High-order-harmonic generation: towards laser-induced phase-matching control and relativistic effects

We present a review of some recent results on high-order-harmonic generation, aiming at optimizing the photon flux to allow for future applications in extreme-ultra-violet non-linear optics. We first present new schemes to control phase matching of high harmonics in gases, by using the effect of the spatially varying atomic phase displayed by the high harmonics. An enhancement by a factor of 50 is observed in neon in conditions for which the gradient of the atomic dispersion balances the electronic dispersion. A new scheme to manipulate the laser field was demonstrated, and shown to improve phase matching. We then turn to high-harmonic generation by solid targets, and show that high harmonics generated by an intense 30-fs laser pulse remain collimated even at the threshold of the relativistic regime. Received: 5 December 2001 / Published online: 24 April 2002     

Phase matching of second-harmonic generation in birefringent porous silicon

Optical second-harmonic generation is investigated in free-standing (110) porous silicon films having strong in-plane birefringence. Based on the measured values of the refractive indices, the conditions of phase matching are calculated and verified in the experiments on angular and polarization dependences of second-harmonic generation. Filling pores with a transparent dielectric liquid allows phase matching to be achieved and the second-harmonic signal to be increased by two orders of magnitude. The results of these experiments suggest an opportunity to form new-type nonlinear-optical media consisting of birefringent porous silicon as a phase-matching matrix for the materials embedded in the pores. Received: 30 April 2001 / Published online: 7 June 2001     

Generation of high order optical harmonics from solid surfaces

Received: 26 November 1998     

High-order optical harmonic generation from solid surfaces

During the interaction of an intense ultrashort laser pulse with solid targets, a thin layer of surface plasma is generated in which the density drops to the vacuum level in a distance much shorter than the wavelength. This sharp plasma-vacuum boundary performs an oscillatory motion in response to the electromagnetic forces of the intense laser light. It is shown that the generation of reflected harmonics can be interpreted as a phase modulation experienced by the light upon reflection from the oscillating boundary. The modulation side-bands of the reflected frequency spectrum correspond to odd and even harmonics of the laser frequency. Retardation effects lead to a strong anharmonicity for high velocities of the plasma-vacuum boundary. As a result, harmonic generation is strongly enhanced in the relativistic regime of laser intensities.Prof. F. P. Schäfer on the occasion of his 65th birthday.     

Simultaneous measurements of second-harmonic generation and two-photon photoelectric emission from Au

Received: 1 October 1998 / Accepted: 30 October 1998     

Homodyne detection of second-harmonic generation as a probe of electric fields

Received: 16 December 1998     

Investigation of the phase of the second-order susceptibility measured in off-resonant surface second-harmonic generation

Received: 20 September 1998     

DC-electric-field-modified second-harmonic generation at the Si(100) surface

1 resonances for clean and H covered surfaces shift as a function of the dc field in agreement with experiment. This suggests the presence of built-in electric fields whose strength depends on the H coverage, and which are strongly localized in the subsurface region. Received: 20 September 1998     

Intracavity second-harmonic generation of 1.06 μm in GdCa4O(BO3)3 crystals

The characteristics of intracavity second-harmonic generation (SHG) at 1.06 μm in GdCa₄O(BO₃)₃ (GdCOB) crystals cut for different type I phase-matching (PM) directions of (θ,φ)=(66.8°, 132.3°); (19.4°, 0°); (90°, 46°) have been investigated. It was found that the intracavity SHG was significantly efficient in the PM direction of (66.8°, 132.3°), and that the intrinsic lower effective nonlinear coefficient (d_eff) was responsible for the less-efficient SHG in the other two directions. A maximum CW SHG output power of 2.81 W was obtained with an optical conversion efficiency of 18.7%, while the corresponding effective intracavity SHG efficiency was determined to be 41.3%. The intracavity SHG efficiency of GdCOB has been found to reach two-thirds of that obtained with type II phase-matching KTiOPO₄ (KTP). Received: 26 April 2000 / Revised version: 3 July 2000 / Published online: 5 October 2000     

Characterization of femtosecond pulses via transverse second-harmonic generation in random nonlinear media

We study, both experimentally and theoretically, the process of second-harmonic generation by two noncollinear beams in ferroelectric crystals with a disordered distribution of ferroelectric domains. We show that this parametric process results in generation of second-harmonic wave in the direction transverse to the propagation of the fundamental beam. We demonstrate how this effect can be used for the femtosecond pulse characterization enabling the estimation of both width and chirp of the pulse.     

Switching behaviour of ferroelectric liquid crystals probed by optical second-harmonic generation

Ferroelectric properties of thin (1.5–4 μm planar cells of a ferroelectric liquid crystal (FLC) mixture are studied using electro-optic measurements, second-harmonic generation (SHG) and SHG interferometry. A switching behaviour of the FLC cells in external dc electric fields is observed. It is characterised by rotation of the polarisation plane of the transmitted light and by changes in the SHG intensity, phase and anisotropy dependences, which are attributed to a collective motion of the system as a ferroelectric uniform state with C₂ symmetry. Received: 16 October 2001 / Revised version: 18 March 2002 / Published online: 6 June 2002     

Probing photo-induced alignment in poly(vinyl cinnamate) films by surface second-harmonic generation

Received: 20 September 1998 / Revised version: 18 December 1998     

Self-action effects in ionization and fragmentation of toluene by femtosecond laser pulses

Occurrence and influence of several self-action effects, induced in the entrance window of a time-of-flight interaction chamber, on the ion and fragment yields of the toluene molecule in the focus of a Ti:sapphire laser pulse are analyzed. Experimental data are obtained using different focusing geometries and are compared with results from numerical simulations using a nonlinear pulse propagation model as well as those from the strong-field S-matrix theory. It is shown that (a) self-focusing leads to a displacement of the focus while amplified small perturbations of the input beam result in hot spots in the spatial distribution and in an energy-dependent focus area, (b) small self-phase modulation changes the form of the spectrum and broadens it slightly. A strong increase of the toluene fragmentation appears to correlate to linear and nonlinear changes in the focal spot area, while the scenario of excitation of Raman modes proposed in an earlier publication is ruled out as the dominant effect.This revised version was published online in March 2005. In the previous version, the published online date was missing     

Type-I non-critically phase-matched second-harmonic generation in Gd1-xYxCa4O(BO3)3

Second-harmonic generation was z-cut observed Gd_1-xY_xCa₄O(BO₃)₃ (Gd_1-xY_xCOB) and the dependence of the phase-matching wavelength on the mixing ratio x has been investigated. The dependence on both temperature and angle tuning was examined as well. We found the suitable composition for noncritical frequency doubling at 930 nm, which is the lasing wavelength of Nd:YAlO₃ on the ⁴F_3/2?⁴I_9/2 transition. Received: 19 April 1999 / Published online: 5 May 1999     

Does femtosecond time-resolved second-harmonic generation probe electron temperatures at surfaces?

Femtosecond pump-probe second-harmonic generation (SHG) and transient linear reflectivity measurements were carried out on polycrystalline Cu, Ag and An in air to analyze whether the electron temperature affects Fresnel factors or nonlinear susceptibilities, or both. Sensitivity to electron temperatures was attained by using photon energies near the interband transition threshold. We find that the nonlinear susceptibility carries the electron temperature dependence in case of Ag and Au, while for Cu the dependence is in the Fresnel factors. This contrasting behavior emphasizes that SHG is nota priori sensitive to electron dynamics at surfaces or interfaces, notwithstanding its cause.     

Mechanisms of absorption in pulsed excimer laser-induced plasma

2 . Received: 20 January 1997/Accepted: 23 June 1997     

Kilohertz extreme-ultraviolet light source based on femtosecond high-order harmonic generation from noble gases

A compact, versatile table-top kilohertz source of coherent extreme-ultraviolet (XUV) radiation in the wavelength region 18–100 nm, based on high-order harmonic generation from noble gases induced by a 40-femtosecond Ti:sapphire laser system, is presented. The XUV beamline delivers at its output 10⁸ photons/s at a wavelength of 23 nm. The monochromatized XUV radiation is directly focused onto a 10^-2-mm² spot by a toroidal grating, allowing one to reach intensities higher than 10⁶ W/cm². Optimization results are presented for a new XUV-generating geometry, utilizing a ‘semi-infinite’ quasi-static gas cell and strong focusing. In those conditions, we observe an anomalous inversion between the cutoffs of argon and krypton, with the krypton spectrum extending to much higher orders than expected in an adiabatic limit. Received: 9 July 2001 / Revised version: 1 August 2001 / Published online: 7 November 2001     

Ionization effects on field-free molecular alignment observed with high-order harmonic generation

In this paper, high-order harmonic generation (HHG) is demonstrated to provide a sensitive way for studying the dynamic process in the field-free molecular alignment. The dependence of the harmonic yield and the degree of alignment on the intensity of aligning pulse is observed in impulsively aligned CO₂ molecules. A good agreement is found between the experimental and calculated results. At low pump intensities, the harmonic yield increases monotonously until the ionization induced refractive index gradient and neutral molecule depletion are significant. The results show that the optimum intensity is around 8.95 × 10¹³ W/cm²; this value is related to the molecular ionization potential.     

Far-field distribution of third-harmonic generation by two crossed beams

The far-field intensity distribution of the third harmonic generated in a thin silica plate by two laser beams crossed at a small angle comprises four peaks approximately symmetric with respect to the bisector. The measurement of the intensity ratio of the inner to the outer peaks yielded values scattered from 10 to 20, surprisingly larger than the combinatorial value 9. The phase-matching factor, as determined by the full three-dimensional calculations required by the absence of axial symmetry, accounts for the observed ratio and its fluctuations. Received: 14 November 2002 / Published online: 22 May 2003 RID="*" ID="*"Corresponding author. Fax: +7-95/1941-994, E-mail: fomichev@imp.kiae.ru     

Second-harmonic generation at the surface of cubic ionic crystals

The strength of the different source terms in the isotropic Second Harmonic (SH) response of the surface has been measured in different ionic crystals LiF, NaF, GGG(Gadolinium-Gallium-Garnet), and MgF₂, using as excitation beam the fundamental output of a Nd:YAG laser (1.06 m). The azimuthal dependences of the optical second-harmonic generation has also been measured at the LiF(100), LiF(111), GGG(100), and GGG(111) surfaces. No experimental evidence of a bulk contribution to the anisotropic part of the nonlineau polarization has been observed.