Second-order Nonlinear Susceptibility Research Articles

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.

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.

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.

Enhanced second-order nonlinear susceptibility in type-II asymmetric quantum well structures

Asymmetric quantum wells (AQWs) utilizing interband transitions enhance second-order susceptibility over a wide wavelength range compared to natural crystals. The nonlinear susceptibility is further enhanced in AQWs with type-II band alignment as compared to type-I band alignment, a result of the larger interband charge shift. This enhancement is demonstrated in this work by analyzing three type-I and type-II AQW designs based on the lattice-matched InP/AlGaInAs materials systems using the envelope wavefunction approximation. The calculated interband second-order susceptibility tensor elements in type-II structures range between 20 and 1.60 × 103 pm/V for nearly resonant optical rectification and difference frequency generation applications at near-infrared and terahertz wavelengths, an improvement of nearly 1 order of magnitude over the type-I structures and 1–2 orders of magnitude over natural crystals such as LiNbO3, KTiOPO4 (KTP), or GaAs. A factor of 2–3 further enhancement of the tensor elements is achieved by optimizing the well widths and band offsets of the type-II asymmetric quantum wells. The type-II structure can be implemented in other material systems spanning the longwave infrared to visible wavelengths, enhancing nonlinear susceptibility for various applications, including photonic integrated circuits.

Strong nonlinear-polarization in ZnMgO epitaxial thin-films with Li incorporation

The second-order nonlinear-polarization originated from the interaction between thin-film materials with second-order nonlinear susceptibility (χ (2)) and high-power laser is essential for integrated optics and photonics. In this work, strong second-order nonlinear-polarization was found in a-axis oriented Zn1-x Mg x O (ZnMgO) epitaxial thin-films with Li incorporation, which were deposited by radio-frequency magnetron sputtering. Mg incorporation (x > 0.3) causes a sharp fall in the matrix element χ 33 of χ (2) tensor, although it widens optical bandgap (E opt). In contrast, moderate Li incorporation significantly improves χ 33 and resistance to high-power laser pulses with a little influence on E opt. In particular, a Zn0.67Mg0.33O:Li [Li/(Zn + Mg + Li) = 0.07] thin-film shows a |χ 33| of 36.1 pm V−1 under a peak power density (E p) of 81.2 GW cm−2, a resistance to laser pulses with E p of up to 124.9 GW cm−2, and an E opt of 3.95 eV. Compared to that of ZnO, these parameters increase by 37.8%, 53.4%, and 18.6%, respectively. Specially, the Zn0.67Mg0.33O:Li shows higher radiation resistance than a Mg-doped LiNbO3 crystal with a comparable E opt. First-principle calculations reveal the Li occupation at octahedral interstitial sites of wurtzite ZnO enhances radiation resistance by improving structural stability. X-ray photoelectron spectroscopy characterizations suggest moderate Li incorporation increases χ 33 via enhancing electronic polarization. These findings uncover the close relationship between the octahedra interstitial defects in wurtzite ZnMgO and its nonlinear-polarization behavior under the optical frequency electric field of high-power laser.

Nonlinear Optical Properties of 2D Materials and their Applications.

2D materials are a subject of intense research in recent years owing to their exclusive photoelectric properties. With giant nonlinear susceptibility and perfect phase matching, 2D materials have marvelous nonlinear light-matter interactions. The nonlinear optical properties of 2D materials are of great significance to the design and analysis of applied materials and functional devices. Here, the fundamental of nonlinear optics (NLO) for 2D materials is introduced, and the methods for characterizing and measuring second-order and third-order nonlinear susceptibility of 2D materials are reviewed. Furthermore, the theoretical and experimental values of second-order susceptibility χ(2) and third-order susceptibility χ(3) are tabulated. Several applications and possible future research directions of second-harmonic generation (SHG) and third-harmonic generation (THG) for 2D materials are presented.

NaCl, MgCl2, and AlCl3 Surface Coverages on Fused Silica and Adsorption Free Energies at pH 4 from Nonlinear Optics.

We employ amplitude- and phase-resolved second harmonic generation experiments to probe interactions of fused silica:aqueous interfaces with Al3+, Mg2+, and Na+ cations at pH 4 and as a function of metal cation concentration. We quantify the second-order nonlinear susceptibility and the total interfacial potential in the presence and absence of a 10 mM screening electrolyte to understand the influence of charge screening on cation adsorption. Strong cation:surface interactions are observed in the absence of the screening electrolyte. The total potential is then employed to estimate the total number of absorbed cations cm-2. The contributions to the total potential from the bound and mobile charges were separated using Gouy-Chapman-Stern model estimates. All three cations bind fully reversibly, indicating physisorption as the mode of interaction. Of the isotherm models tested, the Kd adsorption model fits the data with binding constants of 3-30 and ∼300 mol-1 for the low (<0.1 mM) and high (0.1-3 mM) concentration regimes, corresponding to adsorption free energies of -13 to -18 and -24 kJ mol-1 at room temperature, respectively. The maximum surface coverages are around 1013 cations cm-2, matching the number of deprotonated silanol groups on silica at pH 4. Clear signs of decoupled Stern and diffuse layer nonlinear optical responses are observed and found to be cation-specific.

Nonlinear spin-orbit coupling in optical thin films

Tunable generation of vortex beams holds relevance in various fields, including communications and sensing. In this paper, we demonstrate the feasibility of nonlinear spin-orbit interactions in thin films of materials with second-order nonlinear susceptibility. Remarkably, the nonlinear tensor can mix the longitudinal and transverse components of the pump field. We observe experimentally our theoretical predictions in the process of second-harmonic generation from a thin film of aluminum gallium arsenide, a material platform widely spread for its role in the advancement of active, nonlinear, and quantum photonic devices. In particular, we prove that a nonlinear thin film can be used to produce vector vortex beams of second-harmonic light when excited by circularly-polarized Gaussian beams.

Giant electric field-induced second harmonic generation in polar skyrmions

Electric field-induced second harmonic generation allows electrically controlling nonlinear light-matter interactions crucial for emerging integrated photonics applications. Despite its wide presence in materials, the figures-of-merit of electric field-induced second harmonic generation are yet to be elevated to enable novel device functionalities. Here, we show that the polar skyrmions, a topological phase spontaneously formed in PbTiO3/SrTiO3 ferroelectric superlattices, exhibit a high comprehensive electric field-induced second harmonic generation performance. The second-order nonlinear susceptibility and modulation depth, measured under non-resonant 800 nm excitation, reach ~54.2 pm V−1 and ~664% V−1, respectively, and high response bandwidth (higher than 10 MHz), wide operating temperature range (up to ~400 K) and good fatigue resistance (>1010 cycles) are also demonstrated. Through combined in-situ experiments and phase-field simulations, we establish the microscopic links between the exotic polarization configuration and field-induced transition paths of the skyrmions and their electric field-induced second harmonic generation response. Our study not only presents a highly competitive thin-film material ready for constructing on-chip devices, but opens up new avenues of utilizing topological polar structures in the fields of photonics and optoelectronics.

Angular Engineering Strategy for Enhanced Surface Nonlinear Frequency Conversion in Centrosymmetric Topological Semimetal HfGe0.92Te.

Surface nonlinear optics are essential for developments in integrated photonics and micro/nano optoelectronics. However, the nonlinear optical conversion efficiency on a surface is restricted by the finite nonlinear susceptibility of matter and the intrinsic atomic-layered interaction length between light and matter. In this work, based on an angular engineering strategy, it is demonstrated that the centrosymmetric topological semimetal HfGe0.92Te crystal has a giant and anisotropic surface second-order nonlinear susceptibility up to 5535 ± 308pm V-1 and exhibits efficient and unprecedented second-harmonic generation (SHG). The maximum optical conversion efficiency is found to be up to 3.75‰, which is 104 times higher than that obtained from a silicon surface. Because of the linear dispersion over a wide range of energies around the Dirac points, this high conversion efficiency can be maintained with SHG wavelengths ranging from the visible region (779nm) to the deep-UV region (257.5nm). This study can facilitate the development of topological photonics and integrated nonlinear photonics based on topological semimetals.

Absolute local conformation of poly(methyl methacrylate) chains adsorbed on a quartz surface.

Polymer chains at a buried interface with an inorganic solid play a critical role in the performance of polymer nanocomposites and adhesives. Sum frequency generation (SFG) vibrational spectroscopy with a sub-nanometer depth resolution provides valuable information regarding the orientation angle of functional groups at interfaces. However, in the case of conventional SFG, since the signal intensity is proportional to the square of the second-order nonlinear optical susceptibility and thereby loses phase information, it cannot be unambiguously determined whether the functional groups face upward or downward. This problem can be solved by phase-sensitive SFG (ps-SFG). We here applied ps-SFG to poly(methyl methacrylate) (PMMA) chains in direct contact with a quartz surface, shedding light on the local conformation of chains adsorbed onto the solid surface. The measurements made it possible to determine the absolute orientation of the ester methyl groups of PMMA, which were oriented toward the quartz interface. Combining ps-SFG with all-atomistic molecular dynamics simulation, the distribution of the local conformation and the driving force are also discussed.

Interband second-order nonlinear optical susceptibility of asymmetric coupled quantum wells

Asymmetric molecular bonds possess a microscopic second-order nonlinear optical polarizability p(2). Crystals built from them possess a macroscopic second-order nonlinear optical susceptibility, χ(2), if their structure lacks centrosymmetry. χ(2) can be enhanced by introducing additional asymmetry at the meta-structural level. Here, we use a dipole matrix formalism to calculate χ(2) of asymmetric GaAs/AlGaAs coupled quantum well structures at telecommunication frequencies, for which interband (rather than previously considered intersubband) optical transitions govern optical nonlinearities. Using unit cell and envelope wavefunctions and considering all possible transitions between two bound electron and two bound hole states, we predict tenfold enhancement in χ(2) in previously underexplored ranges of quantum well asymmetry and coupling barrier thickness. This work paves the way toward enhanced, tailorable second-order optical nonlinearities for semiconductor digital alloy and superlattice structures.

Complex phase of the nonresonant background in sum frequency generation spectroscopy

Sum frequency generation (SFG) spectroscopy is an interface-selective spectroscopic technique that enables us to selectively observe the vibrational or electronic resonances of molecules within a very thin interface layer. The interfacial properties probed by SFG are contained in a complex quantity called the second-order nonlinear susceptibility (χ2). It is usually believed that the imaginary part of χ2 (Im χ2) exhibits the resonant responses of the system, whereas the nonresonant responses appear solely in the real part of χ2 (Re χ2). However, it was recently theoretically pointed out that a portion of the nonresonant responses actually contributes to the observed Im χ2 spectra when the finite thickness of the interface layer is taken into account. In this study, by considering a simple air/liquid interface without any solutes as a model system, we theoretically evaluate the nonresonant contribution to experimentally accessible Im χ2 as well as to Re χ2, from which the complex phase of the nonresonant background is estimated. It is shown that the deviation of the complex phase from 0° or 180° is less than 1° even if the thickness of the interface layer is taken into account. This means that the nonresonant contribution to Im χ2 is practically negligible, and it is a very good approximation to think that the nonresonant background appears solely in Re χ2 in the case of air/liquid interfaces. This result implies that Im χ2 practically contains only the resonant responses of the system, and molecular resonances at the interface can be conveniently studied using Im χ2 spectra at such interfaces.

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).

First-principles study of water adsorption monolayer on Pt(111): Adsorption energy and second-order nonlinear susceptibility

First-principles study of water adsorption monolayer on Pt(111): Adsorption energy and second-order nonlinear susceptibility

Enhancing second harmonic generation of monolayer WS2 with edge plasmon

Transition-metal dichalcogenide (TMD) monolayers possess large second-order nonlinear susceptibility and have shown great potentials in on-chip nonlinear optical devices. However, the thickness of TMD monolayers is less than 1[Formula: see text]nm, resulting in a rather low second harmonic generation (SHG) efficiency. In this paper, we propose a physical scheme of enhancing SHG of TMD monolayers with edge plasmon. As a proof of concept demonstration, we constructed a hexagonal gold nanoplates/monolayer WS2 heterostructure with high interface quality. By performing SHG measurements, we show that SHG was enhanced by a factor of about 60. Our results set a foundation for on-chip nonlinear optical applications with TMD monolayers.

Berry Curvature Dipole Induced Giant Mid-Infrared Second-Harmonic Generation in 2D Weyl Semiconductor.

Due to its inversion-broken triple helix structure and the nature of Weyl semiconductor, 2D Tellurene (2D Te) is promising to possess a strong nonlinear optical response in the infrared region, which is rarely reported in 2D materials. Here, a giant nonlinear infrared response induced by large Berry curvature dipole (BCD) is demonstrated in the Weyl semiconductor 2D Te. Ultrahigh second-harmonic generation response is acquired from 2D Te with a large second-order nonlinear optical susceptibility (χ(2) ), which is up to 23.3 times higher than that of monolayer MoS2 in the range of 700-1500nm. Notably, distinct from other 2D nonlinear semiconductors, χ(2) of 2D Te increases extraordinarily with increasing wavelength and reaches up to 5.58nmV-1 at ≈2300nm, which is the best infrared performance among the reported 2D nonlinear materials. Large χ(2) of 2D Te also enables the high-intensity sum-frequency generation with an ultralow continuous-wave (CW) pump power. Theoretical calculations reveal that the exceptional performance is attributed to the presence of large BCD located at the Weyl points of 2D Te. These results unravel a new linkage between Weyl semiconductor and strong optical nonlinear responses, rendering 2D Te a competitive candidate for highly efficient nonlinear 2D semiconductors in the infrared region.

A potassium lead 2-methylmalonate-iodide nonlinear optical crystal with strong second-harmonic generation response and large birefringence

Nonlinear optical (NLO) crystals play a significant role in optoelectronic industry. Herein, a new NLO crystal, K(H2O)[KI][PbI(C4H4O4)], has been rationally obtained by tuning halide perovskite materials with 2-methylmalonate group. K(H2O)[KI][PbI(C4H4O4)] features that the highly distorted [PbO4I2] polyhedron with large hyperpolarizability and prominent polarizability anisotropy is served as a bifuntional unit. Remarkably, the distorted [PbO4I2] polyhedrons are aligned in an oriented arrangement that leads to the effective superposition of their microscopic second-order nonlinear susceptibilities and the enhancement of optical anisotropy. Notably, K(H2O)[KI][PbI(C4H4O4)] exhibits a strong phase-matching SHG response of 5.6 × KDP and a large birefringence (Δnobv. = 0.24@546 nm). Theoretical calculations elucidate that the strong SHG response and the large birefringence are predominantly attributed to the directional arrangement of the highly distorted [PbO4I2] polyhedrons. Our discovery provides an effective path for the rational exploration of high-performance NLO crystals.