Third-order Nonlinear Parameters Research Articles

The functional moieties impact on optical, thermal, and nonlinear properties of chalcone derivatives. A comprehensive study on FT2MP

This study explains the intricate interplay between functional groups and the single crystal structure of the compound 1-(furan-2-yl)-3-(2,4,6-trimethoxyphenyl)prop-2-en-1-one (FT2MP) using Density Functional Theory (DFT) calculations. Notably, geometry optimization at B3LYP using 6-311G+(2d,p) closely aligned with experimental distances from X-ray diffraction (XRD) upon comparison. A Q-switched, frequency-doubled pulsed Nd. YAG laser (532 nm, 7 ns pulses), a 25 cm focal length lens, and a 0.001 mol/L FT2MP solution in Dimethylformamide was used to measure third-order nonlinear optical (NLO) parameters and subsequently the origin of second/third harmonic generation efficiency is discussed. The third-order nonlinear parameters of FT2MP were found to be Δɸ = 0.95, n2 = −9.605 × 10−9 cm2/W, β = 2.74 × 10−6 cm/W, and χ(3) = 5.58 × 10−7 esu. Information about the electronic structure and reactivity of the molecule is provided via the addition of Global Chemical Reactivity Descriptors (GCRD), molecular electrostatic potential (MEP) and Frontier Molecular Orbitals (FMOs) for electronic structure and reactivity insights. Hirshfeld surface analysis was used to study intermolecular interactions. This investigation indicates the potential of FT2MP for third harmonic generation, providing a comprehensive understanding of its molecular structure, reactivity, and intermolecular interactions.

Rapid formation of imidazolium glutarate (IMGA) compound and investigation of its single crystal growth by modified vertical Bridgman technique for optical limiting applications

In this paper, we have examined the formation of the imidazole glutarate adduct by protonation-deprotonation between imidazole and glutaric acid using a direct precipitation method within a short period. Following that, we have succeeded in growing imidazolium glutarate (IMGA) single crystaldirectly from synthesized material and we have also grown IMGA single crystal from the melt methodusing the vertical Bridgman technique for the first time in literature. A special Bridgman furnace was constructed with a slight modification in the winding section for this crystal growth. Crystal structure, phase purity, and growth plane were analyzed for the grown crystal from both single and powder XRD analysis. Functional groups were verified after the growth using FTIR transmittance analysis. The optical homogeneity and growth mechanism were scrutinized by birefringence interferogram and chemical etching studies, respectively. The grown IMGA has 80 % transparency in the entire visible region. The cut-off wavelength of the grown crystal is 235 nm, and the optical band gap energy of IMGA was found to be 5.26 eV. The photocurrent study reveals that IMGA has a negative photoconductivity nature. Third-order nonlinear parameters were found by the Z-scan technique. IMGA has a self-defocusing nature, negative non-linearity, and saturated absorption properties. The calculated χ(3) value is 2.045 x 10-8 esu.

Synthesis, crystal growth, structural and physicochemical properties of N-methylurea benzoic acid single crystal for non-linear optical applications

The organic single crystal of N-methylurea benzoic acid (NMUB) was synthesized and successfully grown from a slow evaporation solution growth technique for the first time in literature. The structure of the NMUB single crystal was analyzed by Single crystal X-ray diffraction (SCXRD); the crystallization of the NMUB crystal was a monoclinic crystal system with the space group P21/c. The crystal structure was combined by the carboxylic groups of H- atoms in benzoic acid with protonated N-methylurea anions. The FTIR and 1H, 13C NMR chemical shifts were analyzed by distinct vibrational groups and molecular structures. The PXRD ascertains the grown crystal crystallographic planes and crystalline nature. The Hirshfeld surfaces analysis determines the theoretical inter and intra-molecular interaction with the aid of color coding. The UV-Vis NIR spectra revealed the low absorption edge, and the optical band gap was anticipated. The crystal thermal and mechanical stability was analyzed by TG/DTA, Vickers microhardness, and void volume. The laser utility limitation for the crystal was determined through laser beam irradiated LDT analysis. The third-order optical non-linear parameters were determined from the z-scan technique.

An Experimental and Computational Investigations on the Linear and Nonlinear Optical Characteristics of Novel Chalcone (E)-1-(4-(1H-imidazol-1-yl)phenyl)-3-(1, 5a1-dihydro pyren-1-yl)prop-2-en-1-one

A novel chalcone based pyrene (E)-1-(4-(1H-imidazol-1-yl)phenyl)-3-(1,5a1-dihydropyren-1-yl)prop-2-en-1-one (EIPDP) has been successfully synthesized by Claisen-Schmidt condensation reaction. The molecular structure was optimized using density functional theory (DFT) at B3LYP/ 6-311++G(d,p) basis set. In addition, molecular electrostatic potential (MEP) was obtained to study the intramolecular charge transfer (ICT) by introducing electrophilic and nucleophilic sites on the compound surfaces. Absorption UV-Vis spectra were performed experimentally and theoretically to study the electron transitions of the EIPDP. Further, the excitation states were characterized using the hybrid exchange-correlation functional of Coulomb Attenuated Method-Becke, 3-parameter, Lee-Yang-Parr (CAM-B3LYP) with the Integral Equation Formalism Polarizable Continuum Model (IEFPCM) in Dimethyl sulfoxide (DMSO) solvent at the same basis set. The nonlinear optical (NLO) properties were investigated using Z-scan techniques with continuous wave (CW) laser at 630nm. The NLO findings disclosed that the third-order nonlinear optical parameter (χ 3) for the title compound is in the order of 10−6 esu.

Early fatigue damage evaluation based on nonlinear Lamb wave third-harmonic phase velocity matching

In this paper, third-harmonic phase velocity matching nonlinear Lamb waves are used for the early fatigue damage detection of aluminum alloys. An analysis is conducted regarding the relationship of third harmonic and third-order nonlinear parameters with fatigue accumulation. According to the analytical results, the amplitude of the third harmonic increases when the fatigue life falls below about 80%. However, when the fatigue life exceeds 80%, the third harmonic starts to decrease, and the third-order nonlinear parameters increase progressively before showing a downward trend. It can be found out that micro-cracks emerge with the accumulation of fatigue, thus reducing the amplitude of the third harmonic and causing the third-order nonlinear parameters to increase gradually and then decline. Furthermore, it is proposed to take the third harmonic amplitude and the third order nonlinear parameters as the indicators of early fatigue damage.

Third harmonic approximate phase velocity matching nonlinear early fatigue damage detection

The phase velocity matching Lamb waves are considered as an effective solution to excitation in the detection of nonlinear ultrasound early fatigue damage. In general, it is difficult to meet the phase velocity matching in real-world measurement. In this paper an approach to approximate phase velocity matching early fatigue damage detection is proposed. With the third harmonic approximate phase velocity matching modes treated as excitation frequencies by the Lamb wave dispersion curve, an analysis is conducted with regard to the time–frequency diagrams of the response signals at different frequencies. The change in the third harmonic amplitude with crack growth is analyzed by Fast Fourier Transform (FFT), which leads to the results suggesting that the third harmonic amplitude declines with crack growth. Moreover, a comparison is performed in the normalized relative third-order nonlinear parameters (NRTNP) of phase velocity matching and approximate phase velocity matching, with the relative deviation falling within 0.12.

Investigation on third-order nonlinear parameters, mechanical and dielectric behavior of alkali metal-organic C2HLiO4 H2O single crystal

A metal-organic lithium hydrogen oxalate hydrate single crystal was developed using the solution growth method. The single-crystal XRD analysis confirmed the triclinic structure and space group P1 along with the lattice parameters a = 3.439 Å, b = 5.097 Å, c = 6.141 Å, α = 78.50°, β = 84.89°, and γ = 81.41° of the grown crystal. The average crystallite size and strain within the material were calculated and compared using Debye Scherrer and Williamson-Hall method. The existence of diverse functional groups in the LHOH crystal was verified with the help of the FTIR analysis. The Z-scan method was carried out to acquire information about the developed material's third-order nonlinear characteristics that showed the material's self-focusing effect. The dielectric behavior of the compound was studied for various temperatures and frequencies. The Vicker’s microhardness analysis was carried out to collect information about the hardness number, yield strength, elastic stiffness, brittle index and fracture toughness of the grown crystal. The hardness number decreased when the applied load was increased, which indicated the normal indentation effect of the material.

Investigation on the growth, structural, optical, thermal and third-order nonlinear optical (NLO) properties of 2,3-dimethyl-N-[(E)-2,4,5-trimethoxybenzylidene] aniline (DTA) organic single crystal

Good-quality organic nonlinear single crystal of 2,3-dimethyl-N-[(E)-2,4,5-trimethoxy benzylidene] aniline (DTA) was synthesized and successfully grown at room temperature by adapting slow evaporation technique using mixed solvent of acetone and methanol. The crystal structure was experimentally confirmed by single-crystal X-ray diffraction, where the DTA crystals crystallize in the centric space group (P $$\overline{1}$$ ) with triclinic crystal system. The surface morphology of DTA was examined by the Field Emission Scanning Electron Microscope (FE-SEM) technique. The presence of various modes of functional groups of the title crystal was analyzed by Fourier-Transform Infra-Red (FT-IR) spectra. Ultraviolet–Visible-Near Infrared (UV–Vis–NIR) spectrum showed high optical transparency of ~ 88% in the Vis and NIR region with a UV–Vis absorption edge of 390 nm. The result of photoluminescence studies suggests that the DTA crystal can be used as source material to exhibit green emission light. From thermogravimetric-differential scanning calorimetry (TG-DSC) analysis, the melting point of the grown crystal was found to be 111 °C. The standard Z-Scan technique was employed to evaluate the third-order nonlinear optical properties of the DTA crystal. The obtained third-order nonlinear parameters were compared with few of the already reported NLO crystals. All these findings indicate that the title crystal may be an attractive material for nonlinear optical device applications.

Experimental results of tomographing the third-order acoustic nonlinear parameter

Tomography of the acoustic nonlinear parameters is a method of obtaining information about biological tissue using nonlinear interaction of acoustic waves. In the schemes under consideration, three plane coded non-collinear signals probe an investigated object and intersect inside it. Each point of the intersection region generates coded signal at the third-order combination frequencies. Correlation processing of received total signal allows determining the combination of the second- and third-order acoustic nonlinear parameters in each resolution element of the object. Results of physical experiment on reconstructing the spatial distribution of the combined acoustic nonlinear parameter by the scheme with one monochromatic and two coded probing signals are presented. Principal disadvantage of this scheme is nonlocality of generation area of the unique coded combination signal carrying information about the object. This makes it impossible to distinguish the signal generated by the only fixed resolution element of the object. As a consequence, reconstructed quantitative values of the nonlinear parameters can be distorted. The next step is the scheme with three coded probing signals, that is more complex for implementation. Nevertheless, now each unique signal is generated by the single resolution element. Thereby, it becomes possible to adequately reconstruct the desired values of nonlinear parameters.

Ag/CeO2 Schottky-type nanoheterostructures: Enhanced third-order nonlinear optical susceptibility under the near infrared irradiation

Cerium dioxide nanoparticles have been synthesized by the hydrothermal method and then have been loaded with Ag metal using the conventional wetness incipient impregnation to form Ag/CeO2 nanoheterojunctions. The physiochemical characteristics of as-synthesized samples have been justified using X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM), energy dispersive spectroscopy (EDS) and transmission electron microscopy (TEM). UV–Vis reflectance spectroscopy (UV–Vis DRS) and photoluminescence (PL) emission techniques have been employed to investigate the linear optical properties. Characterization of UV–Vis DRS has revealed broadened light absorption towards visible light for Ag/CeO2 nanoheterojunctions owing to the presence of the surface plasmon resonance. The PL results have also exhibited more efficient photo-excited charge separation that can be ascribed to the internal electric field formed across Schottky interface. The third-order nonlinear parameters have been examined by single-beam Z-scan setup in the near infrared spectral range using pulsed Nd-YVO4 laser. The Z-scan results have indicated negative values of nonlinear refractive indices providing evidences for the self-defocusing behaviors at the excitation wavelength of 1064 nm. The measured magnitude of the third-order nonlinear susceptibility for Ag/CeO2 nanoheterojunctions has been found to be 78.6 × 10−6 esu, showing an enhancement about 16 times higher than that of pristine CeO2. The increased nonlinear susceptibility in such heterostructures opened up a new way for appropriately designing new types of nonlinearity-based devices having a promising application in the photonic systems.

Structural and optical characteristic features of RF sputtered CdS/ZnO thin films**Project supported by the Deanship of Scientific Research, Taif University, Kingdom of Saudi Arabia (Grant No. 1-440-6136).

In this study, CdS/ZnO (2:3 mol%) thin films are successfully deposited on quartz substrates by using the sputtering technique. Good images on the structural and optical characteristic features of CdS/ZnO thin films before and after annealing are obtained. The CdS/ZnO thin films are annealed respectively at temperatures of 373 K, 473 K, and 573 K and the structural features are examined by XRD, ATR-FTIR, and FESEM. The optical properties of CdS/ZnO thin films such as refractive indices, absorption coefficients, optical band gap energy values, Urbach energy values, lattice dielectric constants, and high frequency dielectric constants are determined from spectrophotometer data recorded over the spectral range of 300 nm–2500 nm. Dispersion parameters are investigated by using a single-oscillator model. Photoluminescence spectra of CdS/ZnO thin films show an overall decrease in their intensity peaks after annealing. The third-order nonlinear optical parameter, and nonlinear refractive index are also estimated.

Effect of Time-Dependent Strength Recovery of Composite Materials: Quantification Through Higher Order Ultrasonic Non-Linearity Using Lamb Waves

Abstract The understanding of strength recovery behavior under a dynamic loading environment provides a guidance for optimizing the design of composite structures for in-service applications. Although established for metals, the quantification of strength recovery in carbon fiber-reinforced viscoelastic composites is still an area under active research. This study aims to understand the effects of fatigue loading rates on the damage behaviors of stress-relaxed carbon fiber-based composites. Hence, the time-dependent strength recovery in woven composites is quantified experimentally using two mutually exclusive approaches under identical fatigue loading environments. In the first approach, the strength recovery is quantified by the dissipated non-linearity in Lamb wave propagation due to the damage state of the composite materials. This is quantified and shown coupled with second- and third-order non-linear parameters. In the second approach, ultrasonic acoustic pressure waves are utilized to quantify the fatigue-induced internal stress and the damage accumulation. A comparison of these two approaches leads to the assessment of strength reduction which is experimentally validated with the remaining strength of the specimens.

Studies on third order nonlinear optical properties of Nickel Boro Phthalate NLO crystal

Single crystals of Nickel Boro Phthalate (NBP) are grown by the slow evaporation technique. The crystals are subjected to Single crystal x-ray diffraction to analyse the crystal lattice parameters, and the crystal structure is found to be triclinic. The presence of functional groups has been estimated qualitatively from the Fourier transform infrared spectroscopy and elemental analysis is done using the Energy dispersive x-ray spectral study. The UV-visible spectral studies indicate a broad window of transparency in the entire visible and infrared region and the fundamental frequency is determined to be 285 nm. Optical properties such as the dielectric constant, polarizability, susceptibility, optical and electrical conductivity are presented graphically. Third-order nonlinear parameters are evaluated by the Z scan technique using continuous wave 532 nm diode- pumped Nd:YAG laser. Closed aperture mode indicates the self-defocusing nature and negative nonlinearity of the crystal. Open aperture mode reveals the saturation absorption within the crystal. The nonlinear optical parameters such as nonlinear refractive index n2, nonlinear absorption coefficient β and nonlinear susceptibility χ(3) are also determined.

Investigation of Material Nonlinearity Measurements Using the Third-Harmonic Generation

With respect to harmonic generation measurements in isotropic materials, the amplitude of the third-harmonic wave generally depends on both β <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (the square of the second-order nonlinear parameter β) and y (the third-order nonlinear parameter). Therefore, some care should be taken when measuring these parameters using the third-harmonic amplitude. The purpose of this paper is to investigate detailed theoretical and measurement techniques for the accurate determination of β <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> which dominates the third-harmonic amplitude in most biological fluids and crystalline solids. The theory deals with harmonic generation in materials with cubic nonlinearity and defines the formula for measuring β <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> with corrections for diffraction and attenuation. These corrections are derived from the Westervelt equation and play an important role in the measurement of nonlinear parameters. The third-harmonic amplitude that varies with the distance in water is obtained for the measurement of β <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . β is also measured from the second-harmonic amplitude for comparison. We also confirm the required input voltage to stably generate the third harmonic and discuss the effects of diffraction and attenuation correction on the β <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> determination. The measured β <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in the propagation range of 0.05-0.2 m agrees well with the square of the measured β, revealing that the third-harmonic amplitude is closely related to β <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , not y. This paper covers comprehensive theories, experimentation, and analysis related to the measurement of third-harmonic generation in isotropic media and can be immediately applied to crystalline solids.

Thermal, mechanical, optical and dielectric properties of piperazinium hydrogen phosphite monohydrate NLO single crystal

Optical transparent crystal of piperazinium hydrogen phosphite monohydrate (PHPM) was grown by slow evaporation method. The grown crystal was characterized by single crystal X-ray diffraction analysis and the crystal belongs to monoclinic system. The functional groups present in PHPM crystal were confirmed by FTIR analysis. UV–Visible spectrum shows that the PHPM crystal is transparent in the visible region. The mechanical behavior of PHPM crystal was characterized by Vickers hardness test. Thermal stability of PHPM crystal was analyzed by thermogravimetric analysis. Dielectric studies were also carried out for the grown crystal. The third-order nonlinear parameters such as nonlinear refractive index and nonlinear absorption coefficient have been calculated using Z scan technique.

Four-wave mixing and nonlinear parameter measurement in a gallium-nitride ridge waveguide

Gallium-nitride (GaN) is a promising material platform for integrated electro-optic devices due to its wide direct bandgap, pronounced nonlinearities and high optical damage threshold. Low-loss ridge waveguides in GaN layers were recently demonstrated. In this work, we provide the first report of four-wave mixing in a GaN waveguide at telecommunication wavelengths, and observe comparatively high nonlinear propagation parameters. The nonlinear coefficient of the waveguide is measured as 1.6 ± 0.45 [W × m]−1, and the corresponding third-order nonlinear parameter of GaN is estimated as 3.4 ± 1e-18 [m2/W]. The results suggest that GaN waveguides could be instrumental in nonlinear-optical signal processing applications.

Ge-rich graded-index Si1-xGex waveguides with broadband tight mode confinement and flat anomalous dispersion for nonlinear mid-infrared photonics.

This work explores the use of Ge-rich graded-index Si1-xGex rib waveguides as building blocks to develop integrated nonlinear optical devices for broadband operation in the mid-IR. The vertical Ge gradient concentration in the waveguide core renders unique properties to the guided optical mode, providing tight mode confinement over a broadband mid-IR wavelength range from λ = 3 µm to 8 µm. Additionally, the gradual vertical confinement pulls the optical mode upwards in the waveguide core, overlapping with the Ge-rich area where the nonlinear refractive index is larger. Moreover, the Ge-rich graded-index Si1-xGex waveguides allow efficient tailoring of the chromatic dispersion curves, achieving flat anomalous dispersion for the quasi-TM optical mode with D ≤ 14 ps/nm/km over a ~1.4 octave span while retaining an optimum third-order nonlinear parameter, γeff. These results confirm the potential of Ge-rich graded-index Si1-xGex waveguides as an attractive platform to develop mid-IR nonlinear approaches requiring broadband dispersion engineering.

Synthesis and characterization of semi-organic nonlinear optical material: Sodium para-nitrophenolate para-nitrophenol dihydrate

Single crystal of sodium para-nitrophenolate para-nitrophenol dihydrate (SPPD) was grown using slow evaporation solution growth technique with the crystal dimensions of 17mm×11mm×6mm. The structure of the SPPD crystal was examined by X-ray diffraction analysis and the functional groups, hydrogen bonding interactions were identified using FT-IR and FT-Raman spectra. The UV–vis-NIR absorption spectrum revealed that the UV lower cut-off wavelength was 260nm and the optical band gap of the crystal was 4.76eV. The material was thermally stable up to 128°C as determined by the TG-DTA curves. The mechanical behavior of the grown crystal was studied using Vickers microhardness. Dielectric constant and dielectric loss were also measured as a function of frequency between 5Hz and 5MHz and temperature between 40 and 100°C, respectively. The second-harmonic generation efficiency was found to be five times greater than that of KDP. The third-order nonlinear parameters such as nonlinear refractive index (n2), nonlinear absorption coefficient (β) and third-order susceptibility |χ(3)| were calculated using Z-scan technique.

Principles of third-order acoustic tomography based on nonlinear interaction of coded waves

The paper considers a tomography scheme based on nonlinear interaction of three noncollinear primary waves and discusses how a signal appearing due to double second-order interaction affects estimation of the acoustic nonlinear parameters of a studied object. A technique is proposed for obtaining separate estimates of second- and third-order nonlinear parameters in the coding of the three primary waves.

Relationship between second- and third-order acoustic nonlinear parameters in relative measurement

The higher-order acoustic nonlinear parameters are considered effective damage indices in the field of nondestructive evaluation (NDE). They are defined by using the displacement amplitudes of the fundamental frequency and the harmonics, which are called the absolute nonlinear parameters. Generally, however, it is difficult to measure the very small displacement amplitudes of high-frequency harmonics. Therefore, the simplified parameters using the detected wave signal amplitudes, which are known as the relative nonlinear parameters, have been widely used, although their applications are limited to the relative comparison of before and after damage of a single material under consistent experimental circumstances. In this paper, in order to make clear the concept of relative parameter, we presented first that the relative ratio of the simplified parameters is identical to that of the absolute parameters when the detected signal amplitudes are linearly proportional to the actual displacement amplitudes with respect to the fundamental frequency and the harmonics. In addition, the new relationship between the relative ratio of simplified second-order parameter and the relative ratio of simplified third-order parameter was derived from the relationship between the absolute second- and third-order parameters. This new relationship was successfully verified based on experimental results obtained from Al 6061-T6 processed for different heat treatment times, where it was confirmed in advance that the PZT detection signal amplitudes at the fundamental frequency and its second- and third-order harmonics were linearly proportional to the displacement amplitudes.