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In this article, we investigate the molecular first hyperpolarizability of water molecules nearby the liquid-vapor interface. The hyperpolarizability of each molecule is calculated at the quantum level within an explicit, inhomogeneous electrostatic embedding. We report that the average molecular first hyperpolarizability tensor depends on the distance relative to the interface, but it practically respects the Kleinman symmetry everywhere in the liquid. Within this numerical approach, based on the dipolar approximation, the water layer contributing to the Surface Second Harmonic Generation (S-SHG) intensity is less than a nanometer. We show that within this interfacial layer, the common assumption considering a single, constant hyperpolarizability for all water molecules is not supported by our data: hyperpolarizability fluctuations are expected to impact the S-SHG intensity. These results represent a step forward the molecular interpretation of experimental S-SHG signal of aqueous interfaces.

Experimental evidence of scattering of second-harmonic light from the surface of spherical particles of optical dimensions is presented. This mechanism for second-harmonic generation is observed in a suspension of monodisperse spherical colloidal particles, ordered in a centrosymmetric crystalline lattice. In this periodic structure the mechanism of phase matching is provided by the bending of the photon dispersion curve near the Bragg reflection band. A simple theoretical analysis based on the Rayleigh-Gans scattering approximation shows that constructive interference of the second-harmonic light scattered from different portions of a single-sphere surface leads to a nonvanishing field with a quadrupolar distribution intensity pattern.

International audience; Surface Second-Harmonic Generation (S-SHG) experiments provide a unique approach to probe interfaces. One important issue for S-SHG is how to interpret the S-SHG intensities at the molecular level. Established frameworks commonly assume that each molecule emits light according to an average molecular hyperpolarizability tensor β(−2ω,ω,ω). However, for water molecules, this first hyperpolarizability is known to be extremely sensitive to their environment. We have investigated the molecular first hyperpolarizability of water molecules within the liquid–vapor interface, using a quantum description with explicit, inhomogeneous electrostatic embedding. The resulting average molecular first hyperpolarizability tensor depends on the distance relative to the interface, and it practically respects the Kleinman symmetry everywhere in the liquid. Within this numerical approach, based on the dipolar approximation, the water layer contributing to the Surface Second Harmonic Generation (S-SHG) intensity is less than a nanometer. The results reported here question standard interpretations based on a single, averaged hyperpolarizability for all molecules at the interface. Not only the molecular first hyperpolarizability tensor significantly depends on the distance relative to the interface, but it is also correlated to the molecular orientation. Such hyperpolarizability fluctuations may impact the S-SHG intensity emitted by an aqueous interface.

An anomalous optical second-harmonic generation (SHG) signal was previously reported in ${\mathrm{Sr}}_{2}\mathrm{Ir}{\mathrm{O}}_{4}$ and attributed to a hidden odd-parity bulk magnetic state. Here we investigate the origin of this SHG signal using a combination of bulk magnetic susceptibility, magnetic-field-dependent SHG rotational anisotropy, and overlapping wide-field SHG imaging and atomic force microscopy measurements. We find that the anomalous SHG signal exhibits a twofold rotational symmetry as a function of in-plane magnetic field orientation that is associated with a crystallographic distortion. We also show a change in SHG signal across step edges that tracks the bulk antiferromagnetic stacking pattern. While we do not rule out the existence of hidden order in ${\mathrm{Sr}}_{2}\mathrm{Ir}{\mathrm{O}}_{4}$, our results altogether show that the anomalous SHG signal in parent ${\mathrm{Sr}}_{2}\mathrm{Ir}{\mathrm{O}}_{4}$ originates instead from a surface-magnetization-induced electric-dipole process that is enhanced by strong spin-orbit coupling.

International audience; The air–ionic liquid interface for a series of ionic liquids involving imidazolium cations [Cnmim] with different alkyl chain lengths (n = 2, 4, 6, 8, 10, and 12) and the same [NTf2] imide anion has been studied by polarization-resolved second harmonic generation (SHG). An increase as a function of the alkyl chain length of the orientational parameter reveals the increasing ordering of the air–pure ionic liquid interfaces although it is not possible to disentangle the change in mean tilt angle from a change in the tilt angle probability distribution width. Besides, the study of the air–mixed ([C12mim])x([C2mim])1–x[NTf2] ionic liquid interface clearly demonstrates the interfacial nonideality of the mixed ionic liquids. The long alkyl chain cation perturbs the interface as seen from the orientational parameter and displaces the short alkyl chain one for bulk mixture contents as low as 10%. At higher long alkyl chain cation bulk mixture contents, the interface behaves close to a pure long alkyl chain ionic liquid.

Interfaces with room-temperature ionic liquids (ILs) play key roles in many applications of these solvents, but our understanding of their properties is still limited. We investigate how the addition of ILs in the aqueous subphase affects the adsorption of the cationic dye malachite green at the dodecane/water interface using stationary and time-resolved surface second harmonic generation. We find that the interfacial concentration of malachite green depends crucially on the nature of both anionic and cationic constituents. This concentration reports on the overall charge of the interface, which itself depends on the relative interfacial affinity of the ions. Our results reveal that the addition of ILs to the aqueous subphase has similar effects to the addition of conventional salts. However, the IL cations have a significantly higher propensity to adsorb than small inorganic cations. Furthermore, the IL constituents show a synergistic effect, as the interfacial concentration of each of them also depends on the interfacial affinity of the other.

Surface Second Harmonic Generation (SSHG) is an optical non-linear analytical technique that has been applied to various biological and non-biological systems. Its application to biological systems has been limited to imaging and studies of molecular structures. However, its potential as a label-free method to detect bio-molecular interactions was not thoroughly investigated. This study explored, probed and evaluated the potential of SSHG as a viable biosensing technique.

Efficient second harmonic generation (SHG) employing quasi-phase-matching (QPM) method based on the spatial modulation of mode intensity has been demonstrated experimentally and theoretically in th...

This study numerically investigated second harmonic generation (SHG) and the linear optical responses in core–shell nanoparticles comprising a gold core and silicon shell. The effects of the core radius and shell thickness were studied based on the resonance wavelength shifts, linear responses, and SHG efficiency in numerical simulations. By accurately setting the shell thickness, a model was designed where the resonance wavelength was almost constant relative to variations in the core radius for a specific shell thickness (i.e., the resonance wavelength did not shift). Thus, it was possible to optimize the efficiency of the linear optical responses and SHG in the core–shell nanoparticles by only changing the core radius. The desired efficiency can be achieved for this nanoparticle in specific applications by first tuning the resonance wavelength by changing the shell thickness and then by optimizing the efficiency by changing the core radius. The results obtained in this study may facilitate the development and optimization of optical nanodevices for different applications in nanophotonics and nano-optics, such as nanolasers and nanosensors.

In this paper we are reporting the computation for the Nonlinear Optical Rectification (NOR) and the Second and Third Harmonic Generation (SHG and THG) related with electronic states of asymmetric double Si- δ -doped quantum well in a GaAs matrix when this is subjected to an in-plane ( x -oriented) constant magnetic field effect. The work is performed in the effective mass and parabolic band approximations in order to compute the electronic structure for the system by a diagonalization procedure. The expressions for the nonlinear optical susceptibilities, χ 0 ( 2 ) , χ 2 ω ( 2 ) , and χ 3 ω ( 3 ) , are those arising from the compact matrix density formulation and stand for the NOR, SHG, and THG, respectively. This asymmetric double δ -doped quantum well potential profile actually exhibits nonzero NOR, SHG, and THG responses which can be easily controlled by the in-plane ( x -direction) externally applied magnetic field. In particular we find that for the chosen configuration the harmonic generation is in the far-infrared/THz region, thus and becoming suitable building blocks for photodetectors in this range of the electromagnetic spectra.

The linear and nonlinear optical susceptibility dispersion of CsZn 2 B 3 O 7 single crystal are comprehensively investigated for a bulk structure in form of single crystal taking into account the influence of the packing structural units. The calculation highlights that the BO 3 structural units packing is the main source for the large birefringence in CsZn 2 B 3 O 7 due to high anisotropic electron distribution, and, hence, it affects the macroscopic second harmonic generation (SHG) coefficients. The large SHG is due to hyperpolarizablity formed by ZnO 4 tetrahedra and co-parallel BO 3 triangle groups. The absorption edge of CsZn 2 B 3 O 7 occurs at λ = 218 nm and the optical band gap is estimated to be 5.68 eV that is in good agreement with the experimental data (5.69 eV). Therefore, CsZn 2 B 3 O 7 is expected to produce a coherent radiation in deep-ultraviolet (DUV) region with SHG of about 1.5 × KDP (1.5 × 0.39 p.m./V = 0.585 p.m./V) that agrees with the measurements. This work is aimed at the report of reliable SHG value and the details of the NLO tensor for bulk CsZn 2 B 3 O 7 single crystal.

Aspects of second harmonic generation (SHG) in biaxial crystals pumped by focused radiation of a femtosecond laser are investigated. The efficiency of SHG grows when the duration of femtosecond pulses is shortened by raising of the number of nonlinear interactions between the light waves. The growth of SHG spots is explained by the increase in the angles of phase dispersion.

Multiresonant plasmonic nanoantennas have recently gained a lot of attention due to their ability to enhance nonlinear optical processes at the nanoscale. The first nanostructure designed for this purpose was an aluminum antenna composed of three arms, designed to be resonant at both the fundamental and the second harmonic frequencies. It was demonstrated that second harmonic generation induced by its resonances at both the fundamental and second harmonic wavelengths is higher than the one from a simple dipolar nanoantenna supporting a resonance at the fundamental wavelength only. However, the underlying mechanisms leading to this strong nonlinear signal are still unclear. In this study, both advanced simulations and experiments are combined to investigate in details the role of the mode coupling in the enhancement of second harmonic generation. By varying the length of the nanoantenna arms, it is clearly demonstrated that second harmonic generation is enhanced when the coupling between the quadrupole and...

The effects of an off-centre donor impurity on the non-linear optical absorption, second and third harmonic generation in a GaAs two-dimensional disc-shaped quantum ring under magnetic field are investigated within the compact density-matrix formalism and the effective mass approximation. The results reveal that: (i) the absorption spectra extend on larger energy intervals at the increment of the magnetic field; (ii) the possibility of generating second harmonic response from the system is demonstrated for an impurity placed on the repulsive part of the confining potential; (iii) both second harmonic and third harmonic coefficients are one order of magnitude larger for an impurity placed on the repulsive part of the potential and are blue-shifted by the increment of the magnetic field regardless the impurity position.

We investigate the ferroelectric state of a tetragonal BiFeO3 thin film grown on a LaAlO3 (001) substrate using an optical second harmonic generation (SHG) microscope. Whereas the ferroelectric state of this material hosts nanometer-sized domains which again form micrometer-sized domains of four different configurations, we could figure out the characteristic features of each domain from the SHG mapping with various sizes of the probe beam, i.e., from 0.7 to 3.9 μm in its diameter. In particular, we demonstrate that a single micrometer-sized domain contributes to the SHG as a coherent summation of the constituent nanometer-sized domains, and multi-micrometer-sized domains contribute to the SHG as an incoherent summation of each micro-domain.

We use surface second harmonic generation spectroscopy (s-SHG) to study the oxidation of supported, size-selected silver clusters under ultra-high vacuum conditions. The oxidation reaction of small silver clusters between $$\hbox {Ag}_{9}$$ and $$\hbox {Ag}_{55}$$ is monitored by means of their localized surface plasmon resonance. We observe a rapid decline of the SH-intensity, as soon as cluster samples are exposed to an oxygen partial pressure of $$5 \times 10^{-6}$$ mbar, which is attributed to the formation of silver–oxygen-bonds. The evolution of the SH-intensity under exposure to oxygen shows a double-exponential character for all investigated cluster sizes. Since the oxidation of single crystalline silver surfaces follow single-exponential Langmuir-kinetics, the two independent pathways of SH-intensity loss are attributed to a surface- and an interface-oxidation of supported clusters, respectiveley. For small cluster sizes, a complete loss of the SH intensity is obtained, which suggests the complete oxidation of the clusters. For larger clusters a plasmonic resonance is still observed after oxidation, indicating a residual free-electron density.

Transition metal dichalcogenides (TMDs) have provided a fundamental stage to study light–matter interactions and optical applications at the atomic scale due to their ultrathin thickness and their appropriate band gap in the visible region. Here, we report the strong nonlinear optical effects, including second-harmonic generation (SHG) and third-harmonic generation (THG) in spiral WS2 structures. SHG intensity quadratically increases with layer numbers, other than diminishing the oscillation of 2H stacking TMDs. The contrary SHG behavior is attributed to the broken symmetry from twisted screw structures, revealed by aberration-corrected transmission electronic microscope observation. Furthermore, the twist angle of the screw structure (5 degrees) was obtained by high-resolution transmission microscope measurements and confirmed by polarization tests of SHG output. Moreover, we roughly estimate the effective second-order nonlinear susceptibility. The discovery and understanding of the accumulation of nonli...

We report analytically an electro-optically tuned non-critical phase-matched second harmonic generation of a diode pumped solid-state laser in LiNbO3 crystal at room temperature (25 °C).The direction of propagation of fundamental wave of 1064 nm is on x-y plane, making an angle of θ = 90° with z-axis and ϕ = 33° with x-axis of the crystal. By applying an electric field of −7.87 kV/mm along z-axis of the crystal, ordinary and extra ordinary refractive indices of fundamental wave and second harmonic wave are matched to each other respectively. The calculated angular acceptance is 55.7 mrad mm1/2.

International audience; In this study, we have investigated the use of silver cation as nucleating agent in germanotellurite glass matrix of compositions (100−x) [70TeO2–10GeO2–10Nb2O5–10K2O]–xAg2O (x=0-6 mol%), in order to promote bulk crystallization. Density measurements, differential scanning calorimetry, X-ray diffraction, UV-Vis, and Raman spectroscopies have been performed to study the crystallization process. We have observed bulk crystallization of a unique noncentrosymmetric phase, K[Nb1/3Te2/3]2O4.8, which has been investigated for its second-order optical activity. Transparent to translucent glass-ceramics have been successfully tailored under thermal treatment and second harmonic generation signals were recorded on the glass-ceramic samples as a function of their synthesis procedure. It is suggested that the second-order optical properties observed are strongly related to the organization of crystallites within phase-separated domains.

The array behaviour of anionic surfactant sodium dodecylbenzenesulfonate (SDBS) on the air/water interface was investigated using non-resonant surface second harmonic generation (SHG) and molecular simulation. It was found that the SHG intensities changed with surfactant concentrations non-monotonously under Critical Micelle Concentration (CMC). The mean orientational angle of SDBS molecule at the air/liquid interface was calculated, and the molecular array behaviour was analyzed by molecular dynamics (MD) simulation. The simulated results agreed with the experimental results very well, which provided the detailed information about the interfacial molecular configuration of surfactant, not only indicating the SHG intensity related to the Ns and r(θ), but also demonstrates that the microscopic information presented by the MD simulation method is reliable. According to the results, the surfactant molecules get clustered even at very low concentration far lower than the CMC.

Nonlinear effects such as second harmonic generation (SHG) are important for applications such as switching and wavelength conversion. In this study, the generation of second harmonic in metal-insulator-metal (MIM) plasmonic waveguides was investigated for both symmetric and asymmetric structures. This study considered two different structures as plasmonic waveguides for the generation of second harmonic, and analysis was performed using the finite-difference time-domain method. Besides, the structure has grating on both sides for more coupling between photons and plasmons. The wavelength duration of grating per unit length (number of grooves) was optimized to reach the highest second harmonic generation. To perform this optimization, the wavelength of operation (λ = 458 nm) was considered. It was shown that field enhancement in symmetric MIM waveguides can result in the enhancement of SHG magnitude when compared to literature values. Also, asymmetric devices result in more than two orders of magnitude enhancement in SHG, as compared to the symmetric structure. It has been shown that the electric field of the second harmonic depends on the thickness of the crystal (insulator). Hence, its thickness was optimized to achieve the highest electric field.

We investigate optical second harmonic generation (SHG) from individual self-catalyzed zinc-blende (ZB) GaAs nanowires (NWs), where the polarimetry strongly depends on the NW diameter. We report a direct observation on the SHG induced by surface nonlinear susceptibilities in a single, ultra-thin GaAs NW. By considering the contributions from both optical field and structural discontinuities in our theoretical model, we can well explain the optical SHG polarimetry from NWs with different diameters. We also show that the optical in-coupling coefficient arising from the depolarization electromagnetic field can determine the polarization of the SHG. The results open perspectives for further geometry-based studies on the origin and control of SHG in small nanostructures.

An intense short-pulse laser obliquely incident on a clustered gas quickly converts the atomic clusters into hot plasma balls. The laser beam produces a second harmonic due to nonlinear response of cluster and plasma electrons. For enhancement of efficiency of second harmonic generation, there should be appropriate phase-matching between the incident laser beam and the generated harmonic. To achieve the required phase-matching, the ripple in cluster density and plasma electron density outside the cluster is introduced. The efficiency of second harmonic generation is sensitive to the angle between ripple wave vector k → o and the direction of the incident laser beam.

In this study, it was shown that field enhancement in the nonlinear metal-insulator-metal (MIM) plasmonic waveguides can result in a large enhancement of the second harmonic generation (SHG) magnitude as compared with values reported in the literature. The proposed structure has two metals at the top and two metals at the bottom of the crystal. In this structure, a voltage is applied on metals to produce a SHG electrically. Hence, the metals that define the cavity also serve as electrodes capable of generating high direct current electric fields across the nonlinear material. The frequency of a fundamental wave at 458 nm was doubled and modulated in intensity by applying a moderate external voltage to the electrodes, yielding a voltage-dependent nonlinear generation with a higher coupling efficiency. All the simulations here have been calculated by using the finite-element-based commercial COMSOL software.

Surface second-harmonic generation (SHG) in plasmonic metal nanostructures provides a promising approach to design compact and ultrafast nonlinear nanophotonics devices. However, typical plasmonic nanostructures, such as those with tiny gaps that provide strong near-field-amplified nonlinear sources, often suffer from the cancellation of nonlinear fields in the gaps, which results in the so-called silenced SHG and consequently attenuates the overall nonlinear conversion efficiency. In this study, we propose and demonstrate that the silenced SHG in a gold split-ring resonator can be effectively restored by carefully tailoring its gap geometry to avoid the cancellation of nonlinear fields in the gap and simultaneously achieve both spatial and frequency mode matching between the magnetic and the electric dipolar resonances. As a result, the effective nonlinear sources in the gap can be dramatically amplified and the surface second-harmonic emissions can be efficiently coupled out, leading to an SHG intensity enhancement of 7 times compared to a conventional split-ring resonator. The overall SHG conversion efficiency can thus be enlarged to about 1.49 × 10-8 in the near-infrared excitation region. Importantly, the restored surface second-harmonic emission exhibits the scattering characteristics of an ideal electric dipole, which can be very useful for nonlinear far-field manipulation such as beam steering and holograms.

We study surface second-harmonic generation (SHG) from a singular plasmonic structure consisting of touching metallic wires. We use the technique of transformation optics and relate the structure to a rather simpler geometry, a slab waveguide. This allows us to obtain an analytical solution to the problem, revealing rich physical insights. We identify various conditions that govern the SHG efficiency. Importantly, our analysis demonstrates that apart from the mode-matching condition, the phase-matching condition is relevant even for this subwavelength structure. Furthermore, we identify a geometric factor which was not identified before. We support our analysis with numerical simulations.

The process of second-harmonic generation (SHG) in a finite one-dimensional nonlinear medium is analyzed in parallel by the Green-function technique and the Fourier-transform method. Considering the fundamental pump field propagating along a given direction and eliminating back-reflections at the boundaries the terms giving the surface second-harmonic fields in the particular solution of the wave equation are uniquely identified. Using these terms the flow of energy corresponding to the surface second-harmonic fields is analyzed in the vicinity of the boundaries. The formula giving the depth of the nonlinear medium contributing to the surface SHG is obtained. Both approaches for describing the SHG are compared considering complexity and quantization of the interacting fields. In addition, a theoretical model of surface SHG in centrosymmetric media is proposed. The model is built upon assumption that the second-order nonlinearity decays exponentially with distance from the boundary. As an important example, the generation of surface SHG from a thin dielectric nonlinear layer placed on a silicon substrate is analyzed by the proposed model.

We have investigated strong optical nonlinearity of monolayer MoS2(1–x)Se2x across the exciton resonance, which is directly tunable by Se doping. The quality of monolayer alloys prepared by chemical vapor deposition is verified by atomic force microscopy, Raman spectroscopy, and photoluminescence analysis. The crystal symmetry of all of our alloys is essentially D3h, as confirmed by polarization-dependent second-harmonic generation (SHG). The spectral structure of the exciton resonance is sampled by wavelength-dependent SHG (λ = 1000–1800 nm), where the SHG resonance red-shifts in accordance with the corresponding optical gap. Surprisingly, the effect of compositional variation turns out to be much more dramatic owing to the unexpected increase of B-exciton-induced SHG, which indeed dominates over the A-exciton resonance for x ≥ 0.3. The overall effect is therefore stronger and broader SHG resonance where the latter arises from different degrees of red-shift for the two exciton states. We report the corre...

The tunable second harmonic generation (SHG) enhancement factor of gold-dielectric-gold three-layered nanoshells has been theoretically studied using the theory of quasi-static electrodynamics and plasmon hybridization. Because of the local surface plasmon resonance (LSPR)-induced local field effect, the SHG response corresponding to both fundamental frequency and second harmonic has been greatly enhanced. By changing the geometry parameters and local dielectric environment of the three-layered nanostructure, the intensity and shift of the SHG factor peaks could be fine tuned. As the radius of the inner gold sphere is increased, both the fundamental and the second harmonic SHG peaks from the anti-symmetric coupling between the outer bonding shell plasmon and the inner sphere plasmon decrease, whereas the SHG peaks from the symmetric coupling between the outer shell and the inner sphere get intense. These radius-dependent intensity changes of the SHG peaks also depend on the dielectric constant of the separate layer and outer surrounding. Thus, the number of SHG peak could be tuned from two to four. Furthermore, the wavelength gaps between the SHG peaks corresponding to anti-symmetric and symmetric coupling could be greatly reduced by increasing the thickness of the outer gold shell. Therefore, the nonmonotonous intensity change could be observed because of the switching of the SHG peaks. The corresponding physical origin has been illuminated by analyzing the plasmon hybridization and the polarization fields in the nanostructure.

We have tested the possibility of using monomolecular layers of bacteriorhodopsin (BR) for the synthesis of highly sensitive and highly selective sensors based on second harmonic generation and surface plasma waves. We have used various methods to study the optical and nonlinear optical properties of Langmuir-Blodgett films of BR in order to clarify the extent to which specific properties of BR molecules are retained during their transfer from the surface of water to a solid substrate. We show that the second harmonic generation method is efficient for analyzing the molecular orientation and quality of Langmuir-Blodgett films. The experimental nonlinear optical susceptibility of second order BR molecules is 3.4·10 −11 m/V. The relative change in the resonant wave vector is (3.6±0.1)·10 −2 at an excitation light wavelength of 630 nm. We have obtained a BR spectrum with the effective excitation by incident radiation of surface plasma waves. On the basis of these studies, we have proposed new schemes of biosensors operating on the basis of second harmonic generation and surface plasma resonance caused by fundamental frequency reflection from BR monomolecular layers. This scheme was tested for a model device and demonstrated the possibility of obtaining sensitivities of the order of 10 11 molecules/cm 3 .

We have studied hydrogen desorption from a flat H-Si (111)1 × 1 surface at 711 K by observing sum frequency generation (SFG) and second harmonic generation (SHG) spectra. Flat H-Si (111) surfaces were prepared by dosing hydrogen molecules in an ultra-high vacuum chamber with a base pressure of 〜10−8 Pa. Combining the SFG and SHG methods, the desorption order has been clarified over the whole hydrogen coverage range from 1 monolayer (ML) to 0 ML. The hydrogen desorption was assigned as second order in the high coverage range of 1 ML–0.18 ML by using SFG spectroscopy and as first order in the coverage range of 0.18 ML–0.0 ML by using SHG spectroscopy. Copyright © 2016 John Wiley & Sons, Ltd.

The results of theoretical and experimental studies of the second harmonic generation in a Ti:Sapphire femtosecond complex are described. The complex includes a femtosecond pulse generator, a stretcher, a regenerative amplifier, two multipass amplifiers, a compressor, and a second-harmonic generator. The effects of the radiation intensity, beam spatial profile, and the level of the noise component of the first harmonic at a wavelength of 950 nm on the homogeneity of the second harmonic are studied. It is theoretically shown that a good homogeneity of the second harmonic intensity is observed in the absence of the noise component in the beam at the fundamental wavelength. When making the amplitude inhomogeneities in the first harmonic even greater, inhomogeneities in the second harmonic appear. It is experimentally shown that an increase in the noise component in a pumping beam due to the use of a spatial filter allows strong suppression of small-scale inhomogeneities in the second harmonic.

Asymmetric molecular harmonic generation from HeH2+ ion in the presence of the spatially inhomogeneous plasmon-enhanced field has been theoretically investigated by solving the two-dimensional non-Born–Oppenheimer time-dependent Schrodinger equation (both the electron and nuclear motions are considered only along the laser polarisation axis). It shows that (1) for the normal homogeneous field, the harmonic cut-off from the asymmetric molecule is beyond the classical harmonic cut-off energy from the atom (Ip + 3.17 Up). Further analyses show that the multi-channels ionisation–recombination process is responsible for the harmonic extension. (2) For the spatially inhomogeneous plasmon-enhanced field, the harmonic cut-off can be further enhanced, and an optimal 3.0 dB enhanced field with a 482 eV supercontinuum has been obtained. Quantum time-frequency harmonic analyses have been shown to explain the harmonic characteristics and the harmonic extension process. (3) Initial vibrational state and isotopi...

Second harmonic generation is studied in structures containing nanoscale layers of transition metal chalcogenides that are two-dimensional semiconductors and deposited on a SiO2/Si substrate. The second harmonic generation intensity is calculated with allowance for multibeam interference in layers of dichalcogenide and silicon oxide. The coefficient of reflection from the SiO2-layer-based Fabry–Perot cavity is subsequently calculated for pump wave fields initiating nonlinear polarization at every point of dichalcogenide, which is followed by integration of all second harmonic waves generated by this polarization. Calculated second harmonic intensities are presented as functions of dichalcogenide and silicon oxide layer thicknesses. The dependence of the second harmonic intensity on the MoS2 layer thickness is studied experimentally in the layer of 2–140 nm. A good coincidence of the experimental data and numerical simulation results has been obtained.

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.

We numerically study second harmonic generation from plasmonic nanotubes of air-core and ultrathin gold shell using classical nonlocal hydrodynamic model of free electron. We demonstrate that the nonlocal effect of gold significantly affects the linear optical response and second harmonic generation in such ultrathin nanotubes with shell down to a few nanometers or subnanometer scale, comparing with the conventional local Drude model of gold. We specially emphasize second harmonic generation from the nanotube structures of dipole plasmon resonance at fundamental wavelength and dipole/quadrupole resonance at second harmonic wavelength. Our results indicate that, the output of second harmonic generation is dominantly enhanced by the dipole plasmon resonance at fundamental wavelength via the strong local electric field and also can be significantly enhanced by dipole- and quadrupole-resonant scattering at second harmonic wavelength. The nonlinear sources of second harmonic generation in ultrathin gold nanotubes, including nonlinear Coulomb interaction, convective term, Lorentz force, and nonlinear pressure are studied separately, and the dominant contributions from convective term and nonlinear Coulomb term are reported.

We report on an observation of second harmonic generation in an individual KNbO3 nanorod by using a near-field scanning optical microscope. The second harmonic is successfully generated by irradiating with a femtosecond laser having center wavelengths of 1200, 1100, and 972 nm. Such a second harmonic yield shows a clear dependence on the incident laser polarization, where maximum yield is obtained when the incident laser polarization is parallel to the long axis of an individual nanorod. A spatially-resolved second harmonic image shows a bright spot at the edge of the nanorod, which is attributed to the elaborated intensity of both fundamental laser light and second harmonic light inside the nanowire owing to cavity-mode formation.

We perform an exhaustive exploration of profiles of second harmonic generation (SHG) coefficient of impurity-doped quantum dots (QDs) in presence and absence of noise. The quantum dot is doped with Gaussian impurity. Noise has been applied to the system additively and multiplicatively. A perpendicular magnetic field emerges out as a confinement source and a static external electric field has been applied. The SHG profiles have been pursued as a function of incident photon energy when several important parameters such as electric field strength, magnetic field strength, confinement energy, dopant location, Al concentration, dopant potential, and noise strength assume different values. Moreover, the role of mode of application of noise (additive/multiplicative) on the SHG profiles has also been critically analyzed. The SHG profiles are found to be enriched with interesting observations such as shift of SHG peak position and maximization/minimization of SHG peak intensity. Presence of noise alters the features of SHG profiles through some interesting outcomes. Furthermore, the mode of application of noise (additive/multiplicative) also regulates the SHG profiles in diverse as well as often contrasting manners. The observations highlight the possibilities of tuning the SHG coefficient of doped QD systems in presence of noise.

The properties of a series of oxazole yellow dyes, including the dicationic YOPRO-1 and its homodimeric parent YOYO-1 and two monocationic dyes (YOSAC-1 and YOSAC-3), have been investigated at the dodecane/water interface using stationary and time-resolved surface second harmonic generation (SSHG) combined with quantum chemical calculations. Whereas YOYO-1 exists predominantly as a H-dimer in aqueous solution, the stationary SSHG spectra reveal that such dimers are not formed at the interface. No significant H-aggregation was observed with YOPRO-1, neither in solution nor at the interface. In the case of the monocationic YOSAC dyes, a distinct SSHG band due to H-aggregates was measured at the interface, whereas only weak aggregation was found in solution. These distinct aggregation behaviors can be explained by the different orientations of the dyes at the interface, as revealed from the analysis of polarization-resolved experiments, the doubly-charged dyes lying more flat on the interface than the singly charged ones. Although YOYO-1 and YOPRO-1 do not form H-dimer/aggregates at the interface, time-resolved SSHG measurements point to the occurrence of intra- and intermolecular interactions, respectively, which inhibit the ultrafast non-radiative decay of the excited dyes via large amplitude motion, and lead to a nanosecond excited-state lifetime. The distinct behavior evidenced here for YOYO-1 and YOSAC dyes points to their potential use as fluorescent or SHG interfacial probes.

A series of 3-phenyl-5-isoxazolone and 3-methyl-5-isoxazolone-based compounds with different electron donors were synthesized. Fourteen single crystals in this family were obtained by slow evaporation. Single crystal X-ray studies showed that four new 3-phenyl-5-isoxazolone-based crystals, C20H18N2O2 (PDI), C15H11NO2S (PTI), C23H15NO2 (PFI), and C17H13NO2S (PMI-(I)), belong to the noncentrosymmertric space group. The inclinations to achieve noncentrosymmetric space groups in the 3-phenyl-5-isoxazolone-based crystals have been confirmed by first-principles calculations. Powder second harmonic generation (SHG) tests revealed that the abovementioned four acentric crystals exhibited very large SHG intensities that were about 1 to 3 times that of OH1 (a commonly used nonlinear optical crystal) under 2.09 μm light. Their UV-vis absorption, diffuse reflectance spectroscopy, and thermal properties were also characterized. Moreover, widely tunable and monochromatic terahertz difference frequency generation in the 3-phenyl-5-isoxazolone-based crystal C17H13NO3 (MLS) was realized for the first time.

Efficient second harmonic generation (SHG) in a nonlinear transparent conducting oxide (TCO) stripe waveguide that incorporates an organic polymer is theoretically investigated. The phase match condition between the fundamental photonic mode at the second harmonic and the fundamental long-range plasmonic mode at the fundamental frequency can be satisfied by dynamically or statically tuning the free carrier concentration of the TCO. The theoretically generated signal reaches its maximum up to 56.4 mW at a propagation distance of 34.8 μm for a pumping power of 1 W. The corresponding normalized conversion efficiency of the phase-matched SHG is up to 4.65×103 W−1 cm−2.

The structure of the polarised interface between two immiscible electrolyte solutions (ITIES) has usually been deduced from electrocapillarity and capacitance measurements. However, these two methods only offer an indirect access to the surface change density, by differentiation and integration. In this work, we analyse the dependence on the potential difference and the organic phase electrolyte concentration of the surface charge density of the polarised ITIES. Our study is based on electrocapillarity, capacitance and surface second harmonic generation (SHG). This spectroscopic approach allows us to probe directly ionic concentrations and hence surface charge density. By comparing the results provided by these different methods, we confirm that integration of the capacitance curves yields too large values of the charge density. On the other hand, electrocapillarity and SHG provide consistent results over a large potential range. These results depict an ITIES weakly affected by the organic electrolyte concentration. Furthermore, the surface charge density depends quasi-linearly on the potential difference, at all concentrations. Altogether, these results support the model of a polarised ITIES made of two ionic face-to-face layers and devoid of diffuse layer, the so-called discrete Helmholtz model.

Optically nonlinear Pb2 B5 O9 X (X = Cl, Br) borate halides are an important group of materials for second harmonic generation (SHG). Additionally, they also possess excellent photocatalytic activity and stability in the process of dechlorination of chlorophenols, which are typical persistent organic pollutants. It would be of great interest to conduct in situ (photo-) catalysis investigations during the whole photocatalytic process by SHG when considering them as photocatalytic materials. In order to get superior photocatalytic efficiency and maximum surface information, small particles are highly desired. Here, a low-cost and fast synthesis route that allows growing microcrystalline optically nonlinear Pb2 B5 O9 X borate halides at large quantities is introduced. When applying the ionothermal growth process at temperatures between 130 and 170 °C, microcrystallites with an average size of about 1 µm precipitate with an orthorhombic hilgardite-like borate halide structure. Thorough examinations using powder X-ray diffraction and scanning electron microscopy, the Pb2 B5 O9 X microcrystals are indicated to be chemically pure and single-phased. Besides, the Pb2 B5 O9 X borate halides' SHG efficiencies are confirmed using confocal SHG microscopy. The low-temperature synthesis route thus makes these borate halides a highly desirable material for surface studies such as monitoring chemical reactions with picosecond time resolution and in situ (photo-) catalysis investigations.

Optical chirality (OC)-one of the fundamental quantities of electromagnetic fields-corresponds to the instantaneous chirality of light. It has been utilized for exploring chiral light-matter interactions in linear optics, but has not yet been applied to nonlinear processes. Motivated to explore the role of OC in the generation of helically polarized high-order harmonics and attosecond pulses, we first separate the OC of transversal and paraxial beams to polarization and orbital terms. We find that the polarization-associated OC of attosecond pulses corresponds approximately to that of the pump in the quasimonochromatic case, but not in the multichromatic pump cases. We associate this discrepancy with the fact that the polarization OC of multichromatic pumps vary rapidly in time along the optical cycle. Thus, we propose new quantities, noninstantaneous polarization-associated OC, and time-scale-weighted polarization-associated OC, and show that these quantities link the chirality of multichromatic pumps and their generated attosecond pulses. The presented extension to OC theory should be useful for exploring various nonlinear chiral light-matter interactions. For example, it stimulates us to propose a tricircular pump for generation of highly elliptical attosecond pulses with a tunable ellipticity.

Oxides and new functional materials such as oxide-based hetero-structures are very good candidates to achieve the goal of the next generation electronics. One of the main features that rules the electronic behavior of these compounds is the interfacial electric field which confines the charge carriers to a quasi-two-dimensional space region. The sign of the confined charge clearly depends on the electric field direction, which is however a very elusive quantity, as most techniques can only detect its absolute value. Even more valuable would be to access the sign of the interfacial electric field directly during the sample growth, being thus able to optimize the growth conditions directly looking at the feature of interest. For this aim, solid and reliable sensors are needed for monitoring the thin films while grown. Recently optical second harmonic generation has been proposed by us as a tool for non-invasive, non-destructive, real-time, in-situ imaging of oxide epitaxial film growth. The spatial resolution of this technique has been exploited to obtain real-time images of the sample under investigation. Here we propose to exploit another very important physical property of the second harmonic wave: its phase, which is directly coupled with the electric field direction, as shown by our measurements.

Second harmonic generation (SHG), a frequency doubling process through the second order nonlinear light-matter interactions, provides essential symmetry information of the matter that light interacts with. Recently, SHG, owing to its enhanced capability of symmetry, spectral and spatial resolutions and its compatibility of extreme sample environments such as low temperature, magnetic and electric fields, is exploited to probe complex electronic phases in correlated electron systems. In particular, SHG has shown its unique advantages in revealing hidden electronic phases that are invisible to many experimental probes because of their unconventional order parameters, or preserved translational symmetry as the underlying lattice, or small domain size of degenerate states. In this review, we describe the advances in the SHG based techniques that have enabled their applications in searching for the hidden electronic phases. We discuss successful examples of a toroidal order in a magnetoelectric insulator LiCoPO 4 , a parity-broken nematic order in a correlated metal Cd 2 Re 2 O 7 , and a loop-current or magnetic-quadrupole order in a cuprate analogue Sr 2 IrO 4 and in a cuprate high-Tc superconductor YBa 2 Cu 3 O y . Finally, we briefly survey the prospects of second order nonlinear optical responses in addition to SHG in studying hidden phases.

We present a general phenomenological model for surface second-harmonic generation (SSHG) induced by strain fields with up to three spatial coordinates. As an example, we apply it to thermal-mismatch strain fields around cylindrical metallic through-silicon-vias (TSVs) embedded in an Si(001) surface, which are widely used as interconnects between vertically stacked silicon layers to achieve 3D integration. We find that analysis of the four different combinations of s or p incoming and outgoing polarizations enables reconstruction of the strain field. In particular, the sS combination yields tensorial components of the strain field that are different from zero; from this information, the pP, sP, and pS combinations complete the analysis of the strain field.