Second-order Susceptibility Research Articles

Unveiling the Pockels coefficient of ferroelectric nitride ScAlN

Nitride ferroelectrics have recently emerged as promising alternatives to oxide ferroelectrics due to their compatibility with mainstream semiconductor processing. ScAlN, in particular, has exhibited remarkable piezoelectric coupling strength (K2) comparable to that of lithium niobate, making it a valuable choice for RF filters in wireless communications. Recently, ScAlN has sparked interest in its use for nanophotonic devices, chiefly due to its large bandgap facilitating operation in blue wavelengths coupled with promises of enhanced nonlinear optical properties such as a large second-order susceptibility (χ(2)). It is still an open question whether ScAlN can outperform oxide ferroelectrics concerning the Pockels effect—an electro-optic coupling extensively utilized in optical communications devices. In this paper, we present a comprehensive theoretical analysis and experimental demonstration of ScAlN’s Pockels effect. Our findings reveal that the electro-optic coupling of ScAlN, despite being weak at low Sc concentration, may be significantly enhanced and exceed LiNbO3 at high levels of Sc doping, which points the direction of continued research efforts to unlock the full potential of ScAlN.

Two-Dimensional MXene Flakes with Large Second Harmonic Generation and Unique Surface Responses.

MXenes are a family of two-dimensional (2D) materials with broad and varied applications in biology, materials science, photonics, and environmental remediation owing to their layered structure and high surface area-to-volume ratio. MXenes have exhibited significant nonlinear optical characteristics, which have been primarily explored in the context of photonics applications, yet the second-harmonic generation (SHG) behavior of MXenes remains an unexplored aspect of their optical properties. Herein, we demonstrate and quantify large second-order responses of 2D Ti3C2Tx MXenes both in aqueous solutions and on a silicon substrate for the first time. MXene flakes showed strong second-harmonic scattering (SHS) in a dilute suspension with a sensitivity of less than 0.1 μg/mL. Angle-dependent SHS experiments further found that the second-order responses originate from coherent 2D dipole radiation. Through confocal and atomic force microscopies, we found that the intense SHG signal from free-standing MXene flakes increases exponentially with decreasing thickness, while two-photon fluorescence increases linearly with thickness. The second-order susceptibility of the MXenes was determined to be 3.6 pm V-1 with a thickness of 10 nm, almost twice of that for an often-used SHG crystal, beta barium borate. We further explored surface properties of the MXene sheets by investigating the SHS responses upon addition of organic dye molecules to the system. It was found that the adsorption of crystal violet (CV) obeys a Langmuir adsorption model while the addition of malachite green (MG) resulted in almost no change in SHG intensity, even though the adsorption capacities for both CV (61.3 ± 1.7 mg/g) and MG (54.8 ± 2.8 mg/g) are similar. Such a stark difference in adsorption characteristics between cationic organic CV and MG dyes is likely due to their distinct orientational orderings on the MXene surfaces. This work opens many possibilities for the further employment of the family of 2D materials in photonics, optics, and surface catalysis applications.

Designing a 2D van der waals oxide with lone-pair electrons as chemical scissor

Abstract 2D van der Waals (vdW) materials are known for their intriguing physical properties, but their rational design and synthesis remain a great challenge for chemists. In this work, we successfully synthesized a new non-centrosymmetric oxide, i.e. InSbMoO6, with Sb3+ lone-pair electrons serving as chemical scissor to generate its 2D vdW crystal structure. Monolayer and few-layer InSbMoO6 flakes are readily obtained via facile mechanical exfoliation. They exhibit strong second-harmonic generation (SHG) response with an effective second-order nonlinear optical susceptibility $\chi _{{\rm{eff}}}^{{\rm{(2)}}}\ $of 32.4 pm·V−1. Meanwhile, the SHG response is in-plane anisotropic and directly proportional to the layer thickness, independent of layer parity. In addition, the InSbMoO6 flakes exhibit excellent thermal and atmospheric stability, along with pronounced anisotropy in Raman spectroscopy. This work implies that using lone-pair electrons as chemical scissor is an effective strategy for designing and synthesizing new 2D vdW materials for integrated photonic applications.

Individual domain characteristics determined by second-harmonic generation diffractometer for multi-domain multiferroics

We investigated the multi-domain states of a multiferroic La-doped BiFeO3 (BLFO) thin film by examining diffraction patterns in optical second-harmonic generation (SHG) measurement. By directing a laser onto the domain wall within the domain-patterned sample, we observed clear diffraction signatures of SHG waves generated from two ferroelectric domains. We explained the experimental results of the diffraction patterns, including the intensity distribution and the polarization characteristics, using Fresnel propagation of SHG waves. From this, we could determine the amplitude and phase of the SHG waves generated from each domain, and figure out not only the polarization direction of each ferroelectric domain but also the phase related to the complex-valued second-order susceptibility tensor. Consequently, we could present SHG diffractometry as an effective measurement method to reveal the phase details of electric polarization of the multi-domain states of ferroic materials.

Nonlinear geometric phase coded ferroelectric nematic fluids for nonlinear soft-matter photonics

Simultaneous manipulation of multiple degrees of freedom of light lies at the heart of photonics. Nonlinear wavefront shaping offers an exceptional way to achieve this goal by converting incident light into beams of new frequencies with spatially varied phase, amplitude, and angular momenta. Nevertheless, the reconfigurable control over structured light fields for advanced multimode nonlinear photonics remains a grand challenge. Here, we propose the concept of nonlinear geometric phase in an emerging ferroelectric nematic fluid, of which the second-order nonlinear susceptibility carries spin-dependent nonlinearity phase. A case study with photopatterned q-plates demonstrates the generation of second-harmonic optical vortices with spin-locked topological charges by using cascaded linear and nonlinear optical spin-orbit interactions. Furthermore, we present the dynamic tunability of second-harmonic structured light through temperature, electric field, and twisted elastic force. The proposed strategy opens new avenues for reconfigurable nonlinear photonics, with potential applications in optical communications, quantum computing, high-resolution imaging, etc.

Phase-Selective Synthesis of Rhombohedral WS2 Multilayers by Confined-Space Hybrid Metal-Organic Chemical Vapor Deposition.

Rhombohedral polytype transition metal dichalcogenide (TMDC) multilayers exhibit non-centrosymmetric interlayer stacking, which yields intriguing properties such as ferroelectricity, a large second-order susceptibility coefficient χ(2), giant valley coherence, and a bulk photovoltaic effect. These properties have spurred significant interest in developing phase-selective growth methods for multilayer rhombohedral TMDC films. Here, we report a confined-space, hybrid metal-organic chemical vapor deposition method that preferentially grows 3R-WS2 multilayer films with thickness up to 130 nm. We confirm the 3R stacking structure via polarization-resolved second-harmonic generation characterization and the 3-fold symmetry revealed by anisotropic H2O2 etching. The multilayer 3R WS2 shows a dendritic morphology, which is indicative of diffusion-limited growth. Multilayer regions with large, stepped terraces enable layer-resolved evaluation of the optical properties of 3R-WS2 via Raman, photoluminescence, and differential reflectance spectroscopy. These measurements confirm the interfacial quality and suggest ferroelectric modification of the exciton energies.

Substrate Interference and Strain in the Second-Harmonic Generation from MoSe2 Monolayers.

Nonlinear optical materials of atomic thickness, such as non-centrosymmetric 2H transition metal dichalcogenide monolayers, have a second-order nonlinear susceptibility (χ(2)) whose intensity can be tuned by strain. However, whether χ(2) is enhanced or reduced by tensile strain is a subject of conflicting reports. Here, we grow high-quality MoSe2 monolayers under controlled biaxial strain created by two different substrates and study their linear and nonlinear optical responses with a combination of experimental and theoretical approaches. Up to a 15-fold overall enhancement in second-harmonic generation (SHG) intensity is observed from MoSe2 monolayers grown on SiO2 when compared to its value on a Si3N4 substrate. By considering an interference contribution from different dielectrics and their thicknesses, a factor of 2 enhancement of χ(2) was attributed to the biaxial strain: substrate interference and strain are independent handles to engineer the SHG strength of non-centrosymmetric 2D materials.

Covalent Organic Frameworks in Computational Design of Second-Harmonic Generation Materials: Role of Tetrel Atoms and Their Interactions.

Modern approaches to the design of nonlinear optical materials often rely on computational techniques. Here, we discuss the effects of the variation in the center tetrel atoms, Tt = C, Si, or Ge, in a series of covalent organic frameworks of the COF-102 family. The effects of halogen substitution, Hal = Cl, Br, or I on intramolecular tetrel bonding are also discussed. The characteristics of the calculated electron density have been implemented to describe the features of the electron distribution around the central fragment involving a tetrahedral tetrel atom. The effect of the central Tt atom leads to a dramatic change in the character of electron delocalization on the Tt-Car bond with aromatic rings. The location of the halogen atom at the ortho-position of the aromatic ring leads to the formation of tetrel bonds, halogen bonds, or other noncovalent interactions. The changes in the second-order electric susceptibility χ(2) have been studied in order to describe the strength of nonlinear optical properties within the periodic couple-perturbed Kohn-Sham approach. A counterintuitive trend for the χ(2) decrease is observed upon substitution of H > Cl > Br > I at the ortho-position of the phenyl ring. This is due to the corresponding elongation of the Tt-Car bond.

Harnessing complexity: Nonlinear optical phenomena in L-shapes, nanocrescents, and split-ring resonators.

We conduct systematic studies of the optical characteristics of plasmonic nanoparticles that exhibit C2v symmetry. In particular, we analyze three distinct geometric configurations: an L-type shape, a crescent, and a split-ring resonator shaped like the Greek letter π. Optical properties are examined using the finite-difference time-domain method. It is demonstrated that all three shapes exhibit two prominent plasmon modes associated with the two axes of symmetry. This is in addition to a wide range of resonances observed at high frequencies corresponding to quadrupole modes and peaks due to sharp corners. Next, to facilitate nonlinear analysis, we employ a semiclassical hydrodynamic model, where the electron pressure term is explicitly accounted for. This model goes beyond the standard Drude description and enables capturing nonlocal and nonlinear effects. Employing this model enables us to rigorously examine the second-order angular resolved nonlinear optical response of these nanoparticles in each of the three configurations. Two pumping regimes are considered, namely, continuous wave (CW) and pulsed excitations. For CW pumping, we explore the properties of the second harmonic generation (SHG). Polarization and angle-resolved SHG spectra are obtained, revealing strong dependence on the nanoparticle geometry and incident wave polarization. The C2v symmetry is shown to play a key role in determining the polarization states and selection rules of the SHG signal. For pulsed excitations, we discuss the phenomenon of broadband terahertz (THz) generation induced by the difference-frequency generation . It is shown that the THz emission spectra exhibit unique features attributed to the plasmonic resonances and symmetry of the nanoparticles. The polarization of the generated THz waves is also examined, revealing interesting patterns tied to the nanoparticle geometry. To gain deeper insight, we propose an analytical theory that agrees very well with the numerical experiments. The theory shows that the physical origin of the THz radiation is the mixing of various frequency components of the fundamental pulse by the second-order nonlinear susceptibility. An expression for the far-field THz intensity is derived in terms of the incident pulse parameters and the nonlinear response tensor of the nanoparticle. The results presented in this work offer new insights into the linear and nonlinear optical properties of nanoparticles with C2v symmetry. The demonstrated strong SHG response and efficient broadband THz generation hold great promise for applications in nonlinear spectroscopy, nanophotonics, and optoelectronics. The proposed theoretical framework also provides a valuable tool for understanding and predicting the nonlinear behavior of other related nanostructures.

Control of second-and third-order nonlinear optical properties of DCM and Znq2 composites fabricated by the physical vapor co-deposition process

In the present work, investigations on the second and third-order NLO properties of, 4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran (DCM) reddye co-doped bis(8-hydroxyquinoline) Zinc (Znq2) thin films with different concentrations were investigated. The samples have a thickness of 100 nm. They were prepared using the physical vapor deposition (PVD) method under a high vacuum. The morphological properties were studied by atomic force microscopy. The second-order nonlinear susceptibility χ(2) after applying the corona poling technique was estimated using the comparative model of Lee, while the third-order nonlinear susceptibility χ(3) was estimated using the comparative model of Kubodera and Kobayashi. The tested samples varied in terms of the concentration of DCM in the structure, which visibly influenced their nonlinear response. The pure DCM thin film showed a large value of the second and third-order nonlinear susceptibility, while pure Znq2 had only the second harmonic response with a low value. In this study, we have demonstrated that doping with DCM, even with small concentrations, has also strongly enhanced the non-linearity of Znq2. The obtained results show that such compositions can be a good alternative for optoelectronic applications.

Polarization-entangled photon-pair source with van der Waals 3R-WS2 crystal

Ultracompact entangled photon sources are pivotal to miniaturized quantum photonic devices. Van der Waals (vdW) nonlinear crystals promise efficient photon-pair generation and on-chip monolithic integration with nanophotonic circuitry. However, it remains challenging to generate maximally entangled Bell states of photon pairs with high purity, generation rate, and fidelity required for practical applications. Here, we realize a polarization-entangled photon-pair source based on spontaneous parametric down conversion in an ultrathin rhombohedral tungsten disulfide (3R-WS2) crystal. This vdW entangled photonic source exhibits a high photon-pair purity with a coincidence-to-accidental ratio of above 800, a generation rate of 31 Hz, and two maximally polarization-entangled Bell states with fidelities exceeding 0.93 and entanglement degree over 0.97. These results stem from scalable optical nonlinearity, enhanced second-order susceptibility by electronic transitions, and a well-defined symmetry-enabled selection rule inherent in 3R-WS2. Our polarization entangled photon source can be integrated with photonic structures for generating more complex entangled states, thus paving an avenue for advanced quantum photonic systems toward computation and metrology.

Phase of the second-order susceptibility in vibrational sum frequency generation spectroscopy: Origins, utility, and measurement techniques.

Vibrational sum frequency generation can provide valuable structural information at surfaces and buried interfaces. Relating the measured spectra to the complex-valued second-order susceptibility χ(2) is at the heart of the technique and a requisite step in nearly all subsequent analyses. The magnitude and phase of χ(2) as a function of frequency reveal important information about molecules and materials in regions where centrosymmetry is broken. In this tutorial-style perspective, the origins of the χ(2) phase are first described, followed by the utility of phase determination. Finally, some practical methods of phase extraction are discussed.

Quantitative Signal Analysis of Sum-Frequency Scattering Experiments from Aerosol Surfaces.

Droplet interfaces are instrumental in processes of biology, engineering, production, and environmental systems. The chemical and physical properties of heterogeneous interfaces are known to be different from those of their underlying bulk phases, and different again when considering the curved surface of submicron aerosol droplets. The recently developed technique of vibrational sum-frequency scattering (VSFS) spectroscopy from airborne particles has emerged as an interface-specific method for the in situ analysis of this unique system. While the technique has shown promise in debut works, a quantitative analysis of the VSFS system has not yet been performed. Here we provide a comprehensive analysis of a VSFS spectrometer with reference to the well-documented planar analog. We decompose the VSFS signal into coherent and incoherent as well as resonant and nonresonant components as a function of incident pulse delay time. We then quantify and compare resonant and nonresonant VSFS and VSFG experimental data using the same laser and detection systems. Using the air/water interface as a guide, we show that the resonant and nonresonant contributions to the SF responses are comparable for the two systems by extracting second-order susceptibilities and hyperpolarizabilities, and using them to estimate single-particle susceptibilities. A quantitative analysis of the signal detection systems for the scattering and planar geometries is made, and conversion efficiencies for VSFG, VSFS, and other nonlinear scattering experiments are compared. Lastly, the possibility of a low-repetition (1 kHz) VSFS spectrometer is considered, determining that it may be possible with modern laser technology but is inevitably less efficient than a high-repetition (100 kHz) system. Though this multistep analysis we obtain a better understanding of the components of the VSFS signal from aerosol particles, further validate the feasibility of the experiments, and provide insight to those wishing to conduct similar experiments and how they may be improved.

Effects of Surface Charge Distribution and Electrolyte Ions on the Nonlinear Spectra of Model Solid-Water Interfaces.

Molecular dynamics simulations of model charged solid/water interfaces were carried out to provide insight about the relationship between the second-order nonlinear susceptibility χ(2) and the structure of the interfacial water layer. The results of the calculations reveal that the density fluctuations of water extend to about 12 Å from the surface regardless of the system, while the orientational ordering of molecules is long-ranged and is sensitive to the presence of electrolytes. The charge localization on the surface was found to affect only the high-frequency part of the Im[χ(2)] spectrum, and the addition of salt has very little effect on the spectrum of the first water layer. For solid/neat water interfaces, the spectroscopically active part of the liquid phase has a thickness largely exceeding the region of density fluctuations, and this long-ranged nonlinear activity is mediated by the electric field of the molecules. The electrolyte ions and their hydration shells act in a destructive way on the molecular field. This effect, combined with the screening of the surface charge by ions, drastically reduces the thickness of the spectroscopic diffuse layer. There is an electrolyte concentration at which the nonlinear response of the diffuse layer is suppressed and the χ(2) spectrum of the interface essentially coincides with that of the first water layer.

Enhanced vertical second harmonic generation from layered GaSe coupled to photonic crystal circular Bragg resonators

Abstract Two-dimensional (2D) layered materials without centrosymmetry, such as GaSe, have emerged as promising novel optical materials due to large second-order nonlinear susceptibilities. However, their nonlinear responses are severely limited by the short interaction between the 2D materials and light, which should be improved by coupling them with photonic structures with strong field confinement. Here, we theoretically design photonic crystal circular Bragg gratings (CBG) based on hole gratings with a quality factor as high as Q = 8 × 103, a mode volume as small as V = 1.18 (λ/n)3, and vertical emission of light field in silicon nitride thin film platform. Experimentally, we achieved a Q value up to nearly 4 × 103, resulting in a 1,200-fold enhancement of second harmonic generation from GaSe flakes with a thickness of 50 nm coupling to the CBG structures under continuous-wave excitation. Our work endows silicon-based photonic platforms with significant second-order nonlinear effect, which is potentially applied in on-chip quantum light sources and nonlinear frequency conversion.

Anatomy of critical fluctuations in hadronic matter

Critical phenomena in phase transitions of strongly interacting matter, governed by quantum chromodynamics, are inherently encoded in the fluctuations of conserved charges. In this work, we study the net-baryon number density fluctuations, including the lowest-lying nucleon and the baryonic resonance Δ(1232), based on the parity doublet model in the mean-field approximation. We focus on the qualitative features of the second-order susceptibility of the net-baryon number density in dense hadronic matter and how the inclusion of Δ(1232) affects it. We demonstrate that the fluctuations of the individual baryons do not necessarily reflect the total net-baryon number fluctuations at finite density, due to the nontrivial correlations between different particle species. Our results highlight the role of baryonic correlations in the interpretation of data from heavy ion collision experiments. Published by the American Physical Society 2024

Second harmonic generation in monolithic gallium phosphide metasurfaces

Abstract Gallium phosphide (GaP) offers unique opportunities for nonlinear and quantum nanophotonics due to its wide optical transparency range, high second-order nonlinear susceptibility, and the possibility to tailor the nonlinear response by a suitable choice of crystal orientation. However, the availability of single crystalline thin films of GaP on low index substrates, as typically required for nonlinear dielectric metasurfaces, is limited. Here we designed and experimentally realized monolithic GaP metasurfaces for enhanced and tailored second harmonic generation (SHG). We fabricated the metasurfaces from bulk (110) GaP wafers using electron-beam lithography and an optimized inductively coupled plasma etching process without a hard mask. SHG measurements showed a high NIR-to-visible conversion efficiency reaching up to 10−5, at the same level as typical values for thin-film-based metasurface designs based on III–V semiconductors. Furthermore, using nonlinear back-focal plane imaging, we showed that a significant fraction of the second harmonic was emitted into the zeroth diffraction order along the optical axis. Our results demonstrate that monolithic GaP metasurfaces are a simple and broadly accessible alternative to corresponding thin film designs for many applications in nonlinear nanophotonics.

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.

Generation of second harmonic at wide conversion band in GRIN multimode fibers

Optical poling of multimode graded-index fibers (GRIN) has emerged as a promising technique for creating periodic inscriptions of the second-order nonlinear optical susceptibility χ(2), enabling the generation of a second harmonic in silica fibers. In this work, we investigate the generation of multiple spectral peaks using a continuous broadband source in the infrared domain, generated in the same fiber by a femtosecond laser with a central wavelength different from the one used for the poling process. Building upon theoretical foundations, this work contributes at explaining how second and third-order nonlinear processes participate to the broad generation of the second harmonic in GRIN fibers.

Giant optical second- and third-order nonlinearities at a telecom wavelength.

A material platform that excels in both optical second- and third-order nonlinearities at a telecom wavelength is theoretically and experimentally demonstrated. In this TiN-based coupled metallic quantum well structure, electronic subbands are engineered to support doubly resonant inter-subband transitions for an exceptionally high second-order nonlinearity and provide single-photon transitions for a remarkable third-order nonlinearity within the 1400-1600 nm bandwidth. The second-order susceptibility χ(2) reaches 2840 pm/V at 1440 nm, while the Kerr coefficient n2 arrives at 2.8 × 10-10 cm2/W at 1460 nm. The achievement of simultaneous strong second- and third-order nonlinearities in one material at a telecom wavelength creates opportunities for multi-functional advanced applications in the field of nonlinear optics.