Nonlinear Optical Research Articles

Synthesis, crystal structures and third-order nonlinear optical properties of Ni2+/Mn2+/Zn2+ naphthalene-1,5-disulfonates

Abstract In this study, we present the synthesis and characterization of three transition metal 1,5-naphthalenedisulfonates: [Ni(PTP)₂]·(1,5-NDS)·2H₂O (1), [Mn(PTP)(1,5-NDS)] (2), and [Zn(PTP)(1,5-NDS)(H₂O)]2·2.5H₂O (3). Herein, PTP refers to 4′-phenyl-2,2′:6′,2″-terpyridine while 1,5-NDS denotes the naphthalene-1,5-disulfonate dianion. Compound 1 exhibits a structure in which the sulfonate groups of the 1,5-naphthalenedisulfonate anions are not engaged in coordination. In compound 2, the Mn(II) ions are interconnected through 1,5-NDS anions to form chains along the c axis. Compound 3 features a chain structure via coordination interactions between the metal cations and the 1,5-naphthalenedisulfonate anions; adjacent chains are linked by hydrogen bonds to create a double-chain arrangement. Solid diffuse reflection spectra reveal that these compounds exhibit maximum absorption around 290 nm. The third-order nonlinear optical (NLO) properties of these complexes was investigated using the single-beam Z-scan techniques under laser irradiation at a wavelength of 532 nm. All three compounds demonstrate significant third-order nonlinear optical absorption effects with absorption coefficients of 1.85 × 10−5 m W−1 for compound 1, 1.12 × 10−5 m W−1 for compound 2 and 1.73 × 10−5 m W−1 for compound 3. The corresponding calculated values for third-order NLO susceptibility χ³ are 3.00 × 10⁻7 esu, 1.81 × 10⁻7 esu and 2.80 × 10⁻7 esu, respectively.

Remote characterization of nonlinear distortions in ultrashort pulses transmitted through dynamic fiber optic links

Ultrashort pulse sources are complex and resource-intensive. To reduce overhead and simplify operations, we had previously developed a method to deliver ultra-short pulses through fiber-optic links to multiple locations and to characterize them remotely using a compact detector module. We created a pulse pair with varying delays at the central location using a pulse shaper before launching them into the fiber links and measured the first and second-order autocorrelations at the satellite location. However, this method proved inadequate for detecting the effects of optical nonlinearities as the spectral broadening seen by a pulse pair with varying degrees of overlap differs from that of a pair of pulses undergoing nonlinear broadening separately. To overcome this drawback, we propose to launch a variable-delay pulse pair with no temporal overlap to avoid combined nonlinear distortions in the fiber link and measure the autocorrelations at the output by adding a fixed-delay interferometer to our detector module. The in-house fabricated fixed-delay element consisted of a quartz plate with its surfaces coated by partially reflecting Bragg mirrors. Using this modified setup, we have been able to detect the nonlinear distortions encountered by sub∼400fs pulses in the delivery links.

Can Low Structural Anisotropy Produce High Optical Anisotropy? Anomalous Giant Optical Birefringent Effect in PI4AlI4 in Focus.

Tetrahedral halides with broad transparency and large second harmonic effects have the potential to serve as mid-infrared wide-bandgap materials with balanced nonlinear-optical (NLO) properties. However, their regular tetrahedral motifs tend to exhibit low optical birefringence (Δn < 0.03) due to limited structural anisotropy, which constrains their practical phase-matched capability. A significant challenge in halide structural chemistry and material exploration is to enhance the Δn of tetrahedral halides while maintaining their balanced properties. The question of whether tetrahedra with low structural anisotropy can produce high optical anisotropy remains unanswered. In this study, in addition to the conventional strategy of enhancing Δn by increasing structural anisotropy, we identify a previously unreported strategy of enhancing Δn by increasing electronic anisotropy. This novel strategy model unprecedentedly enhances the Δn of an existing tetrahedral halide, PI4AlI4, to a degree not achievable by conventional techniques, with the value reaching up to 0.31@1 μm. The anomalous increase in Δn is achieved by anisotropic charge redistribution resulting from a unique charge transfer effect between the anionic and cationic tetrahedral motifs. First-principles analysis provides further corroboration of the detailed chemical bonding electronic distributions and charge transfer illustrations. It is predicted that analogous AsI4AlI4 and TeI4ZnI4 will exhibit a greater propensity for giant Δn (> 0.5@1 μm). This finding will greatly enrich the structural chemistry of sp3-hybridized tetrahedra and provide seminal ideas for the design and modulation of highly birefringent structures.

All-Optical Generation and Detection of Coherent Acoustic Vibrations in Single Gallium Phosphide Nanoantennas Probed near the Anapole Excitation.

Nanostructured high-index dielectrics have shown great promise as low-loss photonic platforms for wavefront control and enhancing optical nonlinearities. However, their potential as optomechanical resonators has remained unexplored. In this work, we investigate the generation and detection of coherent acoustic phonons in individual crystalline gallium phosphide nanodisks on silica in a pump-probe configuration. By pumping the dielectric above its bandgap energy and probing over its transparent region, we observe the radial breathing mode of the disk with an oscillation frequency around 10 GHz. We find that the detection efficiency peaks near the fundamental anapole state, matching numerical simulations. By comparing to reference gold plasmonic resonators, the dielectric nanoantennas display a modulation amplitude up to ∼5 times larger. We further demonstrate the launching of acoustic waves through the underlaying substrate and the mechanical coupling between two nanostructures placed 3 μm apart, laying the basis for photonic-phononic signal processing using dielectric nanoantennas.

Modeling Femtosecond Beam Propagation in Dielectric Hollow-Core Waveguides

The propagation of femtosecond pulses in guided structures is a matter of both fundamental and practical interest in nonlinear optics. In particular, hollow-core waveguides (HCWs) filled with a gas medium are fabricated and used as devices for the generation of attosecond pulses from high-order harmonics. In this process, the configuration of the laser field (intensity and phase) inside the waveguide is of crucial importance for enhancing the (well-known, low) efficiency of high-order harmonic generation (HHG). Here, we present numerical calculations which demonstrate the main features of the propagation process in fabricated HCWs. We consider a variety of experimental parameters like gas pressure, waveguide size, laser wavelength, and pulse energy and duration. In particular, the beam profile at the fiber input is found to be a sensitive parameter which influences the whole evolution of the laser field along the propagation. Our model is based on a split-step method modified to account for propagation in ionized media and is validated against experimental and theoretical data from the literature. Our results contribute to the description of the main features of beam propagation in HCWs and provide guiding directions for designing efficient configurations for HHG.

Exploring novel solitary wave phenomena in Klein–Gordon equation using ϕ6 model expansion method

In this study, the ϕ6-model expansion method is showed to be useful for finding solitary wave solutions to the Klein–Gordon (KG) equation. We develop a variety of solutions, including Jacobi elliptic functions, hyperbolic forms, and trigonometric forms, so greatly enhancing the range of exact solutions attainable. The 2D, 3D, and contour plots clearly show different types of solitary waves, like bright, dark, singular, and periodic solitons. This gives us a lot of information about how the KG equation doesn’t work in a straight line. Our findings highlight the ϕ6 model as a powerful tool to study nonlinear wave equations, improve our understanding of their complex dynamics, and increase the scope for theoretical exploration. The ϕ6 model expansion technique is exceptionally adaptable and may be utilised for a wide array of nonlinear partial differential equations. Despite its versatility, the technique may not be applicable to all nonlinear PDEs, especially those that do not meet the specified requirements or structures manageable by this technique. In theoretical physics, particularly in field theory and quantum mechanics, the Klein–Gordon equation is a classical model. By studying this model, we can illustrate the waves and particles movements at relativistic speeds. Among other areas, its significance in cosmology, quantum field theory, and the study of nonlinear optics are widely considered. Additionally, it provides exact solutions and nonlinear dynamics have various applications in applied mathematics and physics. The study is novel because it provides a new understanding of the complex behaviours and various waveforms of the controlling model by means of detailed evaluation. Future research could focus on further exploring the stability and physical implications of these solutions under different conditions, thereby advancing our knowledge of nonlinear wave phenomena and their applications in physics and beyond.

Two-Dimensional Ferroelectric Materials: From Prediction to Applications

Ferroelectric materials hold immense potential for diverse applications in sensors, actuators, memory storage, and microelectronics. The discovery of two-dimensional (2D) ferroelectrics, particularly ultrathin compounds with stable crystal structure and room-temperature ferroelectricity, has led to significant advancements in the field. However, challenges such as depolarization effects, low Curie temperature, and high energy barriers for polarization reversal remain in the development of 2D ferroelectrics with high performance. In this review, recent progress in the discovery and design of 2D ferroelectric materials is discussed, focusing on their properties, underlying mechanisms, and applications. Based on the work discussed in this review, we look ahead to theoretical prediction for 2D ferroelectric materials and their potential applications, such as the application in nonlinear optics. The progress in theoretical and experimental research could lead to the discovery and design of next-generation nanoelectronic and optoelectronic devices, facilitating the applications of 2D ferroelectric materials in emerging advanced technologies.

Co-assemblies of Silver Nanoclusters and Fullerenols With Enhanced Third-Order Nonlinear Optical Response.

Exploring potential third-order nonlinear optical (NLO) materials attracts ever-increasing attention. Given that the atomically precise and rich adjustable structural features of silver nanoclusters (Ag NCs), as well as the unique π-electron conjugated system of carbon-based nanomaterials, a supramolecular co-assembly amplification strategy to enhance the luminescent intensity and NLO performance of the hybrids of the two components, are constructed and the relationship between structures and optical properties are investigated. By combining water soluble Ag NCs [(NH4)6[Ag6(mna)6] (H2mna = 2-mercaptonicotinic acid, abbreviated to Ag6─NCs hereafter) containing uncoordinated carboxyl groups with water-soluble fullerene derivatives modified with multiple hydroxyl groups (fullerenols, C60─OH), the π-electron delocalization is expanded owing to non-covalent hydrogen bonding effect between Ag6─NCs and C60─OH, which provides a feasible basis for realizing the NLO response. Then, the co-assemblies are doped into a PMMA matrix to prepare composite film and its NLO properties are evaluated by Z-scan technique. Remarkably, the effective nonlinear absorption coefficients β is of two orders magnitude higher than those of the Ag6─NCs assemblies at the absence of C60─OH. This work showcases a new approach for amplifying NLO responses which greatly facilitates the development of integrated photonic devices.

Small-molecule organic ice microfibers.

Small organic molecules are essential building blocks of our universe, from cosmic dust to planetary surfaces to life. Compared to their well-known gaseous and liquid forms that have been extensively studied, small organic molecules in the form of ice at low temperatures receive much less attention. Here, we show that supercooled small-molecule droplets can be drawn into highly uniform amorphous ice microfibers with lengths up to 5 cm and diameters down to 200 nm. In the experimental test, these fiber-like ices manifest excellent mechanical flexibilities with elastic strain up to 3.3%. Meanwhile, they can guide light with loss down to 0.025 dB/cm that approaches the material absorption limit and offer high optical nonlinearity for low-threshold supercontinuum generation. Notable temperature-dependent Young's modulus and icing-induced refractive-index increase are also found. These results may open a promising category of low-temperature materials for both scientific research and technological applications.

A HTO-Type Nonlinear Optical Fluorophosphate with Ultrawide Bandgap.

Compounds having hexagonal tungsten oxides (HTO) topology are of intense research interests owing to their potential functional properties, such as nonlinear optical (NLO) performances. However, most of the reported HTO-type compounds exhibit narrow optical bandgaps because of the d-d electronic transition of compositional d0 transition metals and lone pair electrons effect of Se4+/Te4+, which hinder their applications in the high-energy field, such as deep-ultraviolet (deep-UV) region. In this work, a new fluorophosphate, (NH4)3[Sc3F5(PO4)](PO3F)2 exhibiting HTO-topological structures is reported. Remarkably, the compound shows an ultrawide optical bandgap (Eg(exp.) >6.2eV, Eg(cal.) = 6.724eV), surpassing those of reported HTO-type compounds. The fact is mainly ascribed to the collaborative effect of Sc3+ without destructive d-d transition, the PO4 and PO3F units having large LUMO-HOMO gaps. Furthermore, it exhibits a phase-matchable second-harmonic generation (SHG) response of ca. 0.65 × KDP, underscoring its potential use for NLO applications. This work provides new opportunities for discovering HTO-type NLO crystals with ultrawide bandgaps.

Optical soliton solutions of the M-fractional paraxial wave equation

This research used a modified and extended auxiliary mapping method to examine the optical soliton solutions of the truncated time M-fractional paraxial wave equation. We employed the truncated time M-fractional derivative to eliminate the fractional order in the governing model. The few optical wave examples of the paraxial wave condition can assume an insignificant part in depicting the elements of optical soliton arrangements in optics and photonics for the investigation of different actual cycles, including the engendering of light through optical frameworks like focal points, mirrors, and fiber optics. We identified the solution using a few free parameters regarding hyperbolic function form. We discovered periodic wave, bright and dark kink wave, bell wave, and singular soliton solution for the numerical values of the free parameters. To explain the behavior of various solutions, we have spoken the obtained solutions graphically for a physical explanation using MATLAB. The strategy introduced is fundamental and robust as a smart soliton solution for nonlinear partial differential equations, and it may play a crucial role in nonlinear optics, fiber optics, and communication systems.

Strategies to enhance THz harmonic generation combining multilayered, gated, and metamaterial-based architectures

Graphene has unique properties paving the way for groundbreaking future applications. Its large optical nonlinearity and ease of integration in devices notably makes it an ideal candidate to become a key component for all-optical switching and frequency conversion applications. In the terahertz (THz) region, various approaches have been independently demonstrated to optimize the nonlinear effects in graphene, addressing a critical limitation arising from the atomically thin interaction length. Here, we demonstrate sample architectures that combine strategies to enhance THz nonlinearities in graphene-based structures. We achieve this by increasing the interaction length through a multilayered design, controlling carrier density with an electrical gate, and modulating the THz field spatial distribution with a metallic metasurface substrate. Our study specifically investigates third harmonic generation (THG) using a table-top high-field THz source. We measure THG enhancement factors exceeding thirty and propose architectures capable of achieving a two-order-of-magnitude increase. These findings underscore the potential of engineered graphene-based structures in advancing THz frequency conversion technologies for signal processing and wireless communication applications.

Insight into the Origin of Second Harmonic Generation and Rational Design in the Metal Halide Borates.

Metal halide borates are promising candidates for high-performance nonlinear optical (NLO) applications, yet the origins of their second harmonic generation (SHG) properties remain unclear. Using atom response theory combined with density functional theory calculations, this study investigates why halogen substitution leads to distinctly different SHG responses in halide monoborates (Pb2BO3X) versus halide pentaborates (Pb2B5O9X). We find that the SHG origins vary between these two families due to differences in the strength of the Pb-X interactions. Interestingly, the stereochemically active lone pairs are not shown to be the primary contributors to SHG; instead, these hybridized asymmetric orbitals can introduce negative contributions. Utilizing the deffp vs αsum/(NEg) linear relationship, we predict 12 new NLO borates with strong SHG responses, including the promising NLO material Sn2B5O9I (19.2 × KDP), which is expected to exhibit the highest SHG response among halide borates reported to date. This work provides valuable insights into the relationship between elemental substitution and SHG modulation, guiding the design of advanced NLO materials.

Hafnium-Based Chiral 2D Organic-Inorganic Hybrid Metal Halides: Engineering Polarity and Nonlinear Optical Properties via Para-Substituent Effects.

Two-dimensional (2D) organic-inorganic hybrid metal halides (OIMHs), characterized by noncentrosymmetric structures arising from the incorporation of chiral organic molecules that break inversion symmetry, have attracted significant attention. Particularly, chiral-polar 2D OIMHs offer a unique platform for multifunctional applications, as the coexistence of chirality and polarity enables the simultaneous manifestation of distinct properties such as nonlinear optical (NLO) effects, circular dichroism (CD), and ferroelectricity. In this study, we report the first synthesis of hafnium (Hf)-based chiral 2D OIMHs, achieved through the strategic incorporation of para-substituents on the benzene ring of chiral organic components. By tuning the substituents, we successfully modulate the polarity of the crystal structures, resulting in both chiral-nonpolar and chiral-polar systems. Our analysis of structural and optical properties, supported by density functional theory calculations, demonstrates that the polarity of these materials can be systematically tuned, enabling adjustable band gaps and CD in the UV range (200-280 nm). Notably, halogen substitution at the para-position of the benzene ring in the organic layer produces tunable optical band gaps ranging from 4.33 to 4.48 eV, the widest reported to date for chiral-polar 2D OIMHs. Furthermore, these materials exhibit enhanced NLO properties, including a remarkable 3.3-fold increase in second-harmonic generation intensity in chiral-polar compounds compared to their chiral-nonpolar counterparts. These findings position Hf-based chiral 2D OIMHs as promising candidates for UV-region applications, such as UV NLO devices and self-driven circularly polarized light detectors, offering new opportunities for designing multifunctional optoelectronic materials by harnessing the interplay between chirality and polarity.

Mechanical Twisting-Induced Enhancement of Second-Order Optical Nonlinearity in a Flexible Molecular Crystal.

Flexible molecular crystals are essential for advancing smart materials, providing unique functionality and adaptability for applications in next-generation electronics, pharmaceuticals, and energy storage. However, the optical applications of flexible molecular crystals have been largely restricted to linear optics, with nonlinear optical (NLO) properties rarely explored. Herein, we report on the application of mechanical twisting of flexible molecular crystals for second-order nonlinear optics. The crystal formed through the self-assembly of the model compound 9-anthraldehyde (AA) features an intrinsic chiral and noncentrosymmetric structure, demonstrating high efficiency second harmonic generation (SHG) and NLO circular dichroism, which could be greatly enhanced by macroscopic mechanical twisting. The anisotropic molecular stacking imparts the AA crystal with mechanical flexibility of combined elastic bending and plastic twisting. The isochiral mechanical twisting could greatly enhance the SHG intensities by an order of magnitude depending on their M- or P-configuration. Meanwhile, the SHG circular dichroism factor gSHG-CD of the isochiral twisted crystal is greatly increased, achieving the highest reported NLO anisotropy factor among organic NLO materials. These boosted NLO performances of SHG intensity and nonlinear chiroptical response are expected to greatly expand the photonic applications of flexible molecular crystals.

Technical Routes to Achieve High Circular Polarized Luminescence in Chiral Perovskites: A Mini‐Review

AbstractChiral hybrid organic‐inorganic perovskites (HOIPs) have emerged as promising materials for optoelectronic and spintronic applications, leveraging unique properties such as circularly polarized luminescence (CPL), circularly polarized nonlinear optical (NLO) emission, and chiral‐induced spin selectivity (CISS). However, challenges remain in stabilizing these materials under environmental stresses and precisely controlling chirality for scalable use. This review summarizes five main strategies to induce chirality in HOIPs, i.e., direct incorporation of chiral cations, surface modification with chiral ligands, ion doping, template‐induced chirality, and chiral metasurfaces. Each approach offers distinct advantages for optimizing CPL efficiency and device stability, paving the way for next‐generation applications in CPL detectors, information encryption, spintronic devices, etc.

Tailored Metal‐Oxygen Bonding in Amorphous Perovskite CoSnO3 for Broadband Ultrafast Laser State Active Manipulation

AbstractAmorphous perovskite CoSnO3 has attracted significant attention due to its unique properties and various modification methods. However, modifying metal‐oxygen bonds on the nonlinear optical (NLO) characteristics remains uncharted. In this study, a dehydration method is employed to convert the metal‐hydroxyl bonds (M─OH) of hydroxide CoSn(OH)6 into metal‐oxygen bonds (M─O), successfully preparing amorphous CoSnO3 with oxygen vacancies. Subsequently, effective regulation of the metal‐oxygen bonds in amorphous CoSnO3 is achieved through an ion exchange strategy, yielding Fe‐doped CoSnO3 (Fe‐CoSnO3). Comprehensive characterization and analysis revealed that the regulation of metal‐oxygen bonds accelerated the electron transition rate, resulting in a fast recovery time of ≈245.1 fs for Fe‐CoSnO3, accompanied by a significant boost in broadband NLO properties. Notably, when Fe‐CoSnO3 is utilized as a saturable absorber (SA), it exhibited superior mode‐locking characteristics compared to CoSnO3 in the range of 1–2 µm. Specifically at the communication band of 1.5 µm, the dynamic switching between single‐wavelength and dual‐wavelength mode‐locking operations is achieved. With the ultrafast laser state manipulation, a digital encoding is also demonstrated. This work confirmed that the tailoring of metal‐oxygen bonds makes Fe‐CoSnO3 an excellent NLO material for ultrafast optical applications, and this tailoring strategy provides new insights for designing advanced NLO materials.

Nonlinear Optics in Two-Dimensional Magnetic Materials: Advancements and Opportunities.

Nonlinear optics, a critical branch of modern optics, presents unique potential in the study of two-dimensional (2D) magnetic materials. These materials, characterized by their ultra-thin geometry, long-range magnetic order, and diverse electronic properties, serve as an exceptional platform for exploring nonlinear optical effects. Under strong light fields, 2D magnetic materials exhibit significant nonlinear optical responses, enabling advancements in novel optoelectronic devices. This paper outlines the principles of nonlinear optics and the magnetic structures of 2D materials, reviews recent progress in nonlinear optical studies, including magnetic structure detection and nonlinear optical imaging, and highlights their role in probing magnetic properties by combining second harmonic generation (SHG) and multispectral integration. Finally, we discuss the prospects and challenges for applying nonlinear optics to 2D magnetic materials, emphasizing their potential in next-generation photonic and spintronic devices.

Stacking interactions in stabilizing supramolecular assembly of M[9C]2M complexes: dynamic stability with remarkable nonlinear optical features.

Continual attempts have been made to discover excellent nonlinear optical (NLO) materials. Here, we investigate the role of stacking interactions and van der Waals forces in the designed parallel stacked complexes M[9C]2M (where M = Li, Na, K, Be, Mg, and Ca) using various quantum chemical and molecular dynamics methods. The thermodynamic stability of the present complexes is also revealed by the computed interaction energy, enthalpy of formation, and Gibbs free energy of formation (ΔGf). Molecular dynamics simulations were performed at room temperature to determine the stability of the dimer formation and their complexes. Alkali metals act as a more prominent source of excess electrons at long-range interaction distances. Charge decomposition analysis (CDA) and natural bonding orbital (NBO) analyses suggest excellent charge transfer in the alkalide complexes. In this series, Li[9C]2Li exhibits an excellent hyperpolarizability response up to 2.3 × 106 a.u., while Ca[9C]2Ca performs well in alkaline-earth metal complexes. The NLO response is mostly influenced by the alkalide and earthide characteristics. Dynamic NLO features were computed at externally applied frequencies. Scattering first hyperpolarizability (βHRS) and its associated components were also measured. The effect of solvents on hyperpolarizability is also considered. The quantum theory of atoms in molecules (QTAIM) and NCI are employed to investigate the bonding nature and vdW forces in addition to stacking interactions. TD-DFT and vibrational studies are also performed. We aim for this research to pave the way for the innovative strategies in designing supramolecular assemblies tailored for NLO applications.

Enhanced two-photon absorption in hydrothermally synthesized La2O6Te nanorods for visible light photodetection.

In the present study, lanthanum oxytellurate (LOT) samples with varying La : Te ratios are successfully synthesized using a simple hydrothermal method that has enormous advantages. The prepared samples crystallize in a La2O6Te composite phase with an orthorhombic crystal system. A nanorod-like morphology is observed for each sample, and the presence of constituent elements is verified from EDX results. Chemical compositions and their oxidation states are obtained from XPS studies. Optical studies of the materials demonstrated band gap values between 2.65 and 2.78 eV, confirming the LOT samples' semiconducting nature. Broad photoluminescence (PL) spectra with peaks ranging between 650 and 750 nm were observed, and a red shift occurred by increasing the Te concentration in the samples. Overall, the samples exhibit good photoresponse characteristics under dark and light conditions with high Ion/Ioff ratios and sensitivity values. These parameters confirm the potential of LOT materials to stand out as an alternative for susceptible and effective photodetector devices. Among the samples, LOT-2 showed 10.64 μA W-1 responsivity, 5.8 × 107 Jones of detectivity, and a rise and fall time of 16.25 and 23.13 s, respectively, which was the best photodetection performance compared to the other two samples. Results from the nonlinear optical (NLO) Z-scan study demonstrated the RSA behavior and valley-peak configuration with positive n2 values corresponding to the self-focusing effect. The NLO characteristics of the materials are governed by the two-photon absorption (2PA) mechanism. Here, the LOT-2 sample displayed comparatively better results than the other two. The third-order nonlinear optical NLO susceptibility χ(3) values suggest that LOT materials have the potential to become a new candidate for various NLO applications in the coming days.