Nonlinear magneto-optical diffraction by two-dimensional magnetic superstructures

Nonlinear (at the second-harmonic frequency of the incident light) optical reflection by two-dimensional magnetic superstructures is theoretically studied. A square lattice of magnetic dots and a hexagonal lattice of magnetic bubbles (cylindrical magnetic domains) are considered. Because the periods of these structures are comparable with the wavelengths of the fundamental and the second-harmonic radiation, it would be possible to observe diffraction at the second-harmonic frequency. A polarization analysis of nonlinearly diffracted radiation is performed and the numbers of observable diffraction orders for the above structures are estimated. Received: 10 January 2002 / Published online: 11 June 2002     

固体板中SH板波非线性效应的实验观察

采用微扰近似和导波的模式展开分析方法,从理论上简要分析了SH板波的二次谐波发生效应;尽管在无限大固体介质中单个切变波的二次谐波发生效应非常微弱,但在一定条件下由两个切变波构成的SH板波可具有强烈的非线性效应;本文的主要工作就是对此结论加以实验验证。试制了激发SH板波的切变波斜劈换能器和接收二次谐波信号的液体斜劈换能器,建立了非线性SH板波的实验研究系统;通过详细的理论分析和对比实验研究,阐明了在一定条件下实验观察到的显著二次谐波信号来源于SH板波传播过程中的强烈非线性效应。此外,针对不同的SH板波传播距离,在远场条件下分别测量了相应的二次谐波幅频曲线;在基频SH板波与二倍频对称兰姆波相速度相等所对应的频率值附近,分析了二次谐波的振幅随传播距离的变化关系,结果证明在一定条件下SH板波的二次谐波振幅可随传播距离积累增长,即SH板波可具有强烈的非线性效应。      

SHG on ferromagnetic Gd films: indication of surface-state effects

The magnetization of 10-nm Gd films on W (110) has been investigated with second-harmonic generation (SHG). We observed a strong second-harmonic (SH) yield, which we attribute to resonance enhancement by the well-known Gd (0001) d-like surface state above the Fermi level. Since this state is spin-polarized it enhances the magnetic SHG contrast. The contrast, the relative phase between odd and even SH fields, and the amplitude ratio of these fields depend strongly on wavelength, which confirms the resonance enhancement. Further proof is provided by the fact that oxidation of the Gd surface reduces the SH yield by an order of magnitude. Received: 16 October 2001 / Revised version: 21 March 2002 / Published online: 11 June 2002     

Wavelength dependence of second-harmonic generation at the copper surface

The wavelength dependence of the second-harmonic (SH) generation efficiency has been measured in copper. A strong enhancement of the SH generation has been observed at the onset of interband transitions. Above the absorption edge the second-order polarization is dominated by the nonlinear response of bound electrons.     

Fractional second-harmonic Talbot effect

We demonstrate the fractional second-harmonic (SH) Talbot effect in a hexagonally poled LiTaO3 crystal. We carefully record the SH Talbot images at 1/2, 1/3, and 1/4 Talbot lengths, which are well matched with the simulated images by using the modified Rayleigh-Sommerfeld diffraction formula. A simplified model with a hexagonal array is adopted in the simulations. Also, we use a modified reciprocal vector theory to analytically explain the evolution of the SH array at fractional Talbot lengths. Our results show that the images are sensitive to the duty circle and the background of the array.     

Propagation of second-harmonic wave in quasi-phase-matching nonlinear medium

We studied the propagation of the second-harmonic (SH) wave in a quasi-phase-matching (QPM) medium with a slanted nonlinear grating. By solving the electromagnetic boundary value problem for the SH wave, we derived the propagation law for the SH wave, which can be interpreted as a diffraction phenomenon. Such interpretation was supported by a series of SH generation experiments with a periodically-poled lithium niobate crystal with a slanted QPM grating.     

Non-linear optics and magneto-optics on nano-structured interfaces

The behaviour of the reflectivity and Kerr magneto-optic effects in the non-linear second-harmonic (SH) field diffracted from nano-scale structured ferromagnetic interfaces is reported. Measurements are made in both the linear and non-linear fields at two different fundamental wavelengths (1064 nm and 800 nm) and their associated harmonics. Resonant behaviour observed as a function of angle of incidence is identified with surface-plasmon production that is known to intensify the local field within the interface. Radiation incident at angles of incidence that optimise coupling to the electron plasma produces an increase in the SH field radiated in the vicinity of those angles. Similarly, at those angles of incidence where radiation at the SH wavelengths (532 nm and 400 nm) couples optimally to the electron plasma, troughs are seen in the angular spectrum of the generated SH radiation. Kerr magneto-optic measurements taken in both the linear field and the SH field both show very significant enhancement at angles meeting the plasma-resonance condition. The totality of experimental data presented allows the conclusion that intensification of the interface electric field due to plasmon creation enhances not only the SH reflection coefficient, as was already known, but also the magneto-optic reflection coefficients in both linear and SH fields. Received: 16 October 2001 / Revised version: 14 March 2002 / Published online: 29 May 2002     

Suppression of radiation in a momentum-nonconserving nonlinear interaction

We have considered the quadratic nonlinear radiation from a thin dipole sheet in front of a mirror. Radiation at the second-harmonic (SH) frequency on incidence of a fundamental field can be inhibited or enhanced independently of the SH field intensity stored between the nonlinear layer and the mirror. We have shown that this apparent contradiction can be fully understood only if the quadratic nonlinear interaction includes terms with a momentum mismatch equal to the magnitude of the SH field wave vector, such as the term that accounts for transfer of energy from the reflected SH field back to the incident fundamental.     

Study of second-harmonic generation of shear horizontal modes using modal analysis

In this work a modal analysis was employed to study generation of the second harmonics of shear horizontal (SH) modes in a solid plate. Under second order perturbation, second-harmonic generation will occur accompanying SH mode propagation due to the bulk elastic non-linearity of plate material. In solid plate the total second-harmonic fields of a SH mode propagation are regarded as sum of the fields of a series of double frequency Lamb modes (DFLMs). The contribution of each DFLM component to the total second-harmonic fields is dependent of the difference of phase velocities of the corresponding DFLM and SH mode. The analysis results show that the DFLM field component may have cumulative growth effect once its phase velocity exactly or approximately equals that of a SH mode. It is also found that the fields of the total second harmonics of a SH mode are only symmetrical. The examples of field distributions of several DFLMs on the plate surface are considered.     

Second-harmonic interferometric spectroscopy of buried interfaces of column IV semiconductors

The technique of combined optical second-harmonic (SH) intensity and phase spectroscopy, which is the spectroscopic modification of SH phase measurements, is proposed to study the nonlinear optical response of semiconductor interfaces with spectrally close resonant contributions. The spectral dependences of SH intensity and phase from oxidised Si (111) and Ge (111) surfaces are studied in the range of 3.5- to 5-eV SH photon energy. The resonant behaviour of combined SH spectra is associated with a superposition of contributions from direct interband transitions at several critical points of Si and Ge band structures. Received: 16 October 2001 / Revised version: 16 April 2002 / Published online: 6 June 2002     

双折射吸收非线性介质薄膜中倍频的产生

从二次谐波电场满足的波动方程出发，考虑到介质对二次谐波的吸收以及把完全边界条件应用于基频波和二次谐波在介质的入射面和出射面之间的反射效应，推导出了单光轴非线性薄膜介质中的二次谐波输出功率的计算式.结果表明：当采用复折射率的概念时，可以把非线性无吸收介质的二次谐波输出功率计算式应用到非线性吸收介质二次谐波输出功率计算式中去.     

双折射吸收非线性介质薄膜中倍频的产生

从二次谐波电场满足的波动方程出发,考虑到介质对二次谐波的吸收以及把完全边界条件应用于基频波和二次谐波在介质的入射面和出射面之间的反射效应,推导出了单光轴非线性薄膜介质中的二次谐波输出功率的计算式.结果表明：当采用复折射率的概念时,可以把非线性无吸收介质的二次谐波输出功率计算式应用到非线性吸收介质二次谐波输出功率计算式中去. 关键词： 非线性 倍频 二次谐波功率     

Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations

On the basis of spectral-expansion Green's function theory, we theoretically describe the topography, polarization, and spatial-coherence properties of the second-harmonic (SH) local fields at rough metal surfaces. The spatial distributions of the fundamental frequency and SH local fields are very different, with highly enhanced hot spots of the SH. The spatial correlation functions of the amplitude, phase, and direction of the SH polarization all show spatial decay on the nanoscale in the wide range of the metal fill factors. This implies that SH radiation collected from even nanometer-scale areas is strongly depolarized and dephased, i.e., has the nature of hyper-Rayleigh scattering, in agreement with recent experiments. The present theory is applicable to nanometer-scale nonlinear-optical illumination, probing, and modification.     

K-induced surface structural change of Si(1 1 1)-7 × 7 probed by second-harmonic generation

The growth of thin K films on Si(1 1 1)-7 × 7 has been investigated by selecting the input and output polarizations of second-harmonic generation (SHG) at room temperature (RT) and at an elevated temperature of 350 °C. The SH intensity at 350 °C showed a monotonic increase with K coverages up to a saturated level, where low energy electron diffraction (LEED) showed a 3 × 1 reconstructed structure. The additional deposition onto the K-saturated surface at 350 °C showed only a marginal change in the SH intensity. These variations are different from the multi-component variations up to 1 ML and orders of magnitude increase due to excitation of plasmons in the multilayers at RT. The variations of SHG during desorption of K at 350 °C showed a two-step decay with a marked shoulder which most likely corresponds to the saturation K coverage of the Si(1 1 1)-3 × 1-K surface. The dominant tensor elements contributing to SHG are also identified for each surface.     

Light bullets in quadratic media with normal dispersion at the second harmonic

Stable two- and three-dimensional spatiotemporal solitons (STSs) in second-harmonic-generating media are found in the case of normal dispersion at the second-harmonic (SH). This result, surprising from the theoretical viewpoint, opens the way for experimental realization of STSs. An analytical estimate for the existence of STSs is derived, and full results, including a complete stability diagram, are obtained in numerical form. STSs withstand not only the normal SH dispersion, but also finite walk-off between the harmonics, and readily self-trap from a Gaussian pulse launched at the fundamental frequency.     

Demagnetization following optical excitation in nickel and permalloy films

Time-resolved pump–probe second-harmonic (SH) response following optical excitation has been studied in nickel and permalloy films. Experimental data indicate that the odd SH field represents the transient magnetization, i.e. the behavior of the spin subsystem, while the electron subsystem generates the even SH field. Delays between odd and even SH fields of about 200 fs and 650 fs were detected for nickel and permalloy films, respectively. We found that the dynamics of the odd SH field is influenced by the polarization of the pump pulse. This dependence on excitation conditions suggests a difference in surface and bulk magnetization dynamics. Received: 25 November 2001 / Revised version: 27 March 2002 / Published online: 11 June 2002     

相匹配契伦可夫辐射式倍频

用波导产生倍频波时,如果倍频波进入辐射模区,仍然有相匹配问题。契伦可夫辐射式倍频不是自动地实现相匹配的。相匹配要求导波基波模式场,倍频传输场(自由波),倍频触发场,以及经多次反射透射后的辐射场的迭加形成的总辐射场处于同步的相匹配状态。根据这个相匹配的分析,提出波导契伦可夫相匹配的特有的方法,那就是对波导的模色散进行设计,并指出非对称波导的特有优点,是改变一个边界上的反射相变,即选择不同色散的线性材料作包层,由此可得到相匹配的高效契伦可夫倍频辐射。     

Weak localization effects in the second-harmonic light scattered by random systems of particles

We report rigorous numerical simulations that show the presence of coherent backscattering effects in the second-harmonic generation and scattering of light by random systems of two-dimensional particles. Since the medium composing the particles is assumed to be homogeneous and isotropic, the second-harmonic field is generated mainly by surface effects. For the fundamental frequency, the results present a clear enhanced backscattering peak. In contrast, the second-harmonic scattering patterns present an intensity dip in the backscattering direction.     

Highly efficient second-harmonic nanosource for near-field optics and microscopy

A nanometric source of second-harmonic (SH) light with unprecedented efficiency is demonstrated; it exploits the grazing-incidence illumination of a metal tip, which is conventionally used for atomic force microscopy, by 25-fs laser pulses of a high-energy Ti:sapphire oscillator. Tip scanning around the beam focus shows that the SH generation is strongly localized at its apex. The polarization dependence of the SH light complies with the model of an on-axis nonlinear oscillating dipole.