. Experiments with a continuous atomic beam were carried out by using a pulsed dye laser tuned to 243 nm for excitation of the n = 2-1 transition. The laser beam was focused 0.4 mm below the H-source nozzle, where the H-atom density was estimated to be 5 × 1013 cm-3. Measurements of second-harmonic generation (SHG) at ~122 nm were made at various electric fields up to ~27 kV/cm. It was shown that the SH signal produced at E a = 0 occurs because of a charge-separation field of ~800 V/cm that is caused by three-photon ionization. Measurements of the SHG and ion current were found to vary as I2 L and I3 L , respectively. At high fields (E a > 10 kV/cm) the SH signal at the center of the Stark-split components decreased somewhat from the peak value, but the ion current (corresponding to photon absorption) approached zero. This observation is a clear demonstration of a similar effect, predicted by Harris et al.1 of efficient nonlinear conversion with induced transparency, and it suggests the possibility of obtaining intense Lyman-a radiation.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations

Super-Dressed Two-Level Atom: Very High Harmonic Generation and Multi-Resonances

A. E. Kaplan, P. L. Shkolnikov

We show that a simple nonperturbative two-level model of an atom driven by a very strong periodic field, results in a rich picture of very high harmonic generation and related phenomena. It reproduces experimentally observed plateau, yields for the first time simple analytic formulas for the plateau cutoff frequency, critical driving intensity, and saturation, and predicts intensity-induced multi-resonances. One of the most fascinating phenomenon discovered recently in nonlinear interaction of light with atoms and ions, is very high-order (up to 135) odd harmonic generation (HHG) by intense (∼ 1013 W/cm2 and higher) optical laser radiation in rare gasses and some ions [1], The spectra of generated harmonics drasticly deviate from the perturbation theory predictions [2], In particular, intensity of harmonics, falling monotonically with their orders only up to a certain point, levels off forming a so-called “plateau", and falls monotonically again beyond it. Generally, harmonte generation depends on phase-matching conditions and nonlinear response of individual atoms. It has recently become clear however [3,4] that the major features of HHG, in particular the plateau, result mainly from general properties of atomic nonlinear response. The most direct and apparently successful way so far to approach the problem theoretically has been numerical simulation of the Schrödinger [2,5-7] (including an empiric rule [6]) for many-electron atoms using Hartry-Slater approximation. This approach requires, however, tremendous amount of calculations and involves many processes, making it difficult to gain simple insights. An interesting simplified model [8] based on 3-D delta-potential with a single (ground) level [9] produces results in integration form. The idea of retaining a single energy scale (ionization energy) brings one close to an even simpler system: a two-level model atom. A two-level model of HHG [10], however, due to various complications introduced into it, failed to generate simple results, whereas an analytic solution [11] holds for a virtually degenerate two-level model only (see below) which is unapplicable to the experimental conditions [1-4,7,9]; besides, no relaxation was considered in [10,11].

Shortwavelength: Physics with Intense Laser Pulses•Jan 1, 1993•1 citation

Ellipticity dependence of harmonic generation in atomic hydrogen

Emine Meşe, R. M. Potvliege

The dependence on the ellipticity of the incident laser field of the harmonics generated by atoms of hydrogen in the multiphoton regime is examined for two fundamental wavelengths, 532 and 1064 nm. The single atom response is calculated nonperturbatively using the Floquet method in conjunction with basis sets of complex Sturmian functions. The results are compared with those obtained using lowest order perturbation theory. Nonperturbative effects modify the strength and polarization of the harmonics at the highest intensities investigated, particularly, for the threshold harmonics and in the vicinity of Stark-shift-induced resonances. No anomalous dependence of the rate of harmonic generation on the ellipticity of the fundamental field is found.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 19, 2005•8 citations
We observe harmonics of 526-nm laser light up to the 45th order, 11.7 nm, in helium. We discuss the extension of the harmonic plateau with increasing laser intensity. The data suggest that the highest harmonic order produced depends on the highest intensity seen by the atom before photoionization. Harmonics are generated predominantly from neutrals. Harmonic generation from ions is weak owing to poor phase matching between the fundamental and harmonic fields at high electron densities.
The time-dependent Schr\"odinger equation for the helium atom with a model potential is solved on a numerical grid. The effects of intermediate-state resonance and of the ionization of the atom upon the harmonic generation are investigated. We also evaluate the contribution of the helium ion when the laser intensity is sufficiently high for most of the atoms to be ionized during the laser pulse. We find that the harmonics with order higher than 13 are due to the ion when the photon energy is 5.0 eV, while for photon energy 2.0 eV the atom produces up to about the 49th harmonic.
The phase relationship between an induced atomic dipole moment and a driving laser field is an essential aspect of high harmonic generation (HHG) in a dense medium. A ``phase-matching'' criterion must be fulfilled to obtain coherent amplification of harmonic radiation, which is critical for practical HHG. We have performed numerical calculations on model atoms to survey the intensity dependence of the phase in the case of strong one- or two-frequency laser fields. The calculations show that multiphoton resonances significantly affect the yield of harmonic generation and that in the ``plateau'' regime, the phases exhibit only weak dependence upon the intensity of the driving field. \textcopyright{}1996 The American Physical Society.
We have observed second-harmonic generation in atomic hydrogen in the Lyman-α region, with and without an applied dc electric field, Ea. Experiments with a continuous atomic beam were carried out by using a pulsed dye laser tuned to 243 nm for excitation of the n = 2-1 transition. The laser beam was focused 0.4 mm below the H-source nozzle, where the H-atom density was estimated to be 5 × 1013 cm-3. Measurements of second-harmonic generation (SHG) at ~122 nm were made at various electric fields up to ~27 kV/cm. It was shown that the SH signal produced at E a = 0 occurs because of a charge-separation field of ~800 V/cm that is caused by three-photon ionization. Measurements of the SHG and ion current were found to vary as I2 L and I3 L , respectively. At high fields (E a > 10 kV/cm) the SH signal at the center of the Stark-split components decreased somewhat from the peak value, but the ion current (corresponding to photon absorption) approached zero. This observation is a clear demonstration of a similar effect, predicted by Harris et al.1 of efficient nonlinear conversion with induced transparency, and it suggests the possibility of obtaining intense Lyman-a radiation.
We show that a simple nonperturbative two-level model of an atom driven by a very strong periodic field, results in a rich picture of very high harmonic generation and related phenomena. It reproduces experimentally observed plateau, yields for the first time simple analytic formulas for the plateau cutoff frequency, critical driving intensity, and saturation, and predicts intensity-induced multi-resonances. One of the most fascinating phenomenon discovered recently in nonlinear interaction of light with atoms and ions, is very high-order (up to 135) odd harmonic generation (HHG) by intense (∼ 1013 W/cm2 and higher) optical laser radiation in rare gasses and some ions [1], The spectra of generated harmonics drasticly deviate from the perturbation theory predictions [2], In particular, intensity of harmonics, falling monotonically with their orders only up to a certain point, levels off forming a so-called “plateau", and falls monotonically again beyond it. Generally, harmonte generation depends on phase-matching conditions and nonlinear response of individual atoms. It has recently become clear however [3,4] that the major features of HHG, in particular the plateau, result mainly from general properties of atomic nonlinear response. The most direct and apparently successful way so far to approach the problem theoretically has been numerical simulation of the Schrödinger [2,5-7] (including an empiric rule [6]) for many-electron atoms using Hartry-Slater approximation. This approach requires, however, tremendous amount of calculations and involves many processes, making it difficult to gain simple insights. An interesting simplified model [8] based on 3-D delta-potential with a single (ground) level [9] produces results in integration form. The idea of retaining a single energy scale (ionization energy) brings one close to an even simpler system: a two-level model atom. A two-level model of HHG [10], however, due to various complications introduced into it, failed to generate simple results, whereas an analytic solution [11] holds for a virtually degenerate two-level model only (see below) which is unapplicable to the experimental conditions [1-4,7,9]; besides, no relaxation was considered in [10,11].
The dependence on the ellipticity of the incident laser field of the harmonics generated by atoms of hydrogen in the multiphoton regime is examined for two fundamental wavelengths, 532 and 1064 nm. The single atom response is calculated nonperturbatively using the Floquet method in conjunction with basis sets of complex Sturmian functions. The results are compared with those obtained using lowest order perturbation theory. Nonperturbative effects modify the strength and polarization of the harmonics at the highest intensities investigated, particularly, for the threshold harmonics and in the vicinity of Stark-shift-induced resonances. No anomalous dependence of the rate of harmonic generation on the ellipticity of the fundamental field is found.