Order Susceptibility Tensor Research Articles

Bond model of second harmonic generation in tetragonal and orthorhombic perovskite structures

We apply the simplified-bond-hyperpolarizability model (SBHM) to investigate second harmonic generation (SHG) from tetragonal and orthorhombic methylammonium (MA) lead (Pb) iodide (I) perovskite structures. Assuming that the SHG radiation comes from the anharmonic charges parallel to the Pb-I covalent bond vectors, we show explicitly how the reflective rotational anysotropy SHG (RASHG) intensity profiles arise via dipole superposition from the perovskite surface and that their bulk contribution is zero for both the tetragonal and orthorhombic bulk structures if the contribution from MA molecules can be neglected. In addition, we compare the third order susceptibility tensor obtained from group theory and SBHM and calculate the values for the nonzero components as well as derive the SHG intensity field formulas. We found that the tetragonal and orthorhombic perovskite SHG intensity profiles are different. Furthermore, our results show that even in relative complex systems such as metal halide perovskites (MHPs), RASHG experimental data can be fitted using only one independent fitting parameter, which is the effective Pb-I nonlinear hyperpolarizability. Therefore, the analysis of perovskite using an anharmonic bond model can lead to better efficiencies of photovoltaic devices, while it will also pave a way for the use of SHG in MHP crystals as frequency conversion and optical signal processing.

Generalized relation between electromechanical responses at fixed voltage and fixed electric field

We present a general relation between the electromechanical couplings of infinitesimal strain and electric field to arbitrary order, measured at fixed voltage and at fixed electric field. We show that the improper response at fixed field can be written as the strain derivative of the $n^{\text{th}}$ order susceptibility tensor, and the proper response at fixed voltage drop can be written as the response at fixed field plus corrections for dilations and 90$^{\circ}$ rotations induced by strain. Our theory correctly reproduces the proper piezoelectric response and we go beyond with the electrostrictive response. We present first-principles calculations of the improper electrostrictive response at fixed field, and illustrate how the correction is used to obtain the proper response at fixed voltage. This distinction is of high importance given the recent interest in giant electrostrictors exhibiting electromechanical responses as large as the piezoelectric ones.

Influence of hematoxylin and eosin staining on the quantitative analysis of second harmonic generation imaging of fixed tissue sections.

Second harmonic generation (SHG) microscopy has emerged over the past two decades as a powerful tool for tissue characterization and diagnostics. Its main applications in medicine are related to mapping the collagen architecture of in-vivo, ex-vivo and fixed tissues based on endogenous contrast. In this work we present how H&E staining of excised and fixed tissues influences the extraction and use of image parameters specific to polarization-resolved SHG (PSHG) microscopy, which are known to provide quantitative information on the collagen structure and organization. We employ a theoretical collagen model for fitting the experimental PSHG datasets to obtain the second order susceptibility tensor elements ratios and the fitting efficiency. Furthermore, the second harmonic intensity acquired under circular polarization is investigated. The evolution of these parameters in both forward- and backward-collected SHG are computed for both H&E-stained and unstained tissue sections. Consistent modifications are observed between the two cases in terms of the fitting efficiency and the second harmonic intensity. This suggests that similar quantitative analysis workflows applied to PSHG images collected on stained and unstained tissues could yield different results, and hence affect the diagnostic accuracy.

Anisotropic PCL nanofibers embedded with nonlinear nanocrystals as strong generators of polarized second harmonic light and piezoelectric currents.

Using the electrospinning technique nanofibers consisting of organic nonlinear optical 3-nitroaniline (3NA, C6H6N2O2) nanocrystals embedded in poly-ε-caprolactone (PCL) polymer, 3NA@PCL nanofibers, were produced. Polarimetry optical second harmonic generation and X-ray diffraction studies show that 3NA push–pull molecules crystallize inside the polymer fibers with a strong preferential orientation giving rise to an alignment of the molecular dipole moments along the nanofibers longitudinal axis. This alignment strongly enhances the second order nonlinear optical response of the fibers. Intense second harmonic generation emission was observed from a single nanofiber, corresponding to an effective second order susceptibility of 80 pm V−1, four times greater than the largest second order susceptibility tensor element (21 pm V−1) associated with a macroscopic 3NA crystal. Moreover, when subjected to a modest periodically applied force of 3 N, a piezoelectric current of 70 nA generated by a 4 cm2 electrospun nanofiber mat amounted to 122 nW cm−2 of instantaneous density power, sufficient to power a LCD display. The results show that the electrospinning technique is a powerful technique to fabricate organic functional materials with oriented nanocrystals made of highly polarizable molecules, embedded in a polymer matrix.

Measurement of wavelength-dependent second order susceptibility tensor elements in types I and II collagens

In this work, we measured the second order susceptibility (SOS) tensor ratios of χzzz/χzxx and χxzx/χzxx between 725–875 nm in type I (rat tail tendon) and II (rat trachea) collagen. In this wavelength range, χzzz/χzxx and χxzx/χzxx were found to be frequency-independent. Specifically, χzzz/χzxx and χxzx/χzxx are around 1.4 and 0.7 for collagen I; 1.2 and 0.4 for collagen II, respectively. Therefore, the near-infrared wavelength range of 700–800 nm is sufficiently far from the collagen resonance at 247 nm in order for the SOS tensor ratios to be wavelength independent. Our results suggest that microscopy imaging based on the use of SOS as a contract mechanism can use the simultaneous illumination of different excitation wavelengths with different polarizations for faster implementation of second order susceptibility microscopy.

Depth-Dependent Three-Layer Model for the Surface Second-Harmonic Generation Yield

We present a generalization of the three-layer model to calculate the surface second harmonic generation (SSGH) yield, that includes the depth dependence of the surface nonlinear second order susceptibility tensor $\boldsymbol{\chi}(-2\omega;\omega,\omega)$. This model considers that the surface is represented by three regions or layers. The first layer is a semi-infinite vacuum region with a dielectric function $\epsilon_{v}(\omega)=1$, from where the fundamental electric field impinges on the material. The second layer is a thin layer ($\ell$) of thickness $d$ characterized by a dielectric function $\epsilon_{\ell}(\omega)$, and it is in this layer where the SSHG takes place. We consider the position of $\boldsymbol{\chi}(-2\omega;\omega,\omega)$ within this surface layer. The third layer is the bulk region denoted by $b$ and characterized by $\epsilon_{b}(\omega)$. We include the effects caused by the multiple reflections of both the fundamental and the second-harmonic (SH) fields that take place within the thin layer $\ell$. {\color{red} As a test case, we calculate $\boldsymbol{\chi}(-2\omega;\omega,\omega)$ for the Si(111)(1$\times$1):H surface, and present a layer-by-layer study of the susceptibility to elucidate the depth dependence of the SHG spectrum. We then use the depth dependent three-layer model to calculate the SSHG yield, and contrast the calculated spectra with experimental data. We produce improved results over previous published work, as this treatment can reproduce key spectral features, is computationally viable for many systems, and most importantly remains completely \emph{ab initio}.

Analysis of the second harmonic generation signal from a liquid/air and liquid/liquid interface.

Three different liquid interfaces, water/air, thiophene/air, and water/thiophene, were probed using the second harmonic generation (SHG) technique. Thiophene and water have been chosen because the hyperpolarizability of these molecules has already been measured or calculated and the different values can be found in literature. We have studied the microscopic structure of these interfaces by comparing the components of the second order susceptibility tensor determined from the SHG polarization curve analysis with those determined via a molecular dynamics (MD) simulation of these interfaces. We have indeed computed the structure and orientation of water and thiophene molecules at the liquid/air and liquid/liquid (L/L) interfaces as a function of the distance from the interface. The integrated susceptibility values calculated by MD simulations agree well with SHG results and validate the choice of force fields that should permit to quantify more complex L/L interfaces.

Modeling of strain-induced Pockels effect in Silicon.

We propose a theoretical model to describe the strain-induced linear electro-optic (Pockels) effect in centro-symmetric crystals. The general formulation is presented and the specific case of the strained silicon is investigated in detail because of its attractive properties for integrated optics. The outcome of this analysis is a linear relation between the second order susceptibility tensor and the strain gradient tensor, depending generically on fifteen coefficients. The proposed model greatly simplifies the description of the electro-optic effect in strained silicon waveguides, providing a powerful and effective tool for design and optimization of optical devices.

Effects of surface plasmon polariton-mediated interactions on second harmonic generation from assemblies of pyramidal metallic nano-cavities.

We use polarization-resolved two-photon microscopy to investigate second harmonic generation (SHG) from individual assemblies of site-controlled nano-pyramidal recess templates covered with silver films. We demonstrate the effect of the surface plasmon polaritons (SPPs) at fundamental and second-harmonic frequencies on the effective second order susceptibility tensor as a function of pyramid arrangement and inter-pyramid distance. These results open new perspectives for the application of SHG microscopy as a sensitive probe of coherently excited SPPs, as well as for the design of new plasmonic nanostructure assemblies with tailored nonlinear optical properties.

Acentric Nonlinear Optical 2,4-Dihydroxyl Hydrazone Isomorphic Crystals with Large Linear, Nonlinear Optical Susceptibilities and Hyperpolarizability

A systematic ab initio study of the linear, nonlinear optical susceptibilities, and hyperpolarizability of noncentrosymmetric-monoclinic 2,4-dihydroxyl hydrazone isomorphic crystals (DHNPH) within density functional theory in the local density approximation (LDA), general gradient approximation (GGA), the Engel-Vosko generalized gradient approximation (EV-GGA) and modified Becke-Johnson potential (mBJ) has been performed. The complex dielectric susceptibility dispersion, its zero-frequency limit and the birefringence are studied. Using scissors’ corrected mBJ we find a large uniaxial dielectric anisotropy (-0.56) resulting in a significant birefringence (0.61). We also find that 2,4- DHNPH possess large second harmonic generation. The calculated second order susceptibility tensor components for the static limit |χ(111)(2)(0)| and |χ(111)(2)(ω)| at λ=1.9 μm (0.651 eV) and at λ = 1.064 μm (1.165 eV) are 53, 91, and 209 pm/V, respectively. A remarkable finding, applying the scissors’ correction has a profound effect on value, magnitude and sign of χ(ijk)(2)(ω). In additional we have calculated the microscopic hyperpolarizability, β(111), vector component along the principal dipole moment directions for the dominant component. We find that the value of β(111) equal to 47× 10(-30) esu, in good agreement with the measured value (48.2× 10(-30) esu).

Nonlinear optical properties of TeO2crystalline phases from first principles

We have computed second and third nonlinear optical susceptibilities of two crystalline bulk tellurium oxide polymorphs: $\alpha$-TeO$_{2}$ (the most stable crystalline bulk phase) and $\gamma$-TeO$_{2}$ (the crystalline phase that ressembles the more to the glass phase. Third order nonlinear susceptibilities of the crystalline phases are two orders of magnitude larger than $\alpha$-SiO$_{2}$ cristoballite, thus extending the experimental observations on glasses to the case of crystalline compounds. While the electronic lone pairs of Te contribute to those large values, a full explanation of the anisotropy of the third order susceptibility tensor requires a detailed analysis of the structure, in particular the presence of helical chains, that seems to be linked to cooperative non-local polarizabilty effects. Our results demonstrate that first-principles simulations are a powerful predictive tool to estimate nonlinear optical susceptibilitites of materials.

Nonlinear optical spectroscopy of isotropic and anisotropic metallic nanocomposites

In this work, we studied the nonlinear absorption and refraction of isotropic and anisotropic metallic nanocomposites, which consist of Au and Ag nanoparticles (NPs) embedded in matrices of SiO2. We performed this study at different wavelengths using the Z-scan technique in the picosecond regime. The wavelengths were selected accordingly to the absorption spectra of the nanocomposites, choosing wavelengths into the inter- and intra-band transitions regions, including the surface plasmon (SP) resonance, as well as in the transparent region. For the anisotropic nanocomposites, the polarization and the incident angle were varied in order to evaluate the different components of the third order susceptibility tensor, χ(3). We observed dramatic changes of sign for both, nonlinear refraction and absorption, when passing from Au to Ag and/or varying the wave length. The results accentuate the importance of the hot-electrons contribution to the nonlinear optical response at this temporal regime, when compared to inter-band and intra-band transitions contributions.

Dispersion of linear and non-linear optical susceptibilities for amino acid 2-aminopropanoic CH3CH(NH2)COOH single crystals: experimental and theoretical investigations

A comprehensive experimental and theoretical investigation of dispersion of the linear and nonlinear optical susceptibilities for amino acidL-alanine single crystals is reported. The state-of-the-art full potential linear augmented plane wave method, within a framework of the density functional theory was applied. The atomic positions from X-ray diffraction have been optimized so that the force on each atom is around 1 mRy au−1. This relaxed geometry has been used for the theoretical calculations. The complex dielectric susceptibility dispersion, its zero-frequency limit and the birefringence of amino acidL-alanine single crystals were studied. The crystal exhibits a large uniaxial dielectric anisotropy resulting in a significant birefringence. The calculated birefringence at static limit is 0.072 and 0.074 at λ = 1064 nm (corresponding to 1.165 eV) in good agreement with the measured value (0.073). We also report calculations of the complex second-order optical susceptibility dispersions for the principal tensor components: χ(2)123(ω), χ(2)231(ω) and χ(2)312(ω). The calculated second order susceptibility tensor components |χ(2)123(ω)|, |χ(2)231(ω)|, and |χ(2)312(ω)| at λ = 1064 nm are compared with those obtained from our measurements performed using the 25 ps Nd:YAG pulsed laser at λ = 1064 nm. Our calculations are in reasonably good agreement with our experimental data. In addition we have calculated the microscopic second order hyperpolarizability, β123, vector component along the principal dipole moment directions for the dominant component χ(2)123(ω) and it is found to be 0.21 × 10−21 pm V−1 in the static limit and 0.27 × 10−21 pm V−1 at 1.165 eV (λ = 1064 nm) in comparison with our measured value (0.31 × 10−21 pm V−1) at λ = 1064 nm. Additional study of the second order susceptibilities versus the external laser treatment is performed.

Dispersion of linear and nonlinear optical susceptibilities and the hyperpolarizability of 3-methyl-4-phenyl-5-(2-pyridyl)-1,2,4-triazole

As a starting point for our calculation of 3-methyl-4-phenyl-5-(2-pyridyl)-1,2,4-triazole we used the XRD data obtained by C. Liu, Z. Wang, H. Xiao, Y. Lan, X. Li, S. Wang, Jie Tang, Z. Chen, J. Chem. Crystallogr., 2009 39 881. The structure was optimized by minimization of the forces acting on the atoms keeping the lattice parameters fixed with the experimental values. Using the relaxed geometry we have performed a comprehensive theoretical investigation of dispersion of the linear and nonlinear optical susceptibilities of 3-methyl-4-phenyl-5-(2-pyridyl)-1,2,4-triazole using the full potential linear augmented plane wave method. The local density approximation by Ceperley-Alder (CA) exchange-correlation potential was applied. The full potential calculations show that this material possesses a direct energy gap of 3.4 eV for the original experimental structure and 3.2 eV for the optimized structure. We have calculated the complex's dielectric susceptibility ε(ω) dispersion, its zero-frequency limit ε(1)(0) and the birefringence. We find that a 3-methyl-4-phenyl-5-(2-pyridyl)-1,2,4-triazole crystal possesses a negative birefringence at the low-frequency limit Δn(0) which is equal to about -0.182 (-0.192) and at λ = 1064 nm is -0.193 (-0.21) for the non-optimized structure (optimized one), respectively. We also report calculations of the complex second-order optical susceptibility dispersions for the principal tensor components: χ(ω), χ(ω) and χ(ω). The intra- and inter-band contributions to these susceptibilities are evaluated. The calculated total second order susceptibility tensor components at the low-frequency limit |χ(0)| and |χ(ω)| at λ = 1064 nm for all the three tensor components are evaluated. We established that the calculated microscopic second order hyperpolarizability, β(ijk), the vector component along the dipole moment direction, at the low-frequency limit and at λ = 1064 nm, for the dominant component |χ(ω)| is 4.99 × 10(-30) esu (3.4 × 10(-30) esu) and 7.72 × 10(-30) esu (5.1 × 10(-30) esu), respectively for the non-optimized structure (optimized structure).

Investigation of the Linear and Nonlinear Optical Susceptibilities of KTiOPO4 Single Crystals: Theory and Experiment

Experimental and theoretical studies of the linear and nonlinear optical susceptibilities for single crystals of potassium titanyl phosphate KTiOPO₄ are reported. The state-of-the-art full potential linear augmented plane wave method, based on the density functional theory, was applied for the theoretical investigation. The calculated direct energy band gap at Γ, using the Engel-Vosko exchange correlation functional, is found to be 3.1 eV. This is in excellent agreement with the band gap obtained from the experimental optical absorption spectra (3.2 eV). We have calculated the complex dielectric susceptibility ε(ω)dispersion, its zero-frequency limit ε₁(0) and the birefringence of KTiOPO₄. The calculated birefringence at the zero-frequency limit Δn(0) is equal to about 0.07 and Δn(ω) at 1.165 eV (λ = 1064 nm) is 0.074. We also report calculations of the complex second-order optical susceptibility dispersions for the principal tensor components: χ₁₁₃((2))(ω), χ₂₃₂((2))(ω), χ₃₁₁((2))(ω), χ₃₂₂((2))(ω), and χ₃₃₃((2))(ω). The intra- and interband contributions to these susceptibilities are evaluated. The calculated total second order susceptibility tensor components |χ(ijk)((2))(ω)| at λ = 1064 nm for all the five tensor components are compared with those obtained from our measurements performed by nanosecond Nd:YAG laser at the fundamental wavelength (λ = 1064 nm). Our calculations show reasonably good agreement with our experimental nonlinear optical data and the results obtained by other authors. The calculated the microscopic second order hyperpolarizability, β₃₃₃, vector component along the dipole moment direction for the dominant component χ₃₃₃((2))(ω) is found to be 31.6 × 10⁻³⁰ esu, at λ = 1064 nm.

Mach–Zehnder interferometry method for decoupling electro-optic and piezoelectric effects in poled polymer films

A Mach–Zehnder interferometer (MZI) is utilized to decouple the electro-optic and piezoelectric tensor effects occurring in a poled polymer film. This method has significant advantages over the commonly used Teng-Man reflection ellipsometry technique by allowing for the independent determination of the Pockel’s coefficients r13 and r33 and the piezoelectric coefficient d33. The r33 value of a guest host polymer that consists of AJLZ53 amorphous polycarbonate was found to be 122.69 pm/V and 123.03 pm/V using the MZI and reflection ellipsometry method, respectively. The r33 data fits well to the dispersion of the second order susceptibility tensor based on the two-level model approximation.

Bent-core liquid crystals in a route to efficient organic nonlinear optical materials

The design, synthesis and nonlinear optical (NLO) response of some bent compounds, at both the molecular and macroscopic level, are reported. Based on a bent-core NLO-phore with a μβ0 in the range of 390 × 10−48 esu (1907 nm), the second order susceptibility tensor for second harmonic generation is evaluated at excitation wavelengths of 1064 and 1600 nm in a mesogenic material with a SmCP mesophase. The NLO coefficients are in the range 10–100 pm V−1. Thus it is deduced that a molecular design leading to bent-core liquid crystals with large β values is a correct strategy to achieve NLO-materials for bulk second order effects.

Anisotropic linear and nonlinear optical properties from anisotropy-controlled metallic nanocomposites

High-energy metallic ions were implanted in silica matrices, obtaining spherical-like metallic nanoparticles (NPs) after a proper thermal treatment. These NPs were then deformed by irradiation with Si ions, obtaining an anisotropic metallic nanocomposite. An average large birefringence of 0.06 was measured for these materials in the 300-800 nm region. Besides, their third order nonlinear optical response was measured using self-diffraction and P-scan techniques at 532 nm with 26 ps pulses. By adjusting the incident light's polarization and the angular position of the nanocomposite, the measurements could be directly related to, at least, two of the three linear independent components of its third order susceptibility tensor, finding a large, but anisotropic, response of around 10(-7) esu with respect to other isotropic metallic systems. For the nonlinear optical absorption, we were able to shift from saturable to reverse saturable absorption depending on probing the Au NP's major or minor axes, respectively. This fact could be related to local field calculations and NP's electronic properties. For the nonlinear optical refraction, we passed from self-focusing to self-defocusing, when changing from Ag to Au.

Discrimination of collagen in normal and pathological skin dermis through second-order susceptibility microscopy

Polarization-resolved, second harmonic generation (P-SHG) microscopy at single pixel resolution is utilized for medical diagnosis of pathological skin dermis. In analyzing the large area, pixel by pixel, second-order susceptibility of normal and pathological skin dermis, we found that P-SHG can be used to distinguish normal and dermal pathological conditions of keloid, morphea, and dermal elastolysis. Specifically, we found that the second order susceptibility tensor ratio of d(33)/d(31) for normal skins is 1.27+/-0.20, while the corresponding values for keloid, morphea, and dermal elastolysis are respectively 1.67+/-0.29, 1.79+/-0.30, and 1.75+/-0.31. We also found that the histograms of the d(33)/d(31) ratio for the pathological skins contain two peak values and are 1.5 times wider than that of the normal case, suggesting that the pathological dermal collagen fibers tend to be more structurally heterogeneous. Our work demonstrates that pixel-resolved, second-order susceptibility microscopy is effective for detecting heterogeneity in spatial distribution of collagen fibers and maybe used for future clinical diagnosis and in vivo studies of collagen pathological conditions.

Field-induced non-linear optical features of p-aminoazobenzene crystals

Using ethanol as a solvent p -aminoazobenzene ( p -AAZB), an organic nonlinear optical crystal having good optical quality was grown by slow evaporation solution technique. Structural and optical properties were studied by applying XRD and UV-Vis spectroscopy. The measurement of the second harmonic generation was performed using the fundamental Nd:YAG 10 ns laser beam with wavelength 1.064 μ m. Dependence of the second order susceptibilities for the two principal second order susceptibility tensor components d 14 and d 25 with the simultaneously applied dc- and UV-laser fields were investigated and discussed.