Nonlinear Susceptibility Tensor Research Articles

Polarization entanglement enabled by orthogonally stacked van der Waals NbOCl2 crystals

Polarization entanglement holds significant importance for photonic quantum technologies. Recently emerging subwavelength nonlinear quantum light sources, e.g., GaP and LiNbO3 thin films, benefiting from the relaxed phase-matching constraints and volume confinement, have shown intriguing properties, such as high-dimensional hyperentanglement and robust entanglement anti-degradation. Van der Waals (vdW) NbOCl2 crystal, with strong optical nonlinearities, has emerged as a potential candidate for ultrathin quantum light sources. However, polarization entanglement is inaccessible in the NbOCl2 crystal due to its unfavorable nonlinear susceptibility tensor. Here, by leveraging the twist-stacking degree of freedom inherently in vdW systems, we showcase the preparation of polarization entanglement and quantum Bell states.

Surface populations as a model for the distance-dependence of the interfacial refractive index.

Vibrational sum frequency spectra provide information about interfaces that is sensitive to the orientation of molecules, their electronic environment, and the local electric fields. Here, we use molecular dynamics simulations in order to study a surfactant, para-cyanophenol, at the air-water interface. The volume fractions of water and the organic surfactant are considered at various points over the nanometer-scale region in a Lorentz-Lorenz model. We find that the calculated ratios of nonlinear susceptibility tensor elements are in agreement with experimental data only when this depth profile was considered. We also use these data to evaluate the ratio of the C-N hyperpolarizability tensor elements in the interfacial region.

Second-harmonic generation tensors from high-throughput density-functional perturbation theory

Optical materials play a key role in enabling modern optoelectronic technologies in a wide variety of domains such as the medical or the energy sector. Among them, nonlinear optical crystals are of primary importance to achieve a broader range of electromagnetic waves in the devices. However, numerous and contradicting requirements significantly limit the discovery of new potential candidates, which, in turn, hinders the technological development. In the present work, the static nonlinear susceptibility and dielectric tensor are computed via density-functional perturbation theory for a set of 579 inorganic semiconductors. The computational methodology is discussed and the provided database is described with respect to both its data distribution and its format. Several comparisons with both experimental and ab initio results from literature allow to confirm the reliability of our data. The aim of this work is to provide a relevant dataset to foster the identification of promising nonlinear optical crystals in order to motivate their subsequent experimental investigation.

Understanding Nonlinear Optical Phenomena in N-Pyrimidinyl Stilbazolium Crystals via a Self-Consistent Electrostatic Embedding - DFT Approach.

Density functional theory (DFT) and time-dependent density functional theory (TD-DFT) have been used to investigate the nonlinear optical (NLO) properties of phenolic N-pyrimidinyl stilbazolium cationic chromophore in its corresponding noncentrosymmetric crystals. Such a cationic chromophore, the OPR (4-(4-hydroxystyryl)-1-(pyrimidin-2-yl)pyridinium), consists of a strong electron donor, the 4-hydroxyphenyl group, and a strong electron acceptor, the N-pyrimidinylpyridinium group based on two electron-withdrawing groups. The in-crystal NLO properties were determined by applying a supermolecule approach in combination with an iterative electrostatic scheme, in which the surrounding molecules of a unit cell are represented by point charges. With CAM-B3LYP, our absolute estimates for the largest diagonal component of the second-order nonlinear susceptibility tensor of OPR-based crystals range from 64.00 to 80.34 pm/V in the static regime and from 162.09 to 175.52 pm/V at 1907 nm. These values are significant when compared to those of benchmark stilbazolium-based crystals. Furthermore, the third-order susceptibility, which is related to the nonlinear optical process of the intensity-dependent refractive index, is also significant compared to the results for other organic crystals, such as chalcone derivatives. With TD-CAM-B3LYP, the two-state model effectively explains the similarity in the first hyperpolarizability values in the crystalline phase. This similarity arises from the combination of the oscillator strength and the charge transfer of the crucial transition. Therefore, phenolic organic salt crystals show great promise for various nonlinear optical applications.

Peculiarities of the intrinsic symmetry of linear and nonlinear optical susceptibility tensors in nonabsorbing inhomogeneous media with nonlocality of optical response

We show that using the Landau–Lifshitz form of the constitutive equations to construct electrodynamics of inhomogeneous nonabsorbing media with nonlocality of optical response leads to previously unknown intrinsic symmetry relations of the spatially dependent tensors of local and nonlocal optical susceptibilities guaranteeing that the energy conservation law is fulfilled. The discovered relations drastically differ from the analogous relations for homogeneous spatially dispersive media and make it possible to correctly write down the balance equation for the energy conservation law in inhomogeneous media with nonlocality of optical response without the previously accepted artificial addition of any new terms to the classical constitutive equations suggested by Landau and Lifshitz.

Novel schiff base-azide metal complexes: Synthesis, spectral, nonlinear optics, and DFT studies

In order to enhance nonlinear optics (NLO)-based technologies, current research focuses on the design and synthesis of coordination materials. In this context, to investigate spectral and theoretical linear optical (LO)/nonlinear optical (NLO) behaviors, novel metal complexes including azide {[Mn (L1)2(N3)2], (9), [Ni(L1)2(N3)], (10), [Co2(L1)2(N3)2]⋅2H2O, (11); L1: N-(pyridin-2-ylmethylene)methanamine} were synthesized. The vibrational and electronic spectral features of complexes 9–11 were investigated by UV–Vis and FT–IR spectra. Depending on the central metal ion and coordination geometries of complexes, the microscopic static nonlinear behaviors were examined by using the CAM-B3LYP/and ωB97XD/6–311 + G (d,p)//LanL2DZ levels of density functional theory (DFT). Furthermore, the vibrational and electronic properties of complexes 9–11 based on the same levels of time-dependent/density functional theory (TD-DFT/DFT) were surveyed. Additionally, the theoretical χ(1), χ(2), and χ(3) parameters, known as linear optical, second-, and third-order nonlinear optical susceptibility tensors, as well as linear, second-, and third-order polarization parameters (P(1), P(2), and P(3)) for complexes 9–11 were examined. The greatest <β(0; 0,0)> value for complex 10 found to be 262.55 × 10−30 esu using CAM-B3LYP level is 820.5 and 2019.6 times higher than the urea findings (0.32 × 10−30 esu and 0.130 × 10−30 esu). The <γ(0; 0,0,0)> results indicate that complex 9 having the highest value obtained at 2216.40 × 10−36 esu using CAM-B3LYP level is 47.76 and 316.63 times greater than those of pNA (15 × 10−36 esu) and urea (7 × 10−36 esu), respectively. Complexes 10 and 9 demonstrated promising microscopic second-order and third-order NLO features, respectively. Our research is anticipated to provide insight into NLO materials that may have applications in optoelectronics and telecommunication field.

Terahertz sum-frequency excitation of coherent optical phonons in the two-dimensional semiconductor WSe2

Driving fundamental excitations via strong light fields is one of the most important issues in solid state physics, which opens up new avenues to control material properties. Two-dimensional materials are fruitful platforms for future semiconductor applications, including opto-electronic and phononic devices, yet the phonon dynamics and nonlinear phonon–phonon coupling remain under-explored. Here, we demonstrate coherent phonon excitation in thin films of the layered two-dimensional semiconductor WSe2 induced by intense and broadband ultrafast terahertz (THz) pulses. We performed THz Kerr effect spectroscopy and observed coherent phonon oscillations assigned to the E2g optical phonon mode. The phonon amplitude displays a quadratic THz field strength dependence, indicating a sum-frequency THz excitation process. Furthermore, pump–probe polarization and crystal orientation relationships, supported by symmetry analysis of the nonlinear susceptibility and Raman tensors, provide helpful insight into nonlinear phonon–phonon interactions and potential coherent control schemes for the manipulation of phonon polarization and material properties in WSe2.

Nonlinear response of magnetization obeying inertial dynamics to superimposed dc and ac fields and dynamic magnetic hysteresis

The nonlinear ac stationary responses of magnetization and the dynamic magnetic hysteresis of ferromagnetic particles with uniaxial anisotropy acted on by both external dc and ac magnetic fields are evaluated by employing the inertial Landau–Lifshitz–Gilbert equation. Analytical expressions are obtained for the components of the second- and third-order nonlinear susceptibility tensors using the perturbation method. The dynamic nonlinear susceptibility strongly depends on the dc field strength. The effect of inertia on the area and slope of the dynamic magnetic hysteresis loop is demonstrated. In addition to nutation resonance, the main nonlinear effects previously observed in the ferromagnetic resonance region (frequency doubling and appearance of weak subharmonic resonance peaks) are predicted in the nutation resonance frequency region.

Strong anisotropic third-harmonic generation in layered violet phosphorus.

We demonstrate that layered violet phosphorus, an emerging 2D semiconductor, undergoes strong anisotropic third-harmonic generation (THG). Polarization dependence of in-plane THG presents a cruciate-flower-shaped curve. Through theoretical modeling of the in-plane THG response, done by considering crystalline symmetry of violet phosphorus, we successfully quantify four non-zero third-order nonlinear optical susceptibility tensor elements. From control experiments, the magnitude of third-order nonlinear optical susceptibility |χ3| is calculated to be about 4.0 × 10-19 m2 V-2, which is comparable to those of conventional 2D layered semiconductors. These results indicate that the layered violet phosphorus can serve as an ideal building block for nonlinear optical applications.

Efficient and robust second-harmonic generation in thin-film lithium niobate using modal phase matching

A double-ridge waveguide is designed for efficient and robust second-harmonic generation (SHG) using the thin-film lithium-niobate-on-insulator (LNOI) platform. Perfect phase matching (PhM) is achieved between the fundamental waveguide mode at 1,550 nm and a higher-order mode at the second harmonic. The fabrication tolerances of the PhM condition are simulated using a finite-difference method mode solver, and conversion efficiencies as high as 3.92 W−1 are obtained for a 1-cm long waveguide. This design allows access to the largest element of the second-order nonlinear susceptibility tensor, and represents a scalable alternative to waveguides based on periodically-poled lithium niobate (PPLN). The design has the potential for generating pairs of entangled photons in the infrared C-band by spontaneous parametric down-conversion (SPDC).

Intrinsic symmetry of nonlocal nonlinear optical susceptibility tensor in degenerate multi-wave mixing

Using energy and momentum conservation laws, we obtained the intrinsic symmetry relations for the nonlocal nonlinear optical susceptibility tensor in lossless nth order nonlinear medium of arbitrary symmetry class for the case when less than n + 1 electromagnetic waves with different frequencies interact. Particular attention is devoted to the relations of the components of this tensor, which cannot be obtained as limiting case from the symmetry relations for the nonlocal nonlinear susceptibility tensor describing interaction of exactly n + 1 waves with different frequencies. The examples of these symmetry relations for degenerate second- and third-order processes often considered are given.

Polarimetric second-harmonic generation microscopy of partially oriented fibers I: Digital modeling

Second-harmonic generation (SHG) in biological tissues originates predominantly from noncentrosymmetric fibrillar structures partially oriented within a focal volume (voxel) of a multiphoton excitation microscope. This study is aimed to elucidate fibrillar organization factors influencing SHG intensity, as well as achiral, R, and chiral, C, nonlinear susceptibility tensor component ratios. SHG response is calculated for various configurations of fibrils in a voxel using the digital nonlinear microscope. The R and C ratios are calculated using linear incident and outgoing polarization states that simulate polarization-in polarization-out polarimetric measurements. The investigation shows strong SHG intensity dependence on parallel/antiparallel fiber organization. The R and C ratios are strongly influenced by the fiber chirality, tilting of the fibers out of the image plane, and crossing of the fibers. The computational modeling provides the basis for the interpretation of polarimetric SHG microscopy images in terms of the ultrastructural organization of fibers in each voxel of the samples. The modeling results are employed in the accompanying paper to investigate the ultrastructures with parallel/antiparallel fibers and two-dimensional and tree-dimensional crossing fibers in biological and biomimetic structures.

Terahertz-induced polar state in quantum paraelectric SrTiO3

The second harmonic generation from strontium titanate crystal under the terahertz excitation has studied at room temperature. The obtained anisotropic dependences show the presence of a terahertz electric field induced polar phase. By analyzing the polarization dependencies of the optical second harmonic intensity, the relative values of the third-order nonlinear susceptibility tensor components were obtained.Graphical abstract

Terahertz Spin Current Pulses in Antiferromagnetic Oxide: The Role of Vacancy‐Induced Ferromagnetism

Antiferromagnetic oxides have attracted increasing attention for their outstanding peculiarities in spintronics. Crystal lattice defects that are present in antiferromagnetic oxides can influence their physical properties, such as vacancy‐induced ferromagnetism. Meanwhile, the generation and manipulation of ultrafast spin currents of antiferromagnetic insulators are highly desired. Although the generation and detection of terahertz spin current pulses in antiferromagnetic oxides have been realized, the effect of vacancy‐induced ferromagnetism on spin current in antiferromagnetic oxides is not yet known. Herein, the role of vacancy‐induced ferromagnetism on the terahertz spin current in antiferromagnetic nickel oxide thin films is reported. Structural and magnetic characterizations reveal that nickel vacancies effectively break the strong antiferromagnetic exchange coupling, giving rise to the coexistence of antiferromagnetism and ferromagnetism in NiO thin films. Notably, the enhancement of terahertz radiation associated with the photo‐induced ultrafast spin current of NiO thin film with the strongest ferromagnetism is the most significant. Besides, the nonlinear susceptibility tensor parameters related to the antiferromagnetic property of NiO thin films also change distinctly. The findings indicate that the defects of antiferromagnetic materials play a decisive role in the application of antiferromagnetic spintronics in the terahertz field.

Wide-field Stokes polarimetric microscopy for second harmonic generation imaging.

We employ wide-field second harmonic generation (SHG) microscopy together with nonlinear Stokes polarimetry for quick ultrastructural investigation of large sample areas (700 μm × 700 μm) in thin histology sections. The Stokes vector components for SHG are obtained from the polarimetric measurements with incident and outgoing linear and circular polarization states. The Stokes components are used to construct the images of polarimetric parameters and deduce the maps of ultrastructural parameters of achiral and chiral nonlinear susceptibility tensor components ratios and cylindrical axis orientation in fibrillar materials. The large area imaging was employed for lung tumor margin investigations. The imaging shows reduced SHG intensity, increased achiral susceptibility ratio values, and preferential orientation of collagen strands along the boarder of tumor margin. The wide-field Stokes polarimetric SHG microscopy opens a possibility of quick large area imaging of ultrastructural parameters of tissue collagen, which can be used for nonlinear histopathology investigations.

Enhanced Sum Frequency Generation for Monolayers on Au Relative to Silica: Local Field Factors and SPR Effect

Using metals as signal magnified substrates, surface plasmon-enhanced sum frequency generation (SFG) vibrational spectroscopy is a promising technique to probe weak molecular-level signals at surfaces and interfaces. In this study, the vibrational signals of the n-alkane monolayer on the gold (Au) and silica substrates are investigated using the broadband femtosecond SFG. The enhancement factors are discovered to be up to ∼1076 and ∼31 for the methyl symmetric and asymmetric stretching (ss and as) modes of the monolayer, respectively. By systematically analyzing the second-order nonlinear susceptibility tensor components (χijks), the Fresnel coefficients (Fijks), and the surface plasmon resonance (SPR) effect, we find that the interplay between Fijk and χijk terms and the SPR effect dominate the SFG signal enhancement. Our study reveals that the relative contributions of different influencing factors (i.e., Fresnel coefficients and SPR) to the SFG signal enhancement provide an approach to interpreting enhanced SFG vibrational signals detected from probe molecules on distinct substrates and may finally guide the design of the experimental methodology to improve the detection sensitivity and signal-to-noise ratio.

Misfit-generated structural and optical anisotropies of the natural MoS2−PbS van der Waals heterostructure merelaniite

Significant efforts developing ${\mathrm{MoS}}_{2}\text{\ensuremath{-}}\mathrm{PbS}$-based heterostructure devices with several different architectures show promise for photosensor, solar cell, and chemical sensor applications. Merelaniite $({\mathrm{Mo}}_{4}{\mathrm{Pb}}_{4}{\mathrm{VSbS}}_{15})$ is a newly discovered natural van der Waals heterostructure of the cylindrite type, composed predominantly of heavily modulated pseudotetragonal PbS layers and pseudohexagonal ${\mathrm{MoS}}_{2}$ layers with large misfit-induced anisotropy. For an incommensurate modulated structure, the refined structural model from single-crystal x-ray diffraction analysis is in reasonable agreement with the results obtained by high-resolution scanning transmission electron microscopy, especially in light of the fact that that the two isolated single-crystal domains used for the x-ray and electron diffraction experiments were extracted from two different whiskers and subjected to different sample preparation methods. The effects of the misfit-induced structural anisotropy are studied using angle-resolved polarized Raman spectroscopy. The intensities of 12 Raman modes are studied as a function of incident polarization angle relative to merelaniite's whisker axis, and show maximal intensity with the polarization direction perpendicular to the whisker axis. Polarization-dependent anisotropic third-harmonic generation from ultrathin mechanically exfoliated flakes reveals the anisotropy of the third-order nonlinear susceptibility tensor. Merelaniite demonstrates an expanded structure-chemistry space for engineering stable layered materials for potential device applications.

Ab initio calculation of two-photon absorption in semiconductors

A theoretical derivation of two-photon absorption (2PA) from semiconductors, based on the length gauge analysis and the electron density operator, is formulated; the intraband ${\mathbit{r}}_{i}$ part and the interband ${\mathbit{r}}_{e}$ part of the position operator $\mathbit{r}$ are properly accounted for. Within the independent-particle approximation, the nonlinear third-order susceptibility tensor ${\ensuremath{\chi}}^{\mathrm{a}\mathrm{b}\mathrm{c}\mathrm{d}}(\ensuremath{-}\ensuremath{\omega};\ensuremath{-}\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega},\ensuremath{\omega})$ and the two-photon absorption coefficient are calculated, including the scissors correction needed to correct the well-known underestimation of the local-density-approximation band gap. Using time-reversal symmetry, it is shown that the expression for ${\ensuremath{\chi}}^{\mathrm{a}\mathrm{b}\mathrm{c}\mathrm{d}}(\ensuremath{-}\ensuremath{\omega};\ensuremath{-}\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega},\ensuremath{\omega})$ is finite at $\ensuremath{\omega}=0$, avoiding nonphysical divergences presented in previous calculations when $\ensuremath{\omega}\ensuremath{\rightarrow}0$. Ab initio band structure calculations using different pseudopotential schemes that include spin-orbit coupling are used to calculate the 2PA for several semiconductors, and the calculations are compared with available experimental results for photon energies that are below the optical band gap.

Raman activity of the longitudinal optical phonons of the LiNbO3 crystal: Experimental determination and quantum mechanical simulation

AbstractIn this study, the and the two equivalent / polarized Raman spectra of a LiNbO3 single crystal have been recorded and used as a benchmark test for the density functional theory (DFT) calculation of the longitudinal modes and of their Raman activity. The theoretical approach, based on periodic boundary conditions and a linear combination of atomic orbitals (LCAO), provides excellent predictions of phonon wavenumbers and relative bands intensities for both A1 and E Longitudinal Optical (LO) modes and complements a previous paper limited to the study of Transverse Optical (TO) modes. Overall, the present investigation demonstrates that the LCAO approach, as implemented in the CRYSTAL software, gives results of similar accuracy for the TO and the LO phonons features. By means of a band deconvolution scheme applied to the experimental spectra, we present, for the first time, a quantitative comparison between experimental and theoretically predicted polarized Raman band intensities of LiNbO3 LO modes. This analysis highlights the role of the suitable determination of the static and high‐frequency dielectric matrices that are needed for the prediction of the TO/LO frequency split but also the first nonlinear electric susceptibility tensor for an accurate description of the Raman intensity pattern.

Nonlinear Optical Imaging of In‐Plane Anisotropy in Two‐Dimensional SnS

AbstractTwo‐dimensional (2D) tin(II) sulfide (SnS) crystals belong to a class of orthorhombic semiconducting materials with remarkable properties, such as in‐plane anisotropic optical and electronic response, and multiferroic nature. The 2D SnS crystals exhibit anisotropic response along the in‐plane armchair (AC) and zigzag (ZZ) crystallographic directions, offering an additional degree of freedom in manipulating their behavior. Here, advantage of the lack of inversion symmetry of the 2D SnS crystal, that produces second harmonic generation (SHG), is taken to perform polarization‐resolved SHG (P‐SHG) nonlinear imaging of the in‐plane anisotropy. The P‐SHG experimental data are fitted with a nonlinear optics model, allowing to calculate the AC/ZZ orientation from every point of the 2D crystal and to map with high resolution the AC/ZZ direction of several 2D SnS flakes belonging in the same field of view. It is found that the P‐SHG intensity polar patterns are associated with the crystallographic axes of the flakes and with the relative strength of the second‐order nonlinear susceptibility tensor in different directions. Therefore, the method provides quantitative information of the optical in‐plane anisotropy of orthorhombic 2D crystals, offering great promise for performance characterization during device operation in the emerging optoelectronic applications of such crystals.