High-order harmonic generation from organic molecules in ultra-short pulses

We have studied high-order harmonic generation (HHG) from organic molecules irradiated with near-infrared high intensity laser pulses of 70 fs and 240 fs duration. The molecular systems studied were the aromatics benzene and naphthalene and the alkanes cyclopropane and cyclohexane (cyclic) and n-hexane (linear). Harmonic intensities were measured both as a function of laser intensity (in the range 5×10¹³-5×10¹⁵ W cm^-2) and as a function of ellipticity of the laser field polarisation. The results were compared with those from the xenon atom. For 70 fs pulses, harmonic generation from the organic systems was similar to that of xenon, revealing an atom-like behaviour for molecules when the laser pulse duration is shorter than the fragmentation timescale of the molecule. We note significant differences between molecules with respect to HHG efficiencies and the suppression of HHG in larger species. We discuss these differences in the context of the molecular properties, electronic structure and behaviour of ionisation and fragmentation that result in enhancement of field ionisation in larger systems. Study of the polarisation ellipticity dependence of HHG shows that the harmonic yield in molecules is less sensitive to the polarisation than for atoms (xenon). This is consistent with the expected behaviour given the larger recollision cross-section presented by the core in the molecular system compared to the atom. Our results suggest that study of HHG from molecules exposed to ultra-short pulses is potentially a powerful tool for understanding the electron dynamics of molecules exposed to an intense field. Received 14 September 2000 and Received in final form 6 December 2000     

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.     

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.     

Effects of electron relaxation on multiple harmonic generation from metal surfaces with femtosecond laser pulses

Calculations are presented for the first four (odd and even) harmonics of an 800 nm laser from a gold surface, with pulse widths ranging from 100 down to 14 fs. For peak laser intensities above 1 GW/cm² the harmonics are enhanced because of a partial depletion of the initial electron states. At 10¹¹ W/cm² of peak laser intensity the calculated conversion efficiency for 2nd-harmonic generation is 3 × 10⁻⁹, while for the 5th-harmonic it is 10⁻¹⁰. The generated harmonic pulses are broadened and delayed relative to the laser pulse because of the finite relaxation times of the excited electronic states. The finite electron relaxation times cause also the broadening of the autocorrelations of the laser pulses obtained from surface harmonic generation by two time-delayed identical pulses. Comparison with recent experimental results shows that the response time of an autocorrelator using nonlinear optical processes in a gold surface is shorter than the electron relaxation times. This seems to indicate that for laser pulses shorter than ∼30 fs, the fast nonresonant channel for multiphoton excitation via continuum-continuum transitions in metals becomes important as the resonant channel becomes slow (relative to the laser pulse) and less efficient.     

Study of second harmonic generation by non-linear crystals with phase conjugation

We present the correction of the phase distortion which occurs during the second harmonic generation by non-linear crystals, such as KDP and KTP at high average power laser. This is due to the optical quality and thicknesses of the crystals which in turn influence the quality of the incident laser beam. This phase distortion is corrected by reflecting back the laser beam into the crystal using a phase conjugate mirror. It is found that the conversion efficiency of second harmonic generation without phase conjugation is more than that with phase conjugation. Far field pattern shows that the distortion of the laser beam can be corrected by using the phase conjugate mirror. Fidelity of the beam profile increases significantly with phase conjugation in the case of KDP crystal.     

Efficient self phase matched third harmonic generation of ultrashort pulses in a material with positive dispersion

An ultrafast transient refractive index grating, produced in barium fluoride, a material with positive dispersion, promotes very efficient third harmonic generation. The significant enhancement of the generation up to a conversion efficiency of about 3% is due to self phase matching, involving the instantaneous grating. At the same time several diffraction orders of the third harmonic signal are observed behind the sample. Received: 17 October 2000 / Published online: 21 February 2001     

Optical second harmonic generation from Pt nanowires

We have measured optical second harmonic intensity from arrays of Pt nanowires of 20 nm and 9 nm average widths, as a function of the incident and output light polarizations, the azimuthal angle, and the excitation photon energy. The nanowires were fabricated through shadow deposition on self-organized NaCl(1 1 0) faceted templates. The anisotropy of the SH intensity from the Pt nanowires was found to be stronger than that from the Au nanowires reported previously. The effective nonlinear susceptibility element , with the suffix 2 indicating the direction , was observed for Pt nanowires, although it was not observed for Au nanowires. This difference is suggested to be due to the weaker suppression of the incident fundamental fields by the depolarization field in the Pt nanowires and the larger anisotropy in the nonlinearity of Pt nanowires due to the thinner widths.     

Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams

Second harmonic generation microscopy was conducted on rat-tail tendons with linearly and radially polarized beams. Transverse and axial field components were generated in the focal region through tight focusing of linearly and radially polarized. It was found that the generated SHG signals could not be qualitatively explained with a scalar approximation to the electric field at the focus. Only by accounting for the interactions of the axial and transverse components of the electric field interacting through the nonlinear susceptibility χ⁽²⁾ tensor could the SHG images be explained. For the case of collagen we find that the SHG signal varies as a function of the analyzer angle with a cos² or sin² dependency for linearly polarized beams. For tightly focused radially polarized beams we find that the output SHG is radially polarized after collimation and is independent of the analyzer angle.     

Phase effects at second harmonic generation in the layer media

An analysis is made of quasi-phase-matched interaction at second harmonic generation in a regular domain structure with accounts for losses and change of phases of all the interacting waves. The constant-intensity approximation of basic radiation is applied for this purpose, not to regular domain structure as a whole, but to each separately taken domain. It allows to carry out more strict analysis of quasi-synchronous interaction during the frequency conversion to the polydomain consisting of n layers, forming “grating” periods of modulation of the nonlinear susceptibility. With this, the values of complex amplitudes of basic radiation and second harmonic wave at the outlet of each domain are entrance values of the corresponding complex amplitudes to the following domain. The analytical expression is given for the case of n domains and the factors limiting the efficiency of the process of frequency conversion are analyzed. In the constant-intensity approximation, in contrast to the constant field approximation, the coherent length of domain depends on pump intensity. With increasing pump intensity the optimum length decreases. In a regular domain structure at frequency conversion from a layer to a layer, intensity of the basic radiation changes. Also the optimum length of domains at which conversion efficiency is maximal therefore changes. Thus, it is possible to obtain the high values of conversion frequency at the outlet of a regular domain structure by choice of optimum parameters of a task (length of domains, phase mismatch, pump intensity), as well as using the layers-domains of high quality.     

Generation of subpicosecond vacuum ultraviolet pulses at 126 nm by using harmonics of a subpicosecond Ti:Sapphire laser

Subpicosecond vacuum ultraviolet (VUV) pulses at the wavelength of 126 nm have been generated in rare gases as a result of the 7th harmonic radiation of a subpicosecond Ti:Sapphire laser oscillating at 882 nm. The VUV harmonic intensity was optimized in Xe at the pressure of 1.2 Torr. The behavior of the harmonic emission was qualitatively reproduced by the classical nonlinear optics. The increase of the harmonic intensity was limited by multiphoton ionization of Xe.     

Second harmonic generation in deposited clusters

We analyse theoretically the generation of second and higher harmonics for sodium clusters deposited on an insulating surface. To this end, we use the time-dependent local-density approximation solved on a three-dimensional grid. We explore the impact of the various laser parameters (intensity, frequency, polarisation) on the efficiency of second harmonic generation. The success sensitively depends on a proper tuning of these parameters. We find optimum conditions for which the laser frequency is half the resonance frequency of the system, if the polarisation is directed orthogonal to the surface of the substrate, and if the intensity is large but safely below the critical value for destruction of the electron cloud. Received 22 October 1999 and Received in final form 14 December 1999     

Generation of attosecond pulses in molecular nitrogen

We investigate the carrier-envelope phase dependence of the total ionization yield for single and double ionization of xenon. We compare our results to theoretical calculations and to the phase dependent asymmetry in photoelectron emission. We observe that the phase dependence of the photoion yields, regardless if single or double ionization, is at least 2-3 orders of magnitude below the photoelectron emission signal. We conclude that total photoionization yields are only very weakly dependent on the carrier envelope phase, and that they are not a useful means for measurement of the phase. It seems possible that the broad bandwidth of few-cycle pulses facilitates multiphoton ionization, which leads to a randomization of strong field ionization phase dependencies. Besides, we observe that the spatial asymmetry in photoelectron emission appears to be useful as an indicator for the laser pulse duration in the few cycle regime.     

High efficiency second harmonic generation with a low power diode laser

\valunit{8}{mW} ( corrected for the output mirror reflection) of the cw coherent blue light around by frequency doubling of only from a diode laser. With IR power of we reach the doubling efficiency of . The overall conversion efficiency from the electrical power into the blue light is . By the way of careful analysis of the Blue Light Induced IR Absorption (BLIIRA) in the potassium niobate based external doubling cavity we obtain good agreement with the theoretical conversion efficiency. Received: 29 November 1996     

A way for enhancing second harmonic generation in one-dimensional nonlinear photonic crystals

We investigate one-dimensional nonlinear photonic crystals consisting of ferroelectric domains with the modulated polarization directions. Significant enhancement of second harmonic generation (SHG) is observed from numerical simulations when the frequency of fundamental wave is aimed at the photonic band edge. We devise the model structure with optimal configuration of the polarization directions of the ferroelectric domains in terms of simulated annealing algorithm. The conversion efficiencies of the ‘forward’ and ‘backward’ SHGs can be engineered.     

Intense femtosecond laser-induced second-harmonic generation in atmospheric-pressure air

Second-harmonic generation (SHG) in atmospheric-pressure air is experimentally studied using single focused linear-polarized Ti:sapphire intense femtosecond laser pulses at 810 nm. The efficiency of SHG is found to reach a maximum at the optical breakdown threshold of ≈2.9×10¹⁴ W/cm². The spectral distribution and polarization property of the second harmonic are investigated. The contribution to SHG from electric-field-induced third-order mixing plays the main role even after the optical breakdown had occurred. Received: 23 May 2000 / Published online: 16 August 2000     

Proposal of high quality walk-off compensated sum frequency generation of ultra-short pulses

A multi-crystal and a frequency-selective group-velocity compensating schemes are proposed for the sum frequency-third harmonic generation of low power ultra-short pulses from a Ti:sapphire femtosecond laser. The mechanisms of compensation are analyzed accordingly. It is shown that the temporal walk-off can be effectively compensated without any dispersive element. By use of BBO, calcite crystals together with specially designed composite phase delay plates and dichroic beamsplitters, high quality third harmonic ultra-violet pulses within 300 nm can be generated by the two schemes.     

Temporal characterization of ultra short laser pulses based on multiple harmonic generation on a gold surface

Received: 29 July 1996     

Phase effects at second harmonic generation of powerful laser radiation in noncentrosymmetrical media

There has been developed the theory of second harmonic generation of the intensive laser fields in the existence of both quadratic and cubic polarization in medium in the constant-intensity approximation accounting for the reverse effect of the excited wave on the exciting one and simultaneously allowing us to take into account phase mismatch and the damping of all the interacting waves. It is shown that the changes of pump intensity through self-phase and cross-phase modulation processes effect optimum phase relationship between interacting waves, the change of the spatial beating period. The conditions of compensating undesirable phase shifts between interacting waves have been determined, the analytical expressions for calculation of optimum values of phase mismatch, length of noncentrosymmetrical medium and the spatial beating period are offered. It is shown that in the absence of linear phase mismatch with an increase of basic radiation intensity the spatial beating period is being reduced. The numerous analysis has been made of frequency doubling process efficiency for KDP and LiNbO₃ crystals.     

Second harmonic generation in generalized Thue-Morse ferroelectric superlattices

In this paper the second harmonic generation (SHG) in generalized Thue-Morse (GTM(m, n)) ferroelectric superlattices is studied. Under the small-signal approximation, the SHG spectra in both real and reciprocal spaces are investigated. It is found that: (1) only when the structure parameters l, l_A, and l_B are all chosen to be proper, can SHG in GTM(m, n) ferroelectric superlattices be generated; (2) for Family A of generalized Thue-Morse, GTM(m, 1) ferroelectric systems, with the increase of parameter m, the intense peaks of SHG concentrate on the long wavelength (the fundamental beam (FB) wavelength is within ), but for Family B of generalized Thue-Morse, GTM(1, n) ferroelectric superlattices, with the increase of parameter n, the intense peaks of SHG concentrate on the middle wavelength ; and (3) for GTM(m, 1) ferroelectric superlattices, the bigger the m, the stronger the relative integral intensity (RII) of SHG would be, but for GTM(1, n) ferroelectric systems, the bigger the n, the weaker the RII of SHG would be.     

Six-Watt mid-infrared laser using harmonic generation with Tl3AsSe3

An output of 6 W at 30 kHz was achieved using Tl₃AsSe₃ as the nonlinear second-harmonic generator. It was pumped with a CO₂ laser source at a wavelength of 9.25 m with 20 ns pulses, and the laser beam was focussed to a spot size of 150 m. The focussed spot was scanned to reduce the continuous-wave power loading, and the system could be operated for extended periods of time under these conditions.