Second-order Nonlinear Coefficient Research Articles

A comparison of eight weakly dispersive Boussinesq-type models for non-breaking long-wave propagation in variable water depth

Weakly dispersive Boussinesq-type models are extensively used to model long-wave propagation in coastal areas and their interaction with coastal infrastructures. Many equations falling in this category have been formulated during the last decades, but few detailed comparisons between them can be found in the literature. In this work, we investigate theoretically and with computational experiments eight variants of the most popular models used by the coastal engineering community. Both weakly nonlinear and fully nonlinear models are considered, hoping to understand better when the additional complexity of the latter class of models is necessary or justified. We provide an overview and discuss the properties of these models, including the linear dispersion relation in uniform water depth, the second-order nonlinear coupling coefficient, the shoaling gradient, and the sensitivity to wave trough instabilities. The models are then numerically discretised using the same general strategy in a single numerical code, using fourth-order methods for time and space discretisation. Their capacity to simulate coastal wave propagation and their transformation when approaching the shore is assessed on three challenging one-dimensional benchmarks. It appears that fully nonlinear models are more consistent than their weakly nonlinear counterparts, which can occasionally perform better but show different behaviours depending on the case.

Investigation into NSAW excitation and modulation utilizing the grating mask technique

Narrowband surface acoustic wave (NSAW) method is a promising ultrasonic detection technique, with its laser-induced excitation technology offering the advantages of non-contact and flexible regulation. This paper proposes an NSAW excitation and modulation system based on the grating mask method to detect the nonlinear characteristics of the spectra caused by the variation in material surface properties. According to Doyer’s sharp line excitation theory, a strip line source array excitation model formed by superposition principle is established, and the effects of duty ratios of the masks on NSAW spectra amplitude characteristics are interpreted. An NSAW excitation and B-scan experimental system that can realize line source spacing changes is developed, and the effects of cylindrical lens height and masks with different duty ratios on NSAW spectra modulation are studied. The experimental results show that the amplitude ratios (the ratio of the double frequency amplitude to the second harmonic amplitude) are consistent with the results of the Doyer superimposed strip line source array excitation model in which the excitation light source energy is evenly distributed. The second-order nonlinear coefficients extracted from the experimental spectra can effectively characterize the surface properties of 6061 aluminum alloy at different annealing temperatures.

Helically twisted nonlinear photonic crystals.

Nonlinear photonic crystals with a helical structure in the second-order nonlinear coefficient (χ(2)) are fabricated using infrared femtosecond laser poling in ferroelectric Sr0.61Ba0.39Nb2O6 crystals. The quasi-orbital angular momentum of the helical χ(2) structure can be imprinted on the interacting photons during nonlinear optical processes, allowing the topological charge of the generated photons at new frequencies to be controlled. Here we study the case of a double-helix nonlinear photonic structure for the generation of a second-harmonic vortex beam from a Gaussian pump beam without phase singularity. The conservation law for orbital angular momentum in the second-harmonic process is also verified, with the topological charge of the pump photons being fully compensated by the double-helix structure. The flexible control of light carrying orbital angular momentum (OAM) at new frequencies will find important applications in both classical and quantum photonics, such as nonlinear wavefront shaping and multidimensional entanglement of photons.

High second-order nonlinearity in single-domain tetragonal PMN-PT single crystal

Recently, Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-xPT) single crystals present tremendous potential in optical applications such as Q-switches and invisible robotic devices because they possess high electro-optic properties and perfect transparency simultaneously. However, due to the difficulties in testing and sample preparation, the nonlinear optical properties of PMN-PT single crystals have not been reported yet, which poses a bottleneck for exploring its nonlinear application. In this work, a large second-order nonlinear coefficient (d31 ∼ 77.9 pm V−1) of single domain PMN-0.39PT single crystal has been revealed, which is times times higher than the maximum nonlinear coefficient of commercial LiNbO3 single crystal (d33 = 25.4 pm V−1). The complete set of nonlinear coefficients of the sample has been determined by second harmonic generation microscopy. This work presents the promising nonlinear optical property in PMN-PT single crystals and opens a door for designing high-performance nonlinear optical devices.

Combining ultrahigh index with exceptional nonlinearity in resonant transition metal dichalcogenide nanodisks

Second-order nonlinearity in solids gives rise to a plethora of unique physical phenomena ranging from piezoelectricity and optical rectification to optical parametric amplification, spontaneous parametric down-conversion and the generation of entangled photon pairs. Monolayer transition metal dichalcogenides, such as MoS2, exhibit one of the highest known second-order nonlinear coefficients. However, the monolayer nature of these materials prevents the fabrication of resonant objects exclusively from the material itself, necessitating the use of external structures to achieve the optical enhancement of nonlinear processes. Here we exploit the 3R phase of a molybdenum disulfide multilayer for resonant nonlinear nanophotonics. The lack of inversion symmetry—even in the bulk of the material—provides a combination of massive second-order susceptibility, extremely high and anisotropic refractive index in the near-infrared region (n > 4.5) and low absorption losses, making 3R-MoS2 highly attractive for nonlinear nanophotonics. We demonstrate this by fabricating 3R-MoS2 nanodisks of various radii, which support resonant anapole states, and observing substantial (>100-fold) enhancement of second-harmonic generation in a single resonant nanodisk compared with an unpatterned flake of the same thickness. The enhancement is maximized at the spectral overlap between the anapole state of the disk and the material resonance of the second-order susceptibility. Our approach unveils a powerful tool for enhancing the entire spectrum of optical second-order nonlinear processes in nanostructured van der Waals materials, thereby paving the way for nonlinear and quantum high-index transition metal dichalcogenide nanophotonics.

Effect of the nonlinear dispersive coefficient on time-dependent variable coefficient soliton solutions of the Kolmogorov-Petrovsky-Piskunov model arising in biological and chemical science

In this article, we study the soliton solutions with a time-dependent variable coefficient to the Kolmogorov-Petrovsky-Piskunov (KPP) model. At first, this model was used as the genetics model for the spread of an advantageous gene through a population, but it has also been used as a number of physics, biological, and chemical models. The enhanced modified simple equation technique applies to get the time-dependent variable coefficient soliton solutions from the KPP model. The obtained solutions provide diverse, exact solutions for the different functions of the time-dependent variable coefficient. For the special value of the constants, we get the kink, anti-kink shape, the interaction of kink, anti-kink, and singularities, the interaction of instanton and kink shape, instanton shape, kink, and bell interaction, anti-kink and bell interaction, kink and singular solitons, anti-kink and singular solitons, the interaction of kink and singular, and the interaction of anti-kink and singular solutions to diverse nature wave functions as time-dependent variable coefficients. The presented phenomena are clarified in three-dimension, contour, and two-dimension plots. The obtained wave patterns are powerfully exaggerated by the variable coefficient wave transformation and connected variable parameters. The effect of second-order and third-order nonlinear dispersive coefficients is also explored in 2D plots.

Extending the propagation length of graphene plasmons via nonlinear frequency conversion

Graphene plasmons (GPs) are broadband and electrically tunable mid-infrared (MIR)/terahertz (THz) excitations, exhibiting high confinement factors exceeding two orders of magnitude. Such highly confined modes are extremely attractive for nonlinear frequency conversion owing to the large inherent field enhancement. However, this high confinement is also accompanied by losses, and together with the centrosymmetric nature of graphene practical usage of its properties in second-order nonlinear processes remains hindered. In this paper, we introduce an approach for realizing quasi-phase-matching (QPM) of propagating GPs, by placing the graphene on an orientationally patterned GaAs substrate—a transparent material in the MIR/THz range with a large second-order nonlinear coefficient. We analyze the complete frequency/Fermi-level space for QPMed second-harmonic generation of GPs in the MIR and THz and demonstrate GP amplification and loss compensation. We find that our approach provides extended GP propagation lengths that are more than twice larger than the state-of-the-art cryogenic temperature propagation lengths. The approach is general to all second-order nonlinear processes, such as sum and difference frequency generation, thus opening a path for efficient and electrically tunable QPM nonlinear processes at the atomic scale.

Nonlinear photonic crystals for completely independent asymmetric holographic imaging.

Nonlinear photonic crystals (NPCs) are microstructures characterized by a spatially modulated second-order nonlinear coefficient that have been extensively used for the generation and beam-shaping of coherent light at new frequencies. NPCs for asymmetric optical transmission have a significant impact on novel and multifunction photonic devices. However, nonreciprocal NPCs capable of completely independent asymmetric holographic imaging for the opposite propagation directions have not been reported. Here, we propose a holographic combiner for a different independent image generation at the second-harmonic (SH) wavelength when illuminated from opposite sides of NPCs. The design of the holographic combiner is based on a 3D nonlinear detour phase holography and an orbital angular momentum (OAM) multiplexing nonlinear holography. This work achieves completely independent asymmetric holographic imaging at the SH frequency by using NPCs, which may have potential applications in classical and quantum optical devices.

Indirect and direct electronic transitions and electron transport properties of van der Waals NbOCl2.

In this paper, the optical and electron transport properties of the two-dimensional (2D) van der Waals (vdW) niobium oxide dichloride (NbOCl2) crystal with extremely high second-order nonlinear coefficients are investigated theoretically. We found that the strong absorption of NbOCl2 in the infrared region is caused by the indirect transition accompanied by phonons and confirmed that the interaction between layers is very weak. However, the study of electron transport properties shows that the interlayer interaction of NbOCl2 has a certain degree of influence on the scalability of electrical and optical properties. Because of the strong anisotropy of the NbOCl2 material, it will be a more optimized choice for constructing on-chip photoelectric or thermal devices in the Nb-Cl-Nb direction.

Linear and nonlinear optical absorption of 2D monolayer NbOCl2

The in-layer crystal structure of a two-dimensional material is stable, but the interaction force between the atomic layers is much weaker. Niobium oxide dichloride (NbOCl2) not only has high second-order nonlinear coefficients unique to common monolayer two-dimensional materials but also weak electronic coupling between layers. These characteristics make NbOCl2 very suitable as a quantum light source in quantum optical systems. This article mainly studies the linear and nonlinear optical absorption of two-dimensional monolayer NbOCl2. The characterization means include a surface distance projection map and three views, total density of states, photoelectron spectrum, charge density difference, transition dipole moment density, one-photon absorption spectrum, and two-photon absorption spectrum. There is a size effect on the total density of states, photoelectronic energy spectrum, and one-photon absorption spectrum, that is, as the size increases, the total density of states is red-shift, the photoelectronic energy spectrum is blue-shift, and the absorption spectrum has a significant red-shift. The charge density difference indicates that there is charge transfer around the Nb atom of NbOCl2. The transition dipole moment density changes periodically. The study of the two-photon absorption spectrum shows that it is dominated by a one-step transition. In summary, our work provides an in-depth understanding of its optical properties and is of great significance for the miniaturization of quantum light sources.

A Cross-Medium Uplink Communication Model Merging Acoustic and Millimeter Waves

Uplink communication across the water–air interface holds great potential for offshore oil surveys and military applications. Among the various methods available for implementing uplink communication, translational acoustic-RF (TARF) communication stands out due to its ability to withstand wave interference and exhibit low absorption losses. However, the physical processes underlying such systems are currently under-researched, and channel models for evaluating its communication performance indicators are lacking. Herein, we propose a signal-to-noise ratio (SNR) channel model for evaluating the performance metrics of an uplink communication system combining acoustic and millimeter waves for the first time and validate the accuracy of the proposed model through experiments. Specifically, in the process of model construction, the physical process of the communication system was deeply studied, and the corrections of multipath effects, box vibrations, and second-order nonlinear coefficients of the amplitude of the water surface were realized. The water-to-air cross-medium communication system was built, and communication experiments were conducted to validate the feasibility of combining acoustic and millimeter wave communication. This research provides a theoretical and experimental foundation for the design and evaluation of TARF communication systems, providing valuable guidance for enhancing the system’s performance metrics and promising an innovative approach for modern seaborne communication.

Adapted poling to break the nonlinear efficiency limit in nanophotonic lithium niobate waveguides.

Nonlinear frequency mixing is a method to extend the wavelength range of optical sources with applications in quantum information and photonic signal processing. Lithium niobate with periodic poling is the most widely used material for frequency mixing due to its strong second-order nonlinear coefficient. The recent development using nanophotonic lithium niobate waveguides promises to improve nonlinear efficiencies by orders of magnitude thanks to subwavelength optical confinement. However, the intrinsic nanoscale inhomogeneity of nanophotonic lithium niobate waveguides limits the coherent interaction length, leading to low nonlinear efficiencies. Here we show improved second-order nonlinear efficiency in nanophotonic lithium niobate waveguides that breaks the limit imposed by nanoscale inhomogeneity. This is realized by developing the adapted poling approach to eliminate the impact of nanoscale inhomogeneity. We realize an overall second-harmonic efficiency of 104% W-1 (without cavity enhancement), approaching the theoretical performance for nanophotonic lithium niobate waveguides. The ideal square dependence of the nonlinear efficiency on the waveguide length is recovered. Phase-matching bandwidths and temperature tuneability are improved through dispersion engineering. We finally demonstrate a conversion ratio from pump to second-harmonic power greater than 80% in a single-pass configuration with pump power as low as 20 mW. Our work therefore breaks the trade-off between the conversion ratio and pump power, offering a potential solution for highly efficient and scalable nonlinear-optical sources, amplifiers and converters.

Nonlinear generation of an optical bottle beam in domain-engineered ferroelectric crystals.

Nonlinear wavefront shaping in periodically poled ferroelectric crystals has received great attention because it offers a convenient way to generate a structured light beam at new frequencies. In contrast to structurally uniform beams like Laguerre-Gaussian or Hermite-Gaussian modes, here we demonstrate the possibility to generate a spatially varied optical bottle beam via a frequency doubling process in a domain-engineered Sr0.61Ba0.39Nb2O6 (SBN) crystal. The nonlinear holography method was employed to design the modulation pattern of the second-order nonlinear coefficient χ(2), and the femtosecond laser poling was used to imprint the χ(2) pattern into the SBN crystal via ferroelectric domain inversion. The second harmonic bottle beam with zero intensity in its center that is surrounded in all three dimensions by light was observed with the incidence of a fundamental Gaussian beam. These results are useful for nonlinear generation and control of structured light at new frequencies, which has important applications in nonlinear photonics and quantum optics.

High-Efficiency Second-Harmonic Generation Using Quasi-Bound State in LiNbO3 Metasurface

We numerically demonstrated a high-efficiency second-harmonic generation (SHG) using quasi-bound state in the continuum (quasi–BIC) in thin film LiNbO3 (TFLN) metasurface. The TFLN possessed exceptionally high second-order nonlinear coefficients, contributing to the enhanced SHG performance. An eccentric cylinder unit cell was presented to achieve high Q–factor resonances associated with the asymmetric parameter introduced. Simulations showed that the high efficiency of the second-harmonic conversion was obtained by using the high Q–factor of the asymmetric dielectric cylinder metasurface, and it achieved a high SHG efficiency of 6.5% at pump intensities as low as 1 MW/cm2 at a normal incident. Furthermore, the simulation results indicated that breaking the symmetry through oblique incidence was more effective in achieving a higher Q–factor compared to altering the structural parameters. Specifically, under 1° oblique incidences, the conversion efficiency could reach 1.2% at an incident power of 1 kW/cm². We have proposed a method to achieve a high conversion efficiency of second-harmonic generation in low-refractive-index materials. Our work not only offers theoretical support but also provides valuable insights for the advancement of efficient nonlinear frequency doubling technology, optical communication, and sensing applications.

Assessment of tight-binding models for high-harmonic generation in zinc blende materials.

Using a simulator for semiconductor Bloch equations (SBEs) accounting for the entire Brillouin zone, we examine the tight-binding (TB) description for zinc blende structure as a model for high-harmonic generation (HHG). We demonstrate that TB models of GaAs and ZnSe exhibit second-order nonlinear coefficients that compare favorably with measurements. For the higher-order portion of the spectrum, we use the results published by Xia et al. in Opt. Express26, 29393 (2018)10.1364/OE.26.029393 and show that the HHG spectra measured in reflection can be closely reproduced by our simulations free of adjustable parameters. We conclude that despite their relative simplicity, the TB models of GaAs and ZnSe represent useful tools to study both the low- and higher-order harmonic response in realistic simulations.

Multiplexing Linear and Nonlinear Bragg Diffractions through Volume Gratings Fabricated by Femtosecond Laser Writing in Lithium Niobate Crystal

The femtosecond-laser-writing technique provides a flexible method for fabrication of nonlinear photonic crystals in three dimensions, providing structures that enable efficient complex nonlinear wave interactions and modulation for applications including nonlinear holography, nonlinear beam shaping, and waveguide-integrated wavelength conversion. However, the tightly focused laser pulse inevitably causes structural modification and then changes the local refractive index, resulting in additional linear modulation of the interacting waves. Here, we use the same periodic distributions of the refractive index and the second-order nonlinear coefficient for grating arrays engineered in lithium niobate crystals by femtosecond laser writing to achieve polarization-dependent linear and nonlinear Bragg diffractions simultaneously. The experimental results show that the linear and nonlinear diffraction efficiencies range up to 31% and 2.9 × 10−5, respectively, for grating arrays with dimensions of 100 μm (x) × 100 μm (y) × 100 μm (z). This work paves the way toward the realization of the multiplexing of linear and nonlinear optical modulations in a single structure for potential applications that include multidimensional optical data storage and optical coding.

Fabrication of low-loss III-V Bragg-reflection waveguides for parametric down-conversion

Entangled photon pairs are an important resource for many types of quantum protocols. Semiconductor Bragg-reflection waveguides are a promising photon-pair source due to mature fabrication, integrability, large transparency window in the telecom wavelength range, integration capabilities for electro-optical devices as well as a high second-order nonlinear coefficient. To increase performance, we improved the fabrication of Bragg-reflection waveguides by employing fixed-beam-moving-stage optical lithography, low-pressure, and low chlorine concentration etching, and resist reflow. The reduction in sidewall roughness yields a low optical loss coefficient for telecom wavelength light of αreflow = 0.08 (6) mm−1. Owing to the decreased losses, we achieved a photon-pair production rate of 8800 (300) (mW · s · mm)−1, which is 15-fold higher than in previous samples.

Two Mixed-Alkali-Metal Selenates as Short-Wave Ultraviolet Nonlinear-Optical Materials.

Two novel mixed-alkali-metal selenate nonlinear-optical (NLO) crystals, Na3Li(H2O)3(SeO4)2·3H2O (I) and CsLi3(H2O)(SeO4)2 (II), have been successfully synthesized by an aqueous solution evaporation method. Both compounds feature the unique layers constructed of the same functional moieties including SeO4 and LiO4 tetrahedra: [Li(H2O)3(SeO4)2·3H2O]∞3- layers in I and [Li3(H2O)(SeO4)2]∞- layers in II. The titled compounds display wide optical band gaps of 5.62 and 5.66 eV, respectively, according to the UV-vis spectra. Interestingly, they exhibit significantly different second-order nonlinear coefficients (0.34 × KDP and 0.70 × KDP, respectively). Detailed dipole moment calculations manifest that the large disparity can be attributed to the difference in the dipole moment of the crystallographically independent SeO4 and LiO4 groups. This work confirms that alkali-metal selenate system is an excellent candidate for short-wave ultraviolet NLO materials.

Structural design and characterization of a new chalcone molecular derivative crystal DMNC with high second-order nonlinear coefficient

Structural design and characterization of a new chalcone molecular derivative crystal DMNC with high second-order nonlinear coefficient

Stereochemically Active Lone Pairs and Nonlinear Optical Properties of Two-Dimensional Multilayered Tin and Germanium Iodide Perovskites.

Two-dimensional (2D) metal halide perovskites are promising tunable semiconductors. Previous studies have focused on Pb-based structures, whereas the multilayered Sn- and Ge-based analogues are largely unexplored, even though they potentially exhibit more diverse structural chemistry and properties associated with the more polarizable ns2 lone-pair electrons. Herein, we report the synthesis and structures of 2D tin iodide perovskites (BA)2(A)Sn2I7, where BA = n-butylammonium and A = methylammonium, formamidinium, dimethylammonium, guanidinium, or acetamidinium, and those of 2D germanium iodide perovskites (BA)2(A)Ge2I7, where A = methylammonium or formamidinium. By comparing these structures along with their Pb counterparts, we establish correlations between the effect of group IV-cation's lone-pair stereochemical activity on the perovskite crystal structures and the resulting semiconducting properties such as bandgaps and carrier-phonon interactions and nonlinear optical properties. We find that the strength of carrier-phonon interaction increases with increasing lone-pair activity, leading to a more prominent photoluminescence tail on the low-energy side. Moreover, (BA)2(A)Ge2I7 exhibit strong second harmonic generation with second-order nonlinear coefficients of ∼10 pm V-1 that are at least 10 times those of Sn counterparts and 100 times those of Pb counterparts. We also report the third-order two-photon absorption coefficients of (BA)2(A)Sn2I7 to be ∼10 cm MW-1, which are one order of magnitude larger than those of the Pb counterparts and traditional inorganic semiconductors. These results not only highlight the role of lone-pair activity in linking the compositions and physical properties of 2D halide perovskites but also demonstrate 2D tin and germanium iodide perovskites as promising lead-free alternatives for nonlinear optoelectronic devices.