Hyperpolarizability Model Research Articles

A Novel Sensing Method to Detect Malachite Green Contaminant on Silicon Substrate Using Nonlinear Optics.

We propose a nonlinear-optics-based nanosensor to detect malachite green (MG) contaminants on semiconductor interfaces such as silicon (Si). Applying the simplified bond hyperpolarizability model (SBHM), we simplified the second-harmonic generation (SHG) analysis of an MG-Si(111) surface and were able to validate our model by reproducing experimental rotational anisotropy (RA) SHG experiments. For the first time, density functional theory (DFT) calculations using ultrasoft pseudopotentials were implemented to obtain the molecular configuration and bond vector orientation required by the SBHM to investigate and predict the second-harmonic generation contribution for an MG-Si 001 surface. We show that the SBHM model significantly reduces the number of independent components in the nonlinear tensor of the MG-Si(111) interface, opening up the possibility for real-time and non-destructive contaminant detection at the nanoscale. In addition, we derive an explicit formula for the SHG far field, demonstrating its applicability for various input polarization angles. Finally, an RASHG signal can be enhanced through a simulated photonic crystal cavity up to 4000 times for more sensitivity of detection. Our work can stimulate more exploration using nonlinear optical methods to detect and analyze surface-bound contaminants, which is beneficial for environmental monitoring, especially for mitigating pollution from textile dyes, and underscores the role of nonlinear optics in real-time ambient-condition applications.

Gas Adsorption Mechanism on 2D Materials: The Hyperpolarizability Evolution Analyzed by Nonlinear Optics

AbstractWhile understanding the competitive adsorption behavior of gas sensor is important, it is yet to be unraveled. Especially for the influence of water molecules to the gas adsorbed on 2D materials. This study explores the potential of layered 2D materials as a candidate material for gas sensing, employing non‐destructive measurement, and second harmonic generation (SHG). The investigation focuses on analyzing oxygen, ammonia, and water vapor adsorbed on a WS2 surface by studying the evolutions in electric dipole and electric field. Leveraging the simplified bond hyperpolarizability model (SBHM), a foundation is established for gas sensors utilizing high‐quality 2D materials. This approach facilitates the detection of material modifications in response to environmental influences, including the inevitable water molecules. The obtained hyperpolarizability from SBHM exhibits remarkable consistency with Langmuir's adsorption model, confirming the physical adsorption in the system. In addition, the competitive effects between gases are explored by comparing experimental results with theoretical predictions based on Boltzmann distribution and density functional theory (DFT) calculations. This highlights the effectiveness of SHG and SBHM in studying gas adsorption on layered van der Waals materials.

Second harmonic generation and simplified bond hyperpolarizability model analyses on the intermixing of Si/SiGe stacked multilayers for gate-all-around structure

Si/SiGe stacked multilayers are key elements in fabrication of gate-all-around (GAA) structures and improvement of electrical properties, with the evolution of the Si/SiGe interfaces playing a crucial role. In this work, a model is developed based on the simplified bond hyperpolarizability model (SBHM) to analysis the anisotropic reflective second harmonic generation (Ani-RSHG) on a three-period stacked Si/Si1−x Ge x multilayer, which builds on Si(100) diamond structures. The C 4v symmetry of the Si(100) structure enables the second harmonic generation (SHG) contribution from the bonds to be simplified and the effective hyperpolarizabilities of the interfacial and bulk sources to be obtained. The effective interface dipolar and bulk quadrupolar SHG hyperpolarizabilities in the Si1−x Ge x sample with various Ge concentration profiles are modeled by interpreting the concentration of a component element as the probability of the element occupying an atomic site. On the basis of the developed model, the Ani-RSHG spectra of the as-grown samples with various Ge ratios for each layer and the samples annealed at 850 °C and 950 °C are analyzed to inspect the change in Ge distribution and its gradient in depth. The ani-RSHG analysis on as-grown samples showed difference in Ge distribution in samples with the multi Si/SiGe structure, which is not well observed in synchrotron x-ray diffraction (XRD) spectra. For the annealed samples, the response to changes in Ge concentration and its gradient in depth reveal the Si/Si1−x Ge x interface intermixing. Results of high-angle annular dark-field scanning transmission electron microscopy and energy dispersive x-ray spectroscopy agree well with the Ani-RSHG with SBHM findings. Compared with the Raman and synchrotron XRD spectra, the Ani-RSHG with SBHM simulation result demonstrates much better response to changes in compositions of the Si/Si1−x Ge x stacked multilayered structures, verifying the potential for characterizing the concentration distribution in stacked multilayered thin films for GAA structures.

Quo Vadis Nonlinear Optics? An Alternative and Simple Approach to Third Rank Tensors in Semiconductors

It is well understood that nonlinear optical (NLO) phenomena are deeply related to the material’s symmetry. Mathematically, the material symmetry can be described in terms of the nonzero parameters in the nonlinear susceptibility tensors. Generally, more complex structures involve more nonzero parameters in the tensor. The number of parameters increases rapidly if higher NLO orders are considered, complicating the physical analysis. Conventionally, these parameters are obtained via abstract symmetry analysis, e.g., group theory (GT). This work presents a novel theoretical analysis to approach the nonlinear tensor using the simplified bond hyperpolarizability model (SBHM) and compare it with GT. Our analysis is based on a light–matter interaction classical phenomenological physical framework. Rather than just looking at the symmetry of the crystal, the model applies physical considerations requiring fewer independent parameters in the tensor than GT. Such a simplification significantly improves the determination of the surface–bulk SHG contribution factors, which cannot be extracted from the experiment alone. We also show for the case of perovskite that the SHG contribution can be addressed solely from their surface dipoles with only one independent component in the tensor. Therefore, this work may open the path for a similar analysis in other complicated semiconductor surfaces and structures in the future, with potential applications to nanoscale surface characterization and real-time surface deposition monitoring.

Generation, reflection and transmission of nonlinear harmonic waves by direct superposition of anharmonic dipoles

It is well known that the linear and nonlinear light reflection and transmission formula can be obtained from the standard macroscopic Maxwell equation. In the past, a microscopic approach based on the Ewald–Oseen extinction theorem to derive the reflection and transmission formula by direct dipole summation has been performed by Fearn et al where they successfully derived the Fresnel formula in linear optics. In this work, we extend their work for the first time to derive the nonlinear reflection and transmission formula by direct summation of anharmonically oscillating dipoles for the case of a normal incidence wave, yielding similar results with coupled-mode-theory (CMT). We demonstrate for a decaying incoming field that dipolar radiation is no longer forbidden inside the bulk of a centrosymmetric material. Using the simplified bond hyperpolarizability model (SBHM), we find that these additional bulk dipole contribution must be accounted along with the surface dipoles and bulk quadrupolar contribution to explain recent rotational anisotropy SHG intensity experimental data of Si(111) with high precision.

Bond model of second-harmonic generation in wurtzite ZnO(0002) structures with twin boundaries

We describe second-harmonic generation (SHG) in ZnO(0002) wurtzite structures with [11¯00]/(1102) twin boundaries using the simplified bond hyperpolarizability model (SBHM). We show explicitly how the reflective second-harmonic generation (RSHG) intensity profile for the s-incoming fundamental and s-outgoing SHG polarized light arise via superposition of the SHG dipole fields. The nonlinear fields originate from anharmonic motions of electric charges along each bond. The total dipole fields from within the ZnO bulk sum up to zero but produce a constructive SHG radiation from the unreduced surface and twin boundary. In addition, we compare the third-order susceptibility tensor obtained from group theory and the SBHM and calculate the values for the nonzero components. We found that the off-resonance RSHG intensity data in diatomic wurtzite structures even with the presence of twin boundaries can be modeled using only three independent fitting parameters, namely, the effective bulk, reduced surface, and twin boundary SHG hyperpolarizability. The results show that the SBHM can be used to investigate impurities and surface defects in ZnO as well as their contribution to nonlinear radiation with potential application to frequency conversion in nanoscale optical circuitry.

Third harmonic generation in ZnO semiconductor using the simplified bond hyperpolarizability model

We describe the fourth rank tensor and the related third harmonic generation (THG) light intensity profile in a (0002) wurtzite structure using the simplified bond hyperpolarizability model (SBHM). We show that the resulting THG intensity is isotropic e.g., does not depend on the azimuthal rotation angle of the material. Assuming that THG inside wurtzite structures are dominated solely by bulk dipoles, only one fitting parameter in terms of the effective THG hyperpolarizability is required to generate the Rotational Anisotropy THG (RATHG) experiment result.

Bulk quadrupole contribution to second harmonic generation from classical oscillator model in silicon.

We predict the frequency-dependent bulk quadrupole contribution to second harmonic generation in silicon quantitatively from the linear susceptibility by means of a generalized classical anharmonic oscillator model and the simplified bond hyperpolarizability model. We show that in single-beam setups the main contribution is found for the silicon (111) surface, and only a minor contribution for the (001) and (011) facets. The dipole contribution obtained from our model is compared to literature values for SiC, AlAs and GaAs to demonstrate the viability of the method.

Nonlinear ellipsometry of Si(111) by second harmonic generation

In this paper we present experimental and simulated data of the second harmonic response for arbitrarily oriented linear input polarization and output polarization on Si(111) surfaces. In contrast to other nonlinear optical ellipsometry experiments (e.g. nonlinear optical null ellipsometry) we azimuthally rotate the sample for additional analysis of the crystal structure. In our study, we used the simplified bond hyperpolarizability model (SBHM) to simulate the observed angular shifts of the nonlinear peaks and the change of symmetry features related to a modification of the beam polarizations. Our findings help to identify the corresponding interface dipolar and bulk quadrupolar SHG sources.

Bulk quadrupole and interface dipole contribution for second harmonic generation in Si(111)

The second harmonic generation (SHG) response was measured for arbitrarily oriented linear input polarization on Si(111) surfaces in rotational anisotropy experiments. We show for the first time, using the simplified bond hyperpolarizability model (SBHM), that the observed angular shifts of the nonlinear peaks and symmetry features—related to changes in the input polarization—help to identify the corresponding interface dipolar and bulk quadrupolar SHG sources, yielding excellent agreement with the experiment. Additionally, we evaluate for the s-in/p-out (sp) and p-in/p-out (pp)-polarization SHG intensities the contributions from the individual Si bonds. Furthermore, a relation between the four parameters arising from SBHM and six coefficients of the phenomenological SHG theory needed to reproduce experimental data is established.

Bulk dipolar contribution to second-harmonic generation in zincblende

We present a comprehensive analysis of second-harmonic generation (SHG) in a diatomic zincblende crystal based on the simplified bond hyperpolarizability model (SBHM) and compare the result with two rotational anisotropy (RA)SHG experiments on a nonvicinal zincblende lattice. We show that bulk dipolar sources alone are sufficient to describe the experimental data by implementing the SBHM previously applied for silicon surfaces to bulk lattices containing two different atoms, e.g., Ga and As. It is shown that a second-rank tensor for a Td point group has only one independent component and this tensor is equivalent to the one derived by the SBHM model using an effective bulk hyperpolarizability αGaAs=(αGa−αAs). In addition, SBHM gives an excellent fit with the RA-SHG experiments of GaAs using a single fitting parameter if Fresnel transmission factors are also incorporated in the model, suggesting strongly that bulk dipolar contribution is the dominant SHG source in a zincblende lattice.

The role of Kleinman Symmetry in the Simplified Bond Hyperpolarizability Model

We have shown previously in [J. Opt. Soc. Am. 31, 526-533 (2014)] that Kleinman symmetry plays an important role when comparing the third rank tensor associated with Second Harmonic Generation (SHG) obtained from the Simplified Bond Hyperpolarizability Model (SBHM) and from group theory (GT) for diamond and zincblende lattice. In this work we show that the third rank tensor derived from the SBHM has inherently the assumption of Kleinman symmetry.

Model of third harmonic generation and electric field induced optical second harmonic using simplified bond-hyperpolarizability model

We report for the first time a comprehensive study of the fourth rank tensor describing third harmonic generation (THG) and electric field induced second harmonic (EFISH) in centrosymmetric material from two different viewpoints: Group Theory (GT) and the Simplified Bond Hyperpolarizability Model (SBHM). We show that the fourth rank tensor related to THG and direct current (DC) EFISH can be reduced to two independent elements whereas SBHM always gives only one, reproducing perfectly well EFISH experimental results in Metal Oxyde Semiconductor (MOS). We argue that it is possible to reduce the fourth rank tensor describing EFISH to a third rank tensor and further deliver a classical explanation of EFISH regarding symmetry breaking where the term containing $r^3$ in the potential immediately leads to second harmonic generation (SHG).

Time Correlation Function Modeling of Third-Order Sum Frequency Vibrational Spectroscopy of a Charged Surface/Water Interface.

Sum frequency vibrational spectroscopy (SFVS), a second-order optical process, is interface-specific in the dipole approximation [Perry, A.; Neipert, C.; Moore, P.; Space, B. Chem. Rev. 2006, 106, 1234-1258; Richmond, G. L. Chem. Rev. 2002, 102, 2693-2724; Byrnes, S. J.; Geissler, P. L.; Shen, Y. R. Chem. Phys. Lett. 2011, 516, 115-124]. At charged interfaces, the experimentally detected signal is a combination of enhanced second-order and static-field-induced third-order contributions due to the existence of a static field. Evidence of the importance/relative magnitude of this third-order contribution is seen in the literature [Ong, S.; Zhao, X.; Eisenthal, K. B. Chem. Phys. Lett. 1992, 191, 327-335; Zhao, X.; Ong, S.; Eisenthal, K. B. Chem. Phys. Lett. 1993, 202, 513-520; Shen, Y. R. Appl. Phys. B: Laser Opt. 1999, 68, 295-300], but a molecularly detailed approach to separately calculating the second- and third-order contributions is difficult to construct. Recent work presented a novel molecular dynamics (MD)-based theory that provides a direct means to calculate the third-order contributions to SFVS spectra at charged interfaces [Neipert, C.; Space, B. J. Chem. Phys. 2006, 125, 224706], and a hyperpolarizability model for water was developed as a prerequisite to practical implementation [Neipert, C.; Space, B. Comput. Lett. 2007, 3, 431-440]. Here, these methods are applied to a highly abstracted/idealized silica/water interface, and the results are compared to experimental data for water at a fused quartz surface. The results suggest that such spectra have some quite general spectral features.

Photoswitching of the Second Harmonic Generation from Poled Phenyl-Substituted Dithienylethene Thin Films and EFISH Measurements

The photoswitching of the second harmonic generation signal of poled phenyl-substituted dithienylethene/polystyrene thin films evidence a different behavior in function by their molecular structure. The three nonzero χXXZ(2), χZXX(2), and χZZZ(2) coefficients of second order susceptibility at 1064 nm have been measured for both isomeric forms of substituted diarylethene in polymer films. The relationship between χXXZ(2), χZXX(2), and χZZZ(2) for symmetrical diarylethene (OMe–OMe and CN–CN) differs from that found for the asymmetrical OMe–CN chromophore, suggesting for the two symmetrically substituted molecules a two-dimensional first hyperpolarizability. The two-dimensional first hyperpolarizability model has been checked by a statistical analysis from the correlation between susceptibility and first hyperpolarizability. Analysis of βxxz, βzxx, and βzzz values confirm for OMe–OMe and CN–CN a two-dimensional charge flow pattern, which is different from the monodimensional OMe–CN. Moreover, the goodness of...

Optical second‐harmonic and reflectance‐anisotropy spectroscopy of molecular adsorption at Si(001) step‐edges

AbstractReflectance‐anisotropy spectroscopy (RAS) and spectroscopic second harmonic generation (SHG) are used to probe a single‐domain reconstructed stepped Si(001) surface offcut 6° toward [110] before and after dissociative adsorption of H2 at the DB step edges. Preliminary analysis with a simplified bond hyperpolarizability model supports the mutual consistency of RA and SHG spectra and suggests that hydrogen termination redistributes oscillator strength from the chemically active step dangling bond into the step back bonds. The data provide a benchmark for first‐principles calculations of the optical response of stepped Si surfaces to step edge molecular adsorption. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A Distributed Hyperpolarizability Model for Liquid Water

In a recent work a novel, molecular dynamics (MD) based, theory was presented that provides a direct means to calculate the third order contributions to sum frequency vibrational spectroscopy (SFVS) at charged interfaces.[1] This contribution is described by a time correlation function (TCF) of the system's total hyperpolarizability (β) and dipole. A system's hyperpolarizability[2, 3, 4, 5] is difficult to calculate on the fly – no appropriate non-electronic structure (ES) techniques exist. In this work, such a model is developed for liquid water based on a formalism proposed previously.[1] The model is parametrized from and tested against, ab initio ES calculations. It was found that it is possible to reproduce the hyperpolarizability tensor of a gas phase water molecule and a water dimer accurately. Also, most relevant components of the hyperpolarizability derivative tensor of both the water and water dimer were also accurately fit, however, some elements were not able to be simultaneously reproduced. The model was also tested to assess whether or not it could reproduce the three non-zero condensed phase water hyperpolarizability tensor components. It was found that the model could capture two of the three relevant components.

Second-harmonic and reflectance-anisotropy spectroscopy of vicinalSi(001)∕SiO2interfaces: Experiment and simplified microscopic model

We directly compare experimental second-harmonic generation (SHG) spectra and reflectance-anisotropy spectra (RAS) of native-oxidized vicinal Si(001) interfaces with off-cut angles $\ensuremath{\zeta}=0\ifmmode^\circ\else\textdegree\fi{}$, 4\ifmmode^\circ\else\textdegree\fi{}, 6\ifmmode^\circ\else\textdegree\fi{}, 8\ifmmode^\circ\else\textdegree\fi{}, and 10\ifmmode^\circ\else\textdegree\fi{} from (001) toward [110]. We fit the measured azimuthal rotational-dependence of $p$-in/$p$-out SHG at two-photon energies $2.8\phantom{\rule{0.3em}{0ex}}\mathrm{eV}l\ensuremath{\hbar}\ensuremath{\omega}l3.5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ including the ${E}_{1}$ critical point resonance using a simplified bond hyperpolarizability model. The model includes dipolar contributions from tetrahedrally coordinated interfacial bonds as well as quadrupolar contributions from the Si bulk. The fit yields complex axial hyperpolarizability spectra ${\ensuremath{\beta}}_{\ensuremath{\Vert},\ensuremath{\Vert},\ensuremath{\Vert}}(2\ensuremath{\omega})$ and averaged bond angles of the interfacial back-edge, terrace-edge and step-edge bonds, and bulk quadrupolar hyperpolarizability ${\ensuremath{\delta}}_{\ensuremath{\Vert},\ensuremath{\Vert},\ensuremath{\Vert}}(2\ensuremath{\omega})$. The fitted microscopic model accurately reproduces measured $s$-in/$p$-out SHG spectra. We then used a Miller's rule approximation to generate axial linear polarizability spectra ${\ensuremath{\alpha}}_{\ensuremath{\Vert}}(\ensuremath{\omega})$ from the fitted ${\ensuremath{\beta}}_{\ensuremath{\Vert},\ensuremath{\Vert},\ensuremath{\Vert}}(2\ensuremath{\omega})$. The measured RAS was satisfactorily reproduced within the same photon energy range. Including the bulk quadrupole contribution to SHG was crucial to accurately retrieving the RAS and to achieving fitted real and imaginary $\ensuremath{\beta}(2\ensuremath{\omega})$ spectra consistent with a nonlinear Kramers-Kronig relation. The results demonstrate the possibility of formulating a common microscopic model of SHG and RAS responses of complicated interfaces.

Simplified bond model of spectroscopic SHG and RAS of oxidized and reconstructed vicinal Si(001)

A direct experimental comparison of reflectance-anisotropy spectra (RAS) and spectroscopic second harmonic generation (SHG) of both native-oxidized and clean, reconstructed vicinal Si(001) surfaces is presented. SHG rotational anisotropy over the 2-photon energy range 2.75 < hν SH < 3.44 eV is analyzed using a simplified bond hyperpolarizability model, yielding empirically fitted complex hyperpolarizability spectra β (2ω ) of step-edge, terrace- and back-bonds. Linear bond polarizabilities α (2ω ) were then derived from β (2ω ) using a simple oscillator model. Measured RAS was successfully reproduced with these α (2ω ) for all surfaces studied. The results demonstrate a simple empirical approach for accessing the common microscopic origin of RAS and SHG. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Calculation of bulk third-harmonic generation from crystalline Si with the simplified bond hyperpolarizability model

Calculation of bulk third-harmonic generation from crystalline Si with the simplified bond hyperpolarizability model