Second harmonic generation of shear waves in crystals

Nonlinear self-interaction of shear waves in electro-elastic crystals is investigated based on the rotationally invariant state function. Theoretical analyses are conducted for cubic, hexagonal, and trigonal crystals. The calculations show that nonlinear self-interaction of shear waves has some characteristics distinctly different from that of longitudinal waves. First, the process of self-interaction to generate its own second harmonic wave is permitted only in some special wave propagation directions for a shear wave. Second, the geometrical nonlinearity originated from finite strain does not contribute to the second harmonic generation (SHG) of shear waves. Therefore, unlike the case of longitudinal wave, the second-order elastic constants do not involve in the nonlinear parameter of the second harmonic generation of shear waves. Third, unlike the nonlinearity parameter of the longitudinal waves, the nonlinear parameter of the shear wave exhibits strong anisotropy, which is directly related to the symmetry of the crystal. In the calculations, the electromechanical coupling nonlinearity is considered for the 6 mm and 3 m symmetry crystals. Complement to the SHG of longitudinal waves already in use, the SHG of shear waves provides more measurements for the determination of third-order elastic constants of solids. The method is applied to a Z-cut lithium niobate (LiNbO/sub 3/) crystal, and its third-order elastic constant c/sub 444/ is determined.     

Guided-type second harmonic generation in ion implanted MgO:LiNbO3

Abstract

We report guided-type second harmonic generation (SHG) in Mg-doped lithium niobate optical waveguides. SHG in Mg-doped lithium niobate guide is as a comparable efficiency to the undoped lithium niobate waveguides [1] where the efficiency is 0.018% W^?1. We also report a better resistance to the impact of a high intensity pulsed laser at the in-couple facet.     

Second harmonic generation of pseudo mode-locked multi ten milliwatt picosecond Ti:sapphire laser

We report the single-pass second harmonic generation (SHG) of the picosecond Ti:sapphire laser with a periodically poled lithium niobate (PPLN) waveguide. We demonstrate a conversion efficiency of 37% for the 9-mW fundamental input power at 820 nm. This laser source can provide three types of pulsed modes such as picosecond, nanosecond, and contiuous wave, by adjusting the power of the pumping source. We compare the conversion efficiency in each mode, and clearly show that SHG efficiency depends on the pulsewidth, that is, the peak power of the laser source. As the temperature of the PPLN rises, the fundamental wavelength for phase-matching becomes longer. We indicate that the rate is about 0.06 nm/K.     

Second harmonic generation of pseudo mode-locked multi ten milliwatt picosecond Ti:sapphire laser

We report the single-pass second harmonic generation (SHG) of the picosecond Ti:sapphire laser with a periodically poled lithium niobate (PPLN) waveguide. We demonstrate a conversion efficiency of 37% for the 9-mW fundamental input power at 820 nm. This laser source can provide three types of pulsed modes such as picosecond, nanosecond, and contiuous wave, by adjusting the power of the pumping source. We compare the conversion efficiency in each mode, and clearly show that SHG efficiency depends on the pulsewidth, that is, the peak power of the laser source. As the temperature of the PPLN rises, the fundamental wavelength for phase-matching becomes longer. We indicate that the rate is about 0.06 nm/K.     

Harmonic holography: a new holographic principle

The process of second harmonic generation (SHG) has a unique property of forming a sharp optical contrast between noncentrosymmetric crystalline materials and other types of material, which is a highly valuable asset for contrast microscopy. The coherent signal obtained through SHG also allows for the recording of holograms at high spatial and temporal resolution, enabling whole-field four-dimensional microscopy for highly dynamic microsystems and nanosystems. Here we describe a new holographic principle, harmonic holography (H(2)), which records holograms between independently generated second harmonic signals and reference. We experimentally demonstrate this technique with digital holographic recording of second harmonic signals upconverted from an ensemble of second harmonic generating nanocrystal clusters under femtosecond laser excitation. Our results show that harmonic holography is uniquely suited for ultrafast four-dimensional contrast microscopy.     

二次谐波在二维材料结构表征中的应用

二次谐波作为非线性光学的重要分支, 逐渐成为表征晶体结构的重要手段之一。在众多表征方法中, 二次谐波因其无损检测、高稳定性、可调谐性、超快响应、偏振敏感性、通用性、操作简单等特点被广泛应用于二维材料结构表征, 为二维材料的物性研究和功能应用提供了重要信息, 大大推动了二维材料基础研究的快速发展。本文综述了近几年二次谐波在二维材料结构表征中的研究, 简述了二次谐波产生原理, 介绍了飞秒激光器接入共聚焦拉曼光谱仪产生二次谐波测试装置, 分别讨论了二次谐波在二维材料的层间堆垛层数、层间堆垛角度、单层二维材料晶界及晶体取向表征方面的应用。同时, 本文还介绍了采用二次谐波强度直接、灵敏地检测晶体中应变幅度以及通过二次谐波信号变化跟踪材料中的缺陷变化, 接着讨论了二次谐波与拉曼光谱、光致发光的多维度关联分析在材料全面深度表征方面的重要性。最后展望了二次谐波未来在材料结构表征中的潜在研究方向。     

Second harmonic generation diagnostic of layer-by-layer deposition from Disperse Red 1 – functionalized maleic anhydride copolymer

Layer-by-layer (LBL) electrostatic assembly of polyelectrolytes is proving to be an increasingly rich and versatile technique for the formation of multilayered thin films with a wide range of electrical, magnetic, and optical properties. In the present work we synthesized a new non-linear optical (NLO) maleic acid copolymer containing Disperse Red 1 moieties, built-up multilayer assemblies by alternate adsorption of poly(allylamine hydrochloride) (PAH) and maleic copolymer derivative, and carried out an investigation on their second harmonic generation (SHG) properties. The resulting multilayer assemblies exhibit SHG which arises from the non-centrosymmetric alignment of the chromophores in the copolymer. The SHG signal increases with the number of chromophore-containing polymer layers, up to five layers. Further assembly reduces the signal.     

Second harmonic generation diagnostic of layer-by-layer deposition from Disperse Red 1 – functionalized maleic anhydride copolymer

Layer-by-layer (LBL) electrostatic assembly of polyelectrolytes is proving to be an increasingly rich and versatile technique for the formation of multilayered thin films with a wide range of electrical, magnetic, and optical properties. In the present work we synthesized a new non-linear optical (NLO) maleic acid copolymer containing Disperse Red 1 moieties, built-up multilayer assemblies by alternate adsorption of poly(allylamine hydrochloride) (PAH) and maleic copolymer derivative, and carried out an investigation on their second harmonic generation (SHG) properties. The resulting multilayer assemblies exhibit SHG which arises from the non-centrosymmetric alignment of the chromophores in the copolymer. The SHG signal increases with the number of chromophore-containing polymer layers, up to five layers. Further assembly reduces the signal.     

An ultrasonic transducer for second harmonic imaging using a LiNbO3 plate with a local ferroelectric inversion layer

A new lithium niobate (LiNbO3) transducer of separated transmitter-receiver configuration is proposed for application to second harmonic imaging in a high-frequency range. In this transducer, a domain-inverted layer of half the plate thickness is formed selectively by Ti-diffusion and heat treatment in the central part of a LiNbO3 plate. The uniformly polarized surrounding region is used as the transmitter that will generate the fundamental wave component. A transducer with the transmission frequency of 50 MHz and the reception frequency of 100 MHz is fabricated using a 36 degrees rotated Y-cut LiNbO3 plate, and its performance is demonstrated.     

Deep- and vacuum-ultraviolet metaphotonic light sources

Recent demonstrations of deep- and vacuum-ultraviolet (DUV and VUV) light emission from artificially engineered meta-atoms through nonlinear harmonic signal generation processes have opened up new avenues for fundamental engineering approaches and modern applications. While many different phenomena based on optical metasurfaces have been revealed in linear optics, several studies have reported the observation of various nonlinear optical phenomena in such nanosystems, like, for example, second and third harmonic generation (SHG and THG), multiphoton luminescence, higher harmonic generation, and four-wave mixing. Plasmonic and all-dielectric flatland metasurfaces enable successful manipulation of light–matter interactions on ultradense platforms and provide substantial enhancement of driving fields, which make these architectures promising and attractive to efficiently radiate intense and coherent second and third harmonic radiations. In this focused Review, we highlight and discuss the recent state-of-the-art methods that have been developed and proposed for the generation of nonlinear harmonic signal and high-energy DUV and VUV lights. This contribution not only summarizes the strategies that have been exploited for augmenting the intensity of nonlinear UV signal, but also introduces the novel mechanisms to strongly optimize the conversion efficiency of this principle. We envisage that this understanding allows to compare the performance of versatile nonlinear DUV and VUV metasources and paves the way of designing much more efficient light emitting tools such as lasers, super-resolution imaging nanosystems, and nanolithography apertures.     

Spectral Measurement of the Film-Substrate Index Difference in Proton-Exchanged LiNbO(3) Waveguides

We report the spectral characterization of proton-exchanged lithium niobate (PE:LiNbO(3)) waveguides in terms of the variation of the refractive-index difference between the waveguiding layer and the substrate. The dispersion of the extraordinary refractive-index increase (deltan(e)) is measured from 405 to 1319 nm with several light sources. Two types of proton-exchanged waveguide, prepared under different conditions, are studied. These measurements should be of use in the optimization of PE:LiNbO(3) waveguides for nonlinear optical applications, particularly in second-harmonic generation in the blue-green wavelength region.     

Effect of MgO doping of periodically poled lithium niobate on second-harmonic generation of femtosecond laser pulses

We theoretically analyze type-I broadband second-harmonic generation (SHG) of femtosecond laser pulses based on a quasi-phase-matching configuration in periodically poled congruent LiNbO3 (LN) andperiodically poled MgO:LiNbO3 (PPMgLN) (5% and 7%). Group-velocity matching (GVM) can be achieved at the fundamental waves of 1.59, 1.56, and 1.55 microm for SHG when the three types of crystals have grating periods of 22.31, 20.07, and 23.45 microm, respectively. It is found that the central wavelength of the fundamental wave for GVM will increase with the decrease of MgO doping in LN. It is concluded that the shift of the GVM central wavelength is due to the difference of MgO doping, which changes the dispersion of the crystal. Therefore, tunable and high efficiency broadband SHG of femtosecond laser pulses in a long crystal can be realized by selecting different doping rates of PPMgLN.     

Fourth-harmonic generation in a single lithium niobate-crystal with cascaded second-harmonic generation

Tunable second- and fourth-harmonic radiation was generated in a single 1-cm-long lithium niobate (LiNbO(3)) crystal with the Mark III infrared free electron laser at Duke University. The fundamental laser radiation was tuned from 2 to 2.5 μm, yielding 1-1.25-μm radiation (second harmonic) and 0.5-0.625-μm radiation (fourth harmonic). A fundamental-second-harmonic energy conversion efficiency of 66% and a fundamental-fourth-harmonic energy conversion efficiency of 3.3 × 10(-6) were measured. The maximum energy in the fourth harmonic was 3.3 nJ.     

SiC nanocrystals embedded in oligoetheracrylate photopolymer matrices; new promising nonlinear optical materials

Photoinduced optical phenomena in SiC nanocrystallites embedded within the photo-polymer oligoetheracrylate matrices have been studied using experimental nonlinear optics, particularly photoinduced optical second harmonic generation (SHG). The YAG-Nd-laser (λ=1.06 μm; W=30 MW; pulse duration within the 30–50 ps) was used as a source of pumping light and the nitrogen laser (λ=337 nm) has been applied as a source of the photoinducing light. With increasing intensity of the photoinducing beam, the SHG (λ=0.53 μm) signal increased and achieved a maximum (χ₂₂₂=10.1 ± 0.13 pm/V) at a photon flux of about 1.61 GW/cm². With decreasing temperature, the SHG signal strongly increases within the temperature range 25–30 K. Time-dependent probe–pump measurements indicate an existence of the SHG maximum for a pump–probe time delay of about 20 ps. The SiC hexagonal structural components play a key role in the observed photoinduced nonlinear optical effects. Large values of the nonlinear optical constants as well the good technological parameters open a possibility to enhance the nonlinear optical susceptibilities.     

Short reflectors operating at the fundamental and second harmonics on 128 degree LiNbO3

In this work, we study numerically the operation of surface acoustic wave (SAW) reflectors comprising a small number of electrodes on the 128 degree YX-cut lithium niobate (LiNbO3) substrate. The electrodes have a finite thickness, and they are either open circuited or grounded. The center-to-center distance between adjacent electrodes d corresponds roughly either to half of the characteristic wavelength d proportional to lambda0/2 or to d proportional to lambda0, for the reflectors operating at the fundamental and second harmonic modes, respectively. We use software based on the finite-element and boundary-element methods (FEM/BEM) for numerical experiments with a tailored test structure having 3 interdigital transducers (IDTs), simulating experimental conditions with an incident wave and reflected and transmitted SAWs. Using the fast Fourier transform (FFT) and time-gating techniques, calculation of the Y-parameters in a wide frequency range with rather a small step allows us to determine the reflection coefficients, and to estimate the energy loss due to bulk-wave scattering. The detailed dependences of the attenuation and reflectivity on the metallization ratio and the electrode thickness are given for the classic 128 degree-cut of LiNbO3.     

新型紫外非线性光学晶体KNa5Ca5(CO3)8的合成、表征及性能的研究

采用水热法合成出一种新型碳酸盐非线性光学晶体材料KNa₅Ca₅(CO₃)₈, 该晶体属于六方晶系, 空间群为P63mc, 晶胞参数为a=b=1.00786(4) nm, c=1.26256(8) nm, Z=2。其晶体结构可以看作是由站立的[CO₃]基团连接相邻的两个[CaCO₃]_∞层, 从而沿[010]方向形成了四种不同类型的孔洞, 在这些孔洞中填充着K、Na 和[Na_0.67Ca_0.33]原子。KNa₅Ca₅(CO₃)₈晶体的粉末倍频效应为KDP的1.2倍, 且能够在可见光区实现相位匹配。紫外-可见-近红外漫反射光谱测试结果表明其晶体具有较大的光学带隙, 大概为5.95 eV, 是具有潜在应用前景的紫外非线性光学晶体材料。此外, 第一性原理的计算结果表明, 晶体的非线性系数主要来源于CO₃基团。     

Broadband second harmonic generation in an imperfect nonlinear photonic crystal with random defects

In this paper, we study broadband second harmonic generation (SHG) in an imperfect nonlinear photonic crystal in which defects are introduced with random lengths. We show that the efficient SHG output is obtained when the length of each defect varies near certain specialized values. The bandwidth of the SHG output broadens with the increasing randomness of defect length. Moreover, the SHG bandwidth is nearly unaffected only when the total length of the whole structure is long enough. The disordered structure also exhibits good tolerance to the fabrication error, which provides a way to control SHG intensity and bandwidth separately.     

Polarization-Independent Second Harmonic Generation in 2D Van Der Waals Kagome Nb3SeI7 Crystals

Second harmonic generation (SHG) of 2D crystals has been of great interest due to its advantages of phase-matching and easy integration into nanophotonic devices. However, the polarization-dependence character of the SHG signal makes it highly troublesome but necessary to match the laser polarization orientation relative to the crystal, thus achieving the maximum polarized SHG intensity. Here, it is demonstrated a polarization-independent SHG, for the first time, in the van der Waals Nb₃SeI₇ crystals with a breathing Kagome lattice. The Nb₃ triangular clusters and Janus-structure of each Nb₃SeI₇ layer are confirmed by the STEM. Nb₃SeI₇ flake shows a strong SHG response due to its noncentrosymmetric crystal structure. More interestingly, the SHG signals of Nb₃SeI₇ are independent of the polarization of the excitation light owing to the in-plane isotropic arrangement of nonlinear active units. This work provides the first layered nonlinear optical crystal with the polarization-independent SHG effect, providing new possibilities for nonlinear optics.     

Nonlinear optical methods in the nondestructive testing of metal surfaces

The possibilities of using second harmonic generation (SHG) in the nondestructive testing of metal surfaces are discussed on the basis of experimental results. The dependence of SHG on the pump-beam polarization direction gives information about surface roughness. Experiments on a silicon single crystal show that the structural symmetry of the crystal can be determined. Residual strains also seem to give rise to an ordered rotational anisotropy in the second harmonic (SH) signal.     

Second Harmonic Generation in Ion Implanted Lithium Niobate Planar Waveguides

Abstract

We report the first demonstration of second harmonic generation (SHG) in ion implanted lithium niobate optical waveguides. For both ordinary and extraordinary index profiles a computer program was developed to simulate the positions of the modes within the optical well. With the help of this program the theoretical possibility of SHG using mode matching conditions within the guide was then studied as a function of the guide depth and temperature, and from these predictions, practical guides were constructed. Initially, SHG Cerenkov radiation was observed with leaky single implanted guides. Mode matched SHG from m = 0 to m = 2 was subsequently achieved by means of a multiple energy implant which was able to confine both fundamental and harmonic waves. Allowing for coupling and transmission losses, the corrected conversion efficiency is 0–018% W^?1 which compares favourably to a theoretical prediction for this guide of 0–020% W^?1. In this case a wide temperature tuning range was obtained.