Structure and Nonlinear Refractive Index of Bismuth Borate Glass

The method of conventional glass melting is used to study the glass formation region of Bi2O3-B2O3-TiO2-La2O3 system. The instrument of Differential Scanning Calorimeter （DSC） is used to research the glass stability. Raman spectra and IR spectra are used to speculate on the structure of glasses. The refractive index of glass is measured by prism coupler. With increase of Bi2O3, the glass stability, the amount of [BiO3] group and boron-oxygen loops decrease, while the content of B-O- bond, refractive index and nonlinear refractive index increase.

Nonlinear Refractive Index and Absorption Coefficient of Single-Shell Semiconductor Carbon Nanotube

The nonlinear refractive index and absorption coefficient of single\|shell semiconductor carbon nanotubes(CN s ) are calculated based on the two\|band approximation and Genkin\|Mednis approach. The results of nonlinear refractive index and absorption coefficient reach the order of 10 -8 and 10 -4 cm 2\5W -1 separately, which indicates that CN s have wonderful nonlinear optical properties. Taking into account the temperature effect and overlapping of σ and π orbits, the effect of relaxation term and chiral angle is discussed. The results show that the smaller the relaxation term, the larger the nonlinear absorption coefficient and refractive index. At the same time, CN s with different chiral angles have different results due to their different energy gap.

Nonlinear Change in Refractive Index and Transmission Coefficient of ZnSe:Fe²⁺at Long-Pulse 2.94-μm Excitation

An experimental study of the nonlinear changes in refractive index and transmission coefficient of single-crystal ZnSe:Fe2+, fabricated through the Fe-diffusion method, at long-pulse (~300 ns), sub-mJ, 2.94-mm Z-scan probing is reported. As well, a theoretical model based on the generalized Avizonis-Grotbeck equations is developed and applied for straightforward fitting of the open- and closed-aperture Z-scans, obtained for ZnSe:Fe2+ with different Fe2+ centers concentrations. The modeling results reveal that the contributions in the absorption and refractive index nonlinearities of ZnSe:Fe2+ are “common” resonant-absorption saturation (the minor part) and pulse-induced heating of the samples (the major part), which are strongly dependent on Fe2+ concentrations. Large values of the index change (>~10-3) and partial resonant-absorption bleaching (limited by ~50%), both produced via the thermal effect mainly, are the features of the ZnSe:Fe2+ samples inherent to this type of excitation.

Effect of Si δ-Doping on the Linear and Nonlinear Optical Absorptions and Refractive Index Changes in InAlN/GaN Single Quantum Wells

In the framework of effective mass approximation, we theoretically investigate the electronic structure of the Si δ-doped InAIN/GaN single quantum well by solving numerically the coupled equations Schrodinger-Poisson self-consistently. The linear, nonlinear optical absorption coefficients and relative refractive index changes are calculated as functions of the doping concentration and its thickness. The obtained results show that the position and the amplitude of the linear and total optical absorption coefficients and the refractive index changes can be modified by varying the doping concentration and its thickness. In addition, it is found that the maximum of the optical absorption can be red-shifted or blue-shifted by varying the doping concentration. The obtained results are important for the design of various electronic components such as high-power FETs and infrared photonic devices.

Single Beam Z-Scan Measurement of Nonlinear Refractive Index of Crude Oils

Nonlinear properties of two different crude oils from west-south Iran reservoirs have been investigated using the single beam Z-scan technique. The nonlinear refractive indices of the samples were measured by use of diode laser in the CW regime and at the wavelength 660 nm. The experiment results showed that the samples have large and negative refractive index nonlinear refraction coefficient. These results showed that the crude oil has significant nonlinear properties and it could be a candidate for photonic and nonlinear optical devices and also this information can be used in petroleum science and oceanology and etc.

Orientation-enhanced nonlinear optical properties and phase-conjugate reflective system of a novel Azobenzene doped polymer film

This paper reports that the nonlinear refractive index of a novel organic optical storage film doped azodiphenylamine polymer is measured by using the Z-scan technique. The nonlinear refractive index up to 3.7× 10^-6 cm^2/W induced by thermo-optical effect is obtained. It indicates that the sample has excellent optical non- linear properties. The physical mechanism of the great nonlinear optical effect is analysed and the optical conjugate characteristic is also discussed with degenerate four-wave-mixing. The phase conjugate wave diffracted from the formative refractive index grating in the sample is acquired and its equivalent reflectivity reaches about 22%. On this basis, the reflective wave phase-conjugated mirror system was designed, and the image aberration experienced in propagation in the storage experiment is corrected by using the system.

Physical origin of observed nonlinearities in Poly(1-naphthyl methacrylate):Using a single transistor–transistor logic modulated laser beam

A thermal lens technique is adopted using a single modulated continuous wave （cw） 532-nm laser beam to evaluate the nonlinear refractive index n2, and the thermo-optic coefficient dn/dT, in polymer Poly （1-naphthyl methacrylate） （P-1-NM） dissolved in chloroform, tetrahydrofuran （THF）, and dimethyl sulfoxide （DMSO） solvents. The results are compared with Z-scan and diffraction ring techniques. The comparison reveals the effectiveness and the simplicity of the TTL modulation technique. The physical origin is discussed for the obtained results.

Optimal design theories of tuned mass dampers with nonlinear viscous damping

Optimal design theory for linear tuned mass dampers （TMD） has been thoroughly investigated, but is still under development for nonlinear TMDs. In this paper, optimization procedures in the time domain are proposed for design of a TMD with nonlinear viscous damping. A dynamic analysis of a structure implemented with a nonlinear TMD is conducted first. Optimum design parameters for the nonlinear TMD are searched using an optimization method to minimize the performance index. The feasibility of the proposed optimization method is illustrated numerically by using the Taipei 101 structure implemented with TMD. The sensitivity analysis shows that the performance index is less sensitive to the damping coefficient than to the frequency ratio. Time history analysis is conducted using the Taipei 101 structure implemented with different TMDs under wind excitation. For both linear and nonlinear TMDs, the comfort requirements for building occupants are satisfied as long as the TMD is properly designed. It was found that as the damping exponent increases, the relative displacement of the TMD decreases but the damping force increases.

Optical nonlinearity in measurement of urea and uric acid in blood

The Z-scan technique is a simple and effective tool for determining nonlinear optical properties of materials. This technique is utilized in meas-urement of urea and uric acid in blood. The nonlinear refractive index of urea and uric acid are found to vary linearly with concentration. Hence by calculating the nonlinear refractive index it is possible to measure their concentra-tion in the sample. The results of this method are found to be in good agreement with the conventional colorimetric method.

Nonlinear optical characterization of phosphate glasses based on ZnO using the Z-scan technique

The nonlinear optical properties of a phosphate vitreous system [（ZnO）x-（MgO）30-x-（P2O5）70], where x=8, 10, 15, 18, and 20 mol% synthesized through the melt-quenching technique have been investigated by using the Z-scan technique. In the experiment, a continuous-wave laser with a wavelength of 405 nm was utilized to determine the sign and value of the nonlinear refractive （NLR） index and the absorption coefficient with closed and opened apertures of the Z-scan setup. The NLR index was found to increase with the ZnO concentration in the glass samples by an order of 10-10 cm2·W-1. The real and imaginary parts of the third-order nonlinear susceptibility were calculated by referring to the NLR index （n2） and absorption coefficient （β） of the samples. The value of the third-order nonlinear susceptibility was presented by nonlinear refractive or absorptive behavior of phosphate glasses for proper utilization in nonlinear optical devices. Based on the measurement, the positive sign of the NLR index shows a self-focusing phenomenon. The figures of merit for each sample were calculated to judge the potential of phosphate glasses for application in optical switching.

Exact self-similar solitary waves and collisions in nonlinear optical media

This paper analyses bright and dark spatial self-similar waves propagation and collision in graded-index nonlinear waveguide amplifiers with self-focusing and self-defocusing Kerr nonlinearities. It finds an appropriate transformation for the first time such that the nonlinear Schrodinger equation （NLSE） with varying coefficients transform into standard NLSE. It obtains one-solitonlike, two-solitonlike and multi-solitonlike self-similar wave solutions by using the transformation. Furthermore, it analyses the features of the self-similar waves and their collisions.

Application of the value of nonlinear parameters H and ΔH in strong earthquake prediction

In this paper, the relation that the curves of nonlinear parameter H and its difference Δ H bear with strong earthquakes in North China has been studied. First, the RSH algorithm has been applied to the North China region; the schemes of six quantitative prediction indexes have been studied in detail and then tested by tracing back predictions. The result shows that all the six prediction schemes are of certain prediction efficiency and have passed the test. Among the six schemes, A and E are of the best effect, with correlation coefficients R of 0.47 and 0.48 respectively. We recommend these two schemes for practical use in prediction in the future. Furthermore, the relation between the curve of Δ H (the difference of H) and strong earthquake has been studied. Based on the above results, the RSΔH algorithm that uses the Δ H value to predict strong earthquake has been put forward and applied to predict strong earthquakes in North China. The correlation coefficient R of tracing back prediction by this method is 0.45; this means that this method is also of better prediction efficiency. A combined application of these two algorithms has also been proposed. By the combined method, the time length spanned by false predictions can be shortened and thus the R value can be raised.

Nonlinear characterization and optical switching in bromophenol blue solutions

In this paper the results from investigations of the nonlinear refractive index and nonlinear absorption coefficient of Bromophenol Blue using the Z-scan technique with a continuous wave laser beam at wavelengths 488 nm and 514 nm are presented. It was observed that the material exhibited reverse saturation absorption and self defocusing behavior. It was found that the increase in solution concentration resulted in linear increase of the nonlinear refractive index. A pump and probe technique was used to obtain the absorption spectrum of triplet state. Furthermore the nonlinear absorption effect was used to demonstrate all optical switching.

Third Order Optical Nonlinearities and Spectral Characteristics of Methylene Blue

We have investigated third order nonlinear optical properties and spectral characteristics of methylene blue dye in both polymer and liquid mixtures. The spectral characteristics of the dye is studied by recording the absorption and fluorescence spectra of the dye doped in poly(methylmethacrylate) modified with additive n-butyl acetate(nBA) and the dye in MMA and nBA (liquid mixture). The spectral results of the dye doped polymer rod are compared with dye in liquid Mixture. The nonlinear measurements of the dye in liquid and polymer medium were performed using CW He-Ne laser of wavelength 632.8 nm by employing z-scan technique. The dye methylene blue showed a negative nonlinear refractive index.

Nonlinear Optical Properties and Optical Limiting Measurements of {(1Z)-[4-(Dimethylamino)Phenyl]Methylene} 4-Nitrobenzocarboxy Hydrazone Monohydrate under CW Laser Regime

We report results from the investigation of the nonlinear refractive index and nonlinear absorption coefficient of {(1Z)-[4-(Dimethylamino)phenyl]methylene} 4-nitrobenzocarboxy hydrazone mono-hydrate (DMPM4NBCHM) solution using Z-scan technique with a continuous wave (CW) Argon ion laser. The results show that this type of organic material has a large nonlinear absorption and nonlinear refractive index at 488 nm and 514 nm. The origin of the nonlinear effects was discussed. We demonstrate that the light induced nonlinear refractive index variation, leads to limiting effect. The results indicated that DMPM4NBCHM could be promising candidates for application on nonlinear photonic devices and optical limiters.

Investigation of a New Waveguide Structure Based on Negative Index Material for Optoelectronic Applications

In this work, a waveguide structure consisting of a new artificial negative index material (NIM) surrounded by a nonlinear cover and a ferrite (YIG) substrate has been designed and investigated. We apply the boundary conditions and impose the condition of negative effective permeability of the ferrite slab to derive the dispersion relation related to the proposed structure. The NIM permittivity and permeability are not constant and depend on the operating frequency. The dispersion properties of the nonlinear electromagnetic surface waves (NEM) are analyzed and the associated propagation index is calculated. Results show that the dispersion could be tuned and controlled by selecting the NIM film thickness and the film-cover interface nonlinearity. The proposed structure is supporting unusual types of NEM surface waves having a non-reciprocal behavior widely used in designing optoelectronic devices.

A New Approach for Solving Nonlinear Equations by Using of Integer Nonlinear Programming

One of the most important issues in numerical calculations is finding simple roots of nonlinear equations. This topic is one of the oldest challenges in science and engineering. Many important problems in engineering, to achieve the result need to solve a nonlinear equation. Thus, the formulation of a recursive relationship with high order of convergence and low time complexity is very important. This paper provides a modification to the Weerakoon-Fernando and Parhi-Gupta methods. It is shown that, in each iterate, the improved method requires three evaluations of the function and two evaluations of the first derivatives of function. The proposed with the Kou et al., Neta, Parhi-Gupta, Thukral and Mir et al. methods have been applied to a collection of 12 test problem. The results show that proposed approach significantly reduces the number of function calls when compared to the above methods. The numerical examples show that the proposed method is more efficiency than other methods in this class, such as sixth-order method of Parhi-Gupta or eighth-order method of Mir et al. and Thukral. We show that the order of convergence the proposed method is 9 and also, the modified method has the efficiency of .

Linear and nonlinear optical properties of Sb-doped GeSe_2 thin films

Sb-doped GeSe2 chalcogenide thin films are prepared by the magnetron co-sputtering method. The linear optical properties of as-deposited films are derived by analyzing transmission spectra. The refractive index rises and the optical band gap decreases from 2.08 eV to 1.41 eV with increasing the Sb content. X-ray photoelectron spectra further confirm the formation of a covalent Sb--Se bond. The third-order nonlinear optical properties of thin films are investigated under femtosecond laser excitation at 800 nm. The results show that the third-order nonlinear optical properties are enhanced with increasing the concentration of Sb. The nonlinear refraction indices of these thin films are measured to be on the order of 10-18 m2/W with a positive sign and the nonlinear absorption coefficients are obtained to be on the order of 10-10 m/W. These excellent properties indicate that Sb-doped Ge-Se films have a good prospect in the applications of nonlinear optical devices.

Component fault diagnosis for nonlinear systems

In the field of fault diagnosis, the state equation of nonlinear system, including the actuator and the component, has been established. When the faults in the system appear, it is difficult to observe the fault isolation between the actuator and the component. In order to diagnose the component fault in the nonlinear systems, a novel strategy is proposed. The nonlinear state equation with only the component system is built on mathematical equations. The nonlinearity of the component equation is expanded and estimated with Taylor series. If the actuator is perfect, the anomaly of the state equations reflects the component fault. The fault feature index is defined to detect the component fault and the initial fault. The numerical examples of the component faults are simulated for multiple-input multiple-output(MIMO)nonlinear systems. The results show that the component faults,as well as the incipient faults, can be detected. Furthermore, the effectiveness of the proposed strategy is verified. This method can also provide a foundation for the component fault reconfiguration control.

AI-Enhanced Performance Evaluation of Python, MATLAB, and Scilab for Solving Nonlinear Systems of Equations: A Comparative Study Using the Broyden Method

This research extensively evaluates three leading mathematical software packages: Python, MATLAB, and Scilab, in the context of solving nonlinear systems of equations with five unknown variables. The study’s core objectives include comparing software performance using standardized benchmarks, employing key performance metrics for quantitative assessment, and examining the influence of varying hardware specifications on software efficiency across HP ProBook, HP EliteBook, Dell Inspiron, and Dell Latitude laptops. Results from this investigation reveal insights into the capabilities of these software tools in diverse computing environments. On the HP ProBook, Python consistently outperforms MATLAB in terms of computational time. Python also exhibits a lower robustness index for problems 3 and 5 but matches or surpasses MATLAB for problem 1, for some initial guess values. In contrast, on the HP EliteBook, MATLAB consistently exhibits shorter computational times than Python across all benchmark problems. However, Python maintains a lower robustness index for most problems, except for problem 3, where MATLAB performs better. A notable challenge is Python’s failure to converge for problem 4 with certain initial guess values, while MATLAB succeeds in producing results. Analysis on the Dell Inspiron reveals a split in strengths. Python demonstrates superior computational efficiency for some problems, while MATLAB excels in handling others. This pattern extends to the robustness index, with Python showing lower values for some problems, and MATLAB achieving the lowest indices for other problems. In conclusion, this research offers valuable insights into the comparative performance of Python, MATLAB, and Scilab in solving nonlinear systems of equations. It underscores the importance of considering both software and hardware specifications in real-world applications. The choice between Python and MATLAB can yield distinct advantages depending on the specific problem and computational environment, providing guidance for researchers and practitioners in selecting tools for their unique challenges.