Applications of high-order harmonics

We review applications of high-order harmonic generation in different fields of physics, from spectroscopic studies of atoms and molecules, to interferometry and plasma diagnostics and nonlinear optics.Received: 11 December 2002, Published online: 24 April 2003PACS: 32.80.Fb Photoionization of atoms and ions - 42.65.Ky Frequency conversion; harmonic generation, including higher-order harmonic generationD. Descamps: Present address: CEA/DRECAM/SPAM, CEN Saclay, 91105 Gif-sur-Yvette, France.     

Ramsey-type spectroscopy with high-order harmonics

We present an experiment where Ramsey-type spectroscopy is applied to autoionizing states of krypton by using the ninth harmonic (88 nm) of a femtosecond Ti:sapphire laser. The ionization process, detected by an electron-energy spectrometer, shows the characteristic quantum interference pattern. The behavior of the fringe contrast compares favorably with a simple essential-state model, whose parameters have been taken from the literature. The experiment shows the feasibility of high-resolution spectroscopy in the extreme ultraviolet by using high-order laser harmonics.     

Self-induced parametric amplification of high-order harmonics

A theoretical analysis of self-induced parametric amplification of high-order harmonics is given. This mechanism permits the elimination of limitations on the harmonic-generation efficiency that are imposed by absorption.     

Multi-color XUV interferometry using high-order harmonics

We present a novel interferometric setup operating in the XUV spectral range. The interferometer consists of a combination of a double pinhole (similar to Young’s double slit) and a transmission grating. In the case of a light source consisting of discrete spectral lines, it allows recording interferograms for multi-colors simultaneously. We present two experiments in which high-order harmonics generated by a titanium sapphire laser were used as the light source for the interferometer. First, the temporal coherence lengths of the single harmonics were determined, and second, the index of refraction and the absorption of a thin beryllium foil were measured simultaneously in the range of 17–25 nm.     

介质的非均匀性对高次谐波影响的研究

讨论了气体介质的非均匀性对飞秒激光高次谐波产生过程的可能影响.计算结果表明,采用喷阀技术所提供的气体介质的密度梯度和气体原子运动速度的影响很小,不会产生实验上可观测的效果.这一结果支持了喷气靶在高次谐波产生中的广泛应用 关键词： 高次谐波 气体介质 各向异性 飞秒激光     

Two-color pump-probe experiments in helium using high-order harmonics

A pump-probe technique has been applied for measuring the lifetimes and absolute photoionization cross-sections of excited He states. The 1s2p ¹P and 1s3p ¹P states of He are excited by using the 13th and the 14th harmonic, respectively, of a tunable 70 ps dye laser generated in a Kr gas jet. The states are ionized after a varying time delay, by absorption of probe photons with energies between 1.6 and 4.5 eV. Lifetimes of τ(1s2p) = 0.57 ns and τ(1s3p) = 1.76 ns are determined with a precision of about 15%. A significant enhancement of the number of ions present in the lifetime curves at zero time delay for pressures above 6×10^-5 mbar is attributed to direct two-photon ionization of He in combination with AC Stark broadening of the excited state and absorption of the XUV light in the medium. Absolute photoionization cross-sections from the He 1s2p ¹P and He 1s3p ¹P states in the threshold region are determined by measuring the saturation of the ionization process with a precision of ∼ 25%. In addition, the variation of the relative orientation between the polarization vectors of the pump and probe beams enables the determination of partial photoionization cross-sections. Received 3 June 2002 / Received in final form 14 August 2002 Published online 22 October 2002 RID="a" ID="a"Present address: Department of Biophysics, Leiden University, 2333 CA Leiden, The Netherlands. RID="b" ID="b"Present address: Continuum Electro-Optics Inc., 3150 Central Expressway, Santa Clara, CA 95051, USA. RID="c" ID="c"Present address: CEA/DRECAM/SPAM, CEN Saclay, 91105 Gif-sur-Yvette, France. RID="d" ID="d"Present address: Department of Physics, National University of Rwanda, Butare, Rwanda. RID="e" ID="e"Present address: CELIA, Université Bordeaux 1, 33405 Talence, France. RID="f" ID="f"Present address: MAX-Lab, Lund University, Box 118, 221 00 Lund, Sweden. RID="g" ID="g"e-mail: anne.lhuillier@fysik.lth.se     

Extreme ultraviolet interferometry measurements with high-order harmonics

We demonstrate that high-order harmonics generated by short, intense laser pulses in gases provide an interesting radiation source for extreme ultraviolet interferometry, since they are tunable, coherent, of short pulse duration, and simple to manipulate. Harmonics from the 9th to the 15th are used to measure the thickness of an aluminum layer. The 11th harmonic is used to determine the spatial distribution of the electron density of a plasma produced by a 300-ps laser. Electronic densities higher than 2-10(20)electrons/cm>(3) are measured.     

Spatial coherence of short wavelength high-order harmonics

Received: 12 May 1997     

Coherence effects accompanying generation of high-order harmonics

For phase-locked emitters, provided a certain relation exists between the pump wave and atomic beam parameters, a saturation effect is shown to be possible for which the intensity of the high-order harmonics ceases to depend on the atomic density. By means of a simple model that includes variations in the intensity of the pump wave in the plane transverse to the focal axis, an expression is obtained for the optimum atomic density of the medium corresponding to intensity saturation. The dependence of the optimum atomic density on the laser power and harmonic number obtained is found to be in qualitative agreement with recently published experimental data. Zh. éksp. Teor. Fiz. 112, 1978–1984 (December 1997)     

Phase characteristics of high-order harmonics in the cut-off region

The behavior of the phases of high-order harmonics generated upon interaction of intense laser radiation with matter is investigated. Some specific features typical of the harmonic phases in the high-frequency part of plateau (cut-off harmonic phases) are found. First, the phase difference between neighboring harmonics is a constant value. The width of the spectral range in which this regularity occurs determines the minimum duration of the attosecond pulse obtained from these harmonics by the so-called amplitude gating technique. Second, it is shown that the phase of each harmonic in the cut-off region depends linearly on the laser intensity. The proportionality coefficient is the same for all harmonics in this region and proportional to the cube of laser wavelength. Thus, this dependence is especially important for generating high-order harmonics by lasers with a wavelength of few micrometers.     

Higher harmonics of vibrating gas-filled microspheres. Part one: simulations

The acoustic behaviour of an ideal gas bubble in water is considered and the equation of motion is extended to model an Albunex microsphere. Calculations reveal large differences in non-linear behaviour between ideal gas bubbles and Albunex microspheres, due to the additional restoring force of, and friction inside, the shell that surrounds the Albunex microsphere. Simulations with the Albunex contrast agent further reveal that the optimal driving frequency is 1 MHz, resulting in a second harmonic that is 20 dB below the first harmonic at an acoustic pressure of 50 kPa. The difference increases to 25 dB for a driving frequency of 2 MHz.     

Higher harmonics of vibrating gas-filled microspheres. Part two: measurements

Acoustic measurements on diluted Albunex at two driving frequencies (1 and 2 MHz) are reported which show that the level of the second-harmonic response is about 20 dB below the first harmonic at an acoustic pressure amplitude of 50 kPa. It is demonstrated that, under controlled conditions, it is possible to discriminate between Albunex and other scattering/reflecting objects using the non-linear behaviour of the microspheres.     

Pulse width measurement of high-order harmonics by autocorrelation

Pulse widths of the 7th and 9th harmonics of a Ti:sapphire (TiS) laser have been measured by an autocorrelation technique using two-photon and three-photon ionization of He and Ar as nonlinear phenomena. The pulse widths of the 7th and 9th harmonics were 47 fs and 27 fs, respectively, where the pulse width of the fundamental pulse was 34 fs. The pulse width of the 9th harmonic depends strongly on the peak intensity of the fundamental pulse. These results can be explained by quantum theory by taking into account the temporal and spatial distribution of the fundamental beam. Received: 15 June 1999 / Revised version: 8 October 1999 / Published online: 2 February 2000     

Coherent wake emission of high-order harmonics from overdense plasmas

We present a new mechanism for high-order harmonic generation by reflection of a laser beam from an overdense plasma, efficient even at moderate laser intensities (down to Igamma2 approximately 4x10(15) W cm-2 microm2). In this mechanism, a transient phase matching between the electromagnetic field and plasma oscillations within a density gradient leads to the emission of harmonics up to the plasma frequency. These plasma oscillations are periodically excited in the wake of attosecond electron bunches which sweep across the density gradient. This process leads to a train of unevenly spaced chirped attosecond pulses and, hence, to broadened and chirped harmonics. This last effect is confirmed experimentally.     

Temporal coherence of high-order harmonics generated at solid surfaces

We present interferometric measurements of the temporal coherence of high-order harmonics generated by reflection of a titanium sapphire laser off a solid surface. It is found that the coherence length of the harmonic emission is significantly reduced compared with the bandwidth limited case. To identify the responsible mechanism, the acquired data were analyzed by means of particle-in-cell simulations, whose results show good agreement between the calculated spectra and the measured coherence times. We show that the observed broadening can be understood consistently by the occurrence of a Doppler shift induced by the moving plasma surface, which is dented by the radiation pressure of the laser pulse. In this case, this Doppler effect would also lead to positive chirp of the emitted radiation.     

27-fs extreme ultraviolet pulse generation by high-order harmonics

Autocorrelation measurement was demonstrated for the first time to our knowledge in the XUV region to measure the width of a high-order harmonic pulse. Two-photon ionization of rare gases was used as a nonlinear process for the autocorrelation measurement. The 27-fs pulse width that was obtained is, to our knowledge, the shortest in the XUV region.