Surface Nonlinear Susceptibility Research Articles

Proton Configuration in Water Chain on Pt(533).

In this paper, a wetting behavior of Pt(533) is studied by using heterodyne-detected vibrational sum-frequency generation spectroscopy under an ultrahigh-vacuum condition at 145 K. The imaginary parts of the surface nonlinear susceptibility (Imχ(2)) of the H-bonded OH stretching region are successfully obtained for submonolayer water coverage that show negative bands indicating H-down (proton pointing to the substrate) configurations both for the water at the step and at the terrace. The growth manner of the Imχ(2) signal with coverage and the results of an isotopic dilution are consistent with a model in which a one-dimensional (1D) chain at the step forms a "zigzag" structure that contains H-down orientations. This finding resolves the previous controversy in the literature concerning the proton configuration in the 1D water chain at the step.

Observation of Giant Surface Second-Harmonic Generation Coupled to Nematic Orders in the van der Waals Antiferromagnet FePS3.

Second-harmonic generation has been applied to study lattice, electronic, and magnetic proprieties in atomically thin materials. However, inversion symmetry breaking is usually required for the materials to generate a large signal. In this work, we report a giant second-harmonic generation that arises below the Néel temperature in few-layer centrosymmetric FePS3. A layer-dependent study indicates the detected signal is from the second-order nonlinearity of the surface. The magnetism-induced surface second-harmonic response is 2 orders of magnitude larger than those reported in other magnetic systems, with the surface nonlinear susceptibility reaching 0.08-0.13 nm2/V in 2-5 L samples. By combing linear dichroism and second-harmonic generation experiments, we further confirm the giant second-harmonic generation is coupled to nematic orders formed by the three possible Zigzag antiferromagnetic domains. Our study shows that the surface second-harmonic generation is also a sensitive tool to study antiferromagnetic states in centrosymmetric atomically thin materials.

Structural and optical characterization of Mg2SiO4 and Mg2SiO4-Pr6O11 nanocomposite for optical devices

The knowledge on optical properties of magnesium orthosilicate (Mg2SiO4) and its composite materials are very important as these silicate-based materials play a significant role in the field of optics and electronics. Mg2SiO4 nanomaterial and Mg2SiO4-Pr6O11 nanocomposite materials were therefore chosen in the present study, and they were synthesized in the present work, by simple sol-gel route. Powder x-ray diffraction (PXRD) pattern, Fourier-transform infrared (FT-IR) spectroscopy and ultraviolet–visible (UV–vis) spectroscopy techniques were adopted to understand the structural and optical properties of the prepared samples. The crystalline size of the two samples were estimated using Debye–Scherrer's equation and they are found to be 43 nm (Mg2SiO4) and 52 nm (Mg2SiO4-Pr6O11). The FT-IR results of Mg2SiO4-Pr6O11 revealed the SiO4 stretching and PrO vibrations clearly. The optical absorbances were used to determine the absorption coefficient α and hence the optical band gap energies Eg whose values are 5.60 eV and 5.17 eV for the samples Mg2SiO4 and Mg2SiO4-Pr6O11 respectively. Further with the help of UV–Vis spectra, the refractive index (n), extinction coefficient (k), optical conductivity (σ), real and imaginary part of dielectric constant (ε′ and ε''), volume energy loss function (VELF), surface energy loss function (SELF), linear susceptibility and non-linear susceptibility were investigated with respect to the incident photon energy. The Urbach energy was calculated using ln α vs graph and they are found to be 21 meV and 265 meV for Mg2SiO4 and Mg2SiO4-Pr6O11. The non-linear optical properties of the samples were also discussed by deriving the linear and non-linear optical susceptibilities and by exploring the possibilities of usage of this composite in optical devices.

Third-Order Optical Nonlinearity in Two-Dimensional Transition Metal Dichalcogenides**Supported in part by Laboratory of Photonics and Quantum Measurements (LPQM) at EPFL and European Graphene Flagship under Grant No. 696656, as well as Research Deputy of Sharif University of Technology

We present a detailed calculation of the linear and nonlinear optical response of four types of monolayer two-dimensional (2D) transition-metal dichalcogenides (TMDCs), having the formula MX2 with M = Mo, W and X = S, Se. The calculations are based on 6-band tight-binding model of TMDCs, and then performing a semi-classical perturbation analysis of response functions. We numerically calculate the linear and nonlinear surface susceptibility tensors with ωΣ = ωr + ωs + ωt. Both non-degenerate and degenerate cases are studied for third-harmonic generation and nonlinear refractive index, respectively. Computational results obtained with no external fitting parameters are discussed regarding two recent reported experiments on MoS2, and thus we can confirm the extraordinarily strong optical nonlinearity of TMDCs. As a possible application, we demonstrate generation of a π/4-rotated squeezed state by means of nonlinear response of TMDCs, in a silica micro-disk resonator covered with the 2D material. Our proposed method will enable accurate calculations of nonlinear optical response, such as four-wave mixing and high-harmonic generation in 2D materials and their heterostructures, thus enabling study of novel functionalities of 2D photonic integrated circuits.

Efficient second harmonic generation in gold-silicon core-shell nanostructures.

We theoretically investigate the properties of second-harmonic generation (SHG) in gold-silicon core-shell nanostructures. We first study a concentric structure. This structure exhibits strong electric field enhancement in the silicon shell due to the combined toroidal dipole mode and electric dipole mode. Efficient SHG can be obtained and the SHG signal is about 5 times as strong as that of the individual Si shell. Further calculations show that the contribution from a surface nonlinear susceptibility at the inner surface of the silicon shell dominates the SHG signal of the core-shell structure. The SHG as a function of wavelength is considered and it shows a resonance behavior. The cases of nonconcentric core-shell structures have also been considered. The SHG is further enhanced in this kind of configuration and the SHG signal can reach about 10 times as strong as that of the concentric case. Our results reveal the strong modification of the SHGs in dielectric nanostructures by using the metal-dielectric hybrid configurations, and could find applications in nanoscale nonlinear devices.

Structural discontinuity induced surface second harmonic generation in single, thin zinc-blende GaAs nanowires.

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.

How to distinguish various components of the SHG signal recorded from the solid/liquid interface?

Second harmonic generation (SHG) may be an important tool to probe buried solid/liquid interfaces because of its inherent surface sensitivity. A detailed interpretation of dye adsorption onto Si-SiO2 wafer is not straightforward because both adsorbent and adsorbate contribute to the overall SHG signal. The polarization resolved SHG analysis points out that the adsorbent and adsorbate contributions are out of phase by π/2 in the present system. The surface nonlinear susceptibility χ(2) represents thus a complex tensor in which its real part is related to the adsorbent contribution and its imaginary part to the adsorbate one.

Three-layer model for the surface second-harmonic generation yield including multiple reflections

We present the three-layer model to calculate the surface second-harmonic generation (SSHG) yield. This model considers that the surface is represented by three regions or layers. The first layer is the vacuum region with a dielectric function ${\ensuremath{\epsilon}}_{v}(\ensuremath{\omega})=1$ from where the fundamental electric field impinges on the material. The second layer is a thin layer $(\ensuremath{\ell})$ of thickness $d$ characterized by a dielectric function ${\ensuremath{\epsilon}}_{\ensuremath{\ell}}(\ensuremath{\omega})$, and it is in this layer where the SSHG takes place. The third layer is the bulk region denoted by $b$ and characterized by ${\ensuremath{\epsilon}}_{b}(\ensuremath{\omega})$. Both the vacuum and bulk layers are semi-infinite. The model includes the multiple reflections of both the fundamental and the second-harmonic (SH) fields that take place at the thin layer $\ensuremath{\ell}$. We obtain explicit expressions for the SSHG yield for the commonly used $s$ and $p$ polarizations of the incoming $1\ensuremath{\omega}$ and outgoing $2\ensuremath{\omega}$ electric fields, where no assumptions for the symmetry of the surface are made. These symmetry assumptions ultimately determine which components of the surface nonlinear second-order susceptibility tensor $\mathbf{\ensuremath{\chi}}(\ensuremath{-}2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega})$ are different from zero, and thus contribute to the SSHG yield. Then, we particularize the results for the most commonly investigated surfaces, the (001), (110), and (111) crystallographic faces, taking their symmetries into account. We use the three-layer model and compare it against the experimental results of a Si(111)$(1\ifmmode\times\else\texttimes\fi{}1)$:H surface, as a test case, and use it to predict the SSHG yield of a Si(001)$(2\ifmmode\times\else\texttimes\fi{}1)$ surface.

Origin of second-harmonic generation from individual silicon nanowires

We investigate second harmonic generation from individual silicon nanowires and study the influence of resonant optical modes on the far field nonlinear emission. We find that the polarization of the second harmonic has a size-dependent behavior and explain this phenomenon by considering different surface and bulk nonlinear susceptibility contributions. We show that the second harmonic generation has an entirely different origin, depending on the nanowire diameter and on whether the incident illumination is polarized parallel or perpendicular to the nanowire axis. The results open perspectives for further geometry-based studies on the origin and control of second harmonic generation in nanostructures of high-refractive index centrosymmetric dielectrics.

Phenomenological theory of second-harmonic generation from hexagonal centrosymmetric crystals

Theory of second-harmonic generation (SHG) in reflection from the (0001) face of hexagonal centrosymmetric (6/mmm) crystals is developed in a phenomenological approach. The bulk (electric-quadrupole) contribution to azimuthal dependences of SHG response is completely isotropic, whereas the surface (electric-dipole) contribution consists of isotropic and anisotropic parts for the 3m surface symmetry. Anisotropy entirely depends on only one component of the surface nonlinear susceptibility. This allows one to extract it directly by simultaneous measurement of the amplitude and phase of the SH wave in the (s,S) or (p,S) experimental setup. The feature is very important, if the observed anisotropy is strong and makes the surface SHG probing for these crystals completely different from the cases of cubic, rhombohedral, and tetragonal centrosymmetric crystals. In the case of weak anisotropy, the estimation of other surface components from azimuthal or polarization measurements is analyzed in detail.

Numerical Simulation of Ellipsometry Measurements for Determining Ratios of Nonlinear Surface Susceptibility Tensor Components

Numerical Simulation of Ellipsometry Measurements for Determining Ratios of Nonlinear Surface Susceptibility Tensor Components

Numerical simulation of ellipsometry measurements for determining ratios of nonlinear surface susceptibility tensor components

Numerical experiments are outlined to verify if ratios of the nonlinear surface susceptibility tensor components, that govern second harmonic optical effects in centrosymmetric media, can be unambiguously determined by ellipsometry, using a recently proposed technique. The corresponding theoretical model considers only the effects associated with a single, nonmagnetic interface (between two centrosymmetric media) assumed to be an ideal surface, whose crystallographic point group is either 4mm, 6mm or ∞ m The objective has been to explore how both random and systematic errors in the experimental data related to the state of polarization of the second harmonic radiation influence complex values of the ratios in this case. A procedure used for fitting the sample data is shown to deliver unambiguous results for the unknown ratios thus confirming the applicability and usefulness of the technique.

Semi-classical approximation for second-harmonic generation in nanoparticles

Second-harmonic generation by spherical nanoparticles is a non-local optical process that can also be viewed as the result of the nonlinear response of the a interface layer. The classical electrodynamic description, based e.g. on the nonlinear Mie theory, entails the knowledge of the dielectric function and the surface nonlinear optical susceptibility; both quantities are usually assumed to be predetermined, for instance from experiment. We propose here an approach based on the semi-classical approximation for the quantum sum-over-states expression that allows one to capture the second-order optical process from first principles. A key input is the electronic density, which can be obtained from effective single particle approaches such as density-functional theory in the local density implementation. We show that the resulting integral equations can be solved very efficiently rendering thus the treatment of macroscopic systems. As an illustration we present numerical results for the magic Na−2869 cluster.

Basic Theory of Surface Sum-Frequency Generation

A detailed description on the basic theory of optical sum-frequency generation from an interfacial system is presented. Both the interface and the bulk generally contribute to the sum-frequency output. Two seemingly different approaches to specify bulk nonlinearity that includes electric-quadrupole and magnetic-dipole contributions are shown to yield the same sum-frequency output if surface nonlinearity is properly taken into account. The question of whether surface and bulk nonlinearities can be uniquely defined and separately measured is discussed. It is shown that the answer is affirmative. Truly bulk and truly surface nonlinear susceptibilities can be uniquely defined and separately deduced from measurements of transmitted and reflected sum-frequency generation.

Second harmonic response of the Si(111)7 × 7 surface

Optical second harmonic generation spectra have been experimentally obtained from a clean Si(111) 7 × 7 in two different polarization configurations isolating the rotational anisotropic and isotropic contributions. The energy of the fundamental photon is varied from 0.8 eV to 2.5 eV. For comparison, we also use a microscopic formulation based on the semi-empirical tight binding method to evaluate the nonlinear surface susceptibility tensor χ(2 ω). Good agreement between theory and experiment is obtained with respect to the number of resonances, their position in energy, and surface or bulk character.

Isotopic Dilution Study of the Water/Vapor Interface by Phase-Sensitive Sum-Frequency Vibrational Spectroscopy

Phase-sensitive sum-frequency vibrational spectroscopy (PS-SFVS) has been used to probe the isotopically diluted water/vapor interfaces in the spectral regions of OD (2200-2800 cm(-1)) and OH (3000-3800 cm(-1)) stretches. The experimentally measured Im chiS(2) spectra, where chiS(2) is the surface nonlinear susceptibility, permit direct characterization of resonances of the interfaces. The Im chiS(2) spectrum of the HDO/vapor interface that is intrinsically simpler to analyze can be deduced from the result of isotopic dilution. It exhibits in the bonded-OH region a broad band comprising two parts with opposite signs, in contrast to those deduced earlier from fitting of the |chiS(2)|2 spectra and those calculated by MD simulation, but consistent with that obtained for the H2O/vapor interface.

Optical second-harmonic spectroscopy of Au(887) and Au(443) surfaces

In order to investigate the electronic states of step sites on Au surfaces, we have observed the reflected optical second-harmonic (SH) intensity from Au(887) and Au(443) surfaces in ultrahigh vacuum with a normal incident excitation light beam, as a function of the photon energy and the incident and SH light polarizations. The second-order surface nonlinear susceptibility elements observed in this measurement configuration were ${\ensuremath{\chi}}_{xxx}^{(2)}$, ${\ensuremath{\chi}}_{xyy}^{(2)}$, and ${\ensuremath{\chi}}_{yxy}^{(2)}$, where $x$ and $y$ are defined as the $[11\overline{2}]$ and $[\overline{1}10]$ directions, respectively. The step edges lie in the $y$ direction. The ratios of the nonlinear susceptibility elements $|{\ensuremath{\chi}}_{xyy}^{(2)}|/|{\ensuremath{\chi}}_{xxx}^{(2)}|$ and $|{\ensuremath{\chi}}_{yxy}^{(2)}|/|{\ensuremath{\chi}}_{xxx}^{(2)}|$ were different on the two surfaces in the photon energy range from $2\ensuremath{\hbar}\ensuremath{\omega}=2.5$ to 3.3 eV. The deviation of the SH response from that of an ideal $3m$ symmetric Au(111) surface was found to be larger for the Au(443) surface than for the Au(887) surface. This deviation is attributed to the atomic steps created by the miscut of the samples. In order to analyze the observed SH spectra, we calculated the electronic states of a Au(554) slab using a density-functional theory. We found that the low-energy onset of the SH intensity caused by the steps can be qualitatively interpreted by referring to the calculated partial density of the $d$-electronic states of the step and terrace atoms on the Au slab.

Analysis of surface second-harmonic generation by orientational distribution function in a chiral polymer film

By adopting classical models of molecular chirality, contributions of the coupled-oscillator and helix natures to the chiral surface second-order susceptibilities are identified through introduction of a molecular orientational distribution. Experimentally, surface orientational distribution functions at interfaces of an isotropic chiral chitosan polymer film are determined from second harmonic generation measurement. The largest chiral component of surface nonlinear optical susceptibility is from the electric-magnetic coupling with dominant contribution from the helix nature of chitosan.

Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit

The electromagnetic theory of optical second-harmonic generation from small spherical particles comprised of centrosymmetric material is presented. The interfacial region where the inversion symmetry is broken provides a source of the nonlinearity. This response is described by a general surface nonlinear susceptibility tensor for an isotropic interface. In addition, the appropriate weak bulk terms for an isotropic centrosymmetric medium are introduced. The linear optical response of the sphere and the surrounding region is assumed to be isotropic, but otherwise arbitrary. The analysis is carried out to leading order in the ratio of (a/λ), the particle radius to the wavelength of the incident light, and can be considered as the Rayleigh limit for second-harmonic generation from a sphere. Emission from the sphere arises from both induced electric dipole and electric quadrupole moments at the second-harmonic frequency. The former requires a nonlocal excitation mechanism in which the phase variation of the pump beam across the sphere is considered, while the latter is present for a local-excitation mechanism. The locally excited electric dipole term, analogous to the source for linear Rayleigh scattering, is absent for the nonlinear case because of the overall inversion symmetry of the problem. The second-harmonic field is found to scale as (a/λ)3 and to be completely determined by two effective nonlinear susceptibility coefficients formed as a prescribed combination of the surface and bulk nonlinearities. Characteristic angular and polarization selection rules resulting from the mechanism of the radiation process are presented. Various experimental aspects of the problem are examined, including the expected signal strengths and methods of determining the nonlinear susceptibilities. The spectral characteristics associated with the geometry of a small sphere are also discussed, and distinctive localized plasmon resonances are identified.

An in situ second harmonic generation study of the electrochemical oxidation of silicon in fluoride media

The electrochemical oxidation of p-type Si in fluoride solutions has been studied by in situ second harmonic generation (SHG) with the SHG signal being recorded simultaneously with the cyclic voltammogram. The SHG signal is shown to change in tandem with the electrochemical response enabling the identification of transition points between different surface conditions such as hydrogen-terminated, hydrated oxide and oxide. Interpretation of the changes in SHG suggests that the initial response is due to the electric field-induced second harmonic (EFISH) due to the electric field gradient at the interface. It then becomes dominated by the variation in the resonant surface non-linear susceptibility as the changes in local bonding affect the response. SHG signals display a much greater sensitivity to surface conditions than the voltammetric response and allow the real-time identification of the potentials at which significant changes take place in the state of the surface.