Resonant generation of a difference harmonic at a quantized metallic film

Received: 20 September 1998 / Revised version: 27 January 1999     

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

Received: 29 July 1996     

Nonlinear electronic response and SHG from adsorbates on simple metal surfaces

For the chemisorption model of Lang and Williams, the adsorbate-induced electron density changes in linear and nonlinear order of the field were calculated recently. Based on these calculations the relation between the electronic structure of simple atom/metal systems and the process of SHG from surfaces is discussed in terms of relevant factors such as electronegativity, nonlinear atomic polarizability, work-function change, and metal response.Paper presented at the 129th WE-Heraeus-Seminar on Surface Studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994     

Second-harmonic generation from metal surfaces: Beyond jellium

The generation of Second-Harmonic (SH) radiation from simple metals has been the subject of numerous investigations for almost three decades. The use of clean metal surfaces in the experiments and increasingly sophisticated jellium-based theoretical models has led to a convergence on the magnitude and some of the dispersion characteristics of SH generation in free-electron metals like aluminum. However, the sensitivity of the SH-generation process to crystal symmetry, surface morphology, and surface electronic states indicates that nonlinear optical properties are influenced by processes which cannot be explained using a model based on an isotropic electron gas. Here, we review some recent experimental work indicating where deviation from jellium-based models occurs and attempts to understand these.Paper presented at the 129th WE-Heraeus-Seminar on Surface Studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994     

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.     

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.     

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.     

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.     

Transmission second harmonic generation in CdTe at 1.064 μm

Transmission geometry measurements of the efficiency of second harmonic generation in various thicknesses of CdTe samples were made to determine the conversion efficiency dependence on material thickness. Neglecting pump depletion, it is found that for samples of well-defined symmetry, the second harmonic conversion efficiency scales with film thickness, with no observed enhancement owing to coherence length effects. The angular dependence of the observed second harmonic light in films of well-defined symmetry is consistent with second harmonic generation originating in the bulk.     

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     

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.     

Efficient harmonic generation of second, third, and fourth orders from Fourier-transform-limited CO2 laser beam at 10.6 μm in GaSe crystals

Second, 3rd, and 4th order harmonics from a Fourier-transform-limited nanosecond CO₂ laser beam at 10.6 μm were efficiently generated within one or two GaSe crystals. The peak output powers were determined to be 443, 23, and 2 W, respectively, corresponding to conversion efficiencies of 3.0%, 0.13% and 0.0093%, which were significantly improved, compared with all the previous results. The linewidths of the harmonic beams were estimated to be 80, 104, and 116 MHz, respectively.     

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.     

Influence of phase transitions on the second harmonic generation in metal nanoparticles

In this work we use nonlinear optical properties of Ga nanoparticles monolayers of different average sizes embedded in dielectric matrices to investigate the liquid-solid phase transitions in these materials. Ga nanoparticles, formed by exploiting the partial wetting of liquid Ga over a SiO_x surface are irradiated with fs laser pulses from a Ti:sapphire source. The resulting Second Harmonic (SH) generated in the reflection and transmission directions is measured along the phase transitions by cooling the sample from 320 K down to liquid nitrogen temperature. Hysteresis cycles are observed in the nonlinear transmission, which exhibit a strong amplification from the solid to liquid values as compared to the linear optical results. A simple model for SH generation, based on Mie scattering calculations which includes the effect of surface plasmon resonance provides a fair key for the interpretation of the observed effects.     

Topography of antiferromagnetic domains using second harmonic generation with an external reference

2 O₃, in which the time-invariant second-harmonic reference can be generated either intrinsically by the crystal or externally by use of the new technique, so that both methods may be compared. The technique is then used to visualize the domain structure of YMnO₃, an antiferromagnetic crystal which does not provide the time-invariant reference wave intrinsically. The experiments demonstrate the wide applicability of the method. Received: 13 June 1997     

Separation of interface and bulk contributions in second-harmonic generation from magnetic and non-magnetic multilayers

We discuss the separation problem of bulk vs interface contributions in optical Second-Harmonic Generation (SHG). A new method is presented, which — in special cases — provides a full separation of all interface and bulk tensor components. The method is based on measurements in a thin-film geometry, and the relation between two bulk tensor components obtained from group-theoretical arguments. The separation problem in its strict sense is shown to be absent in Magnetization-induced SHG (MSHG). Though, in practice, also in the MSHG case interface and bulk contributions can be closely resemblant. The approach is illustrated by second-harmonic experiments on C₆₀ thin films. SHG in this system is found to be completely dominated by bulk processes.Paper presented at the 129th WE-Heraeus-Seminar on Surface Studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994     

Theory of sum frequency generation from metal surfaces

zzz (ω₁,ω₂). Four types of metal surfaces are considered: simple metals, alkali metal overlayers, noble metals, and charged metal surfaces. Differences and similarities with respect to second harmonic generation from these surfaces are pointed out. Received: 20 September 1998     

Collinear second harmonic generation of 20 wavelengths in a single two-dimensional decagonal nonlinear photonic quasi-crystal

We report on the observation of quasi-phase matched collinear second harmonic generation (SHG) at 20 wavelengths in a two-dimensional nonlinear photonic quasi-crystal with decagonal lattice. We show that at some wavelengths the second harmonics are generated via standard quasi-phase matching, namely a reciprocal vector exists that equals the phase-mismatch vector, while at others the SHG is as a result of the projection-based quasi-phase matching in which the momentum conservation is satisfied up to a projection of a reciprocal vector onto the direction of propagation. In spite of different generation mechanisms, the reciprocal vectors (or their projections) involved in the collinear QPM SHG can be described by a generalized equation.     

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

Received: 20 September 1998     

Theory of multiple harmonic generation in reflection from a metal surface

A microscopic theory is presented for multiple harmonic generation (MHG) from a metal surface in the jellium approximation and for laser intensities below the critical value for plasma formation. Calculations are presented for the second and up to the sixth harmonic, in the case of a gold surface and for laser wavelengths 800 and 1064 nm, with femtosecond and picosecond laser pulses. The peaks of the harmonic pulses are delayed relative to the peak of the incident laser pulse by about 20 to 30 fs due to the finite electron-relaxation times. The calculated relative peak intensities of the various harmonics are most sensitive to the values of the relaxation times, and MHG provides a way of determining these times. An erratum to this article can be found at .