Nonlinear Refractive Index Coefficient Research Articles

Optical fractional solitonic structures to decoupled nonlinear Schrödinger equation arising in dual-core optical fibers

This paper explores a specific class of equations that model the propagation of optical pulses in dual-core optical fibers. The decoupled nonlinear Schrödinger equation with properties of M fractional derivatives is considered as the governing equation. The proposed model consists of group-velocity mismatch and dispersion, nonlinear refractive index and linear coupling coefficient. Different types of solutions, including mixed, dark, singular, bright-dark, bright, complex and combined solitons are extracted by using the integration methods known as fractional modified Sardar subequation method and modified F-expansion method. Optical soliton propagation in optical fibers is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. Furthermore, hyperbolic, periodic and exponential solutions are generated. A fractional complex transformation is applied to reduce the governing model into the ordinary differential equation and then by the assistance of balance principle the methods are used, depending upon the balance number. Also, we plot the different graphs with the associated parameter values to visualize the solutions behaviours with different parameter values. The findings of this work will help to identify and clarify some novel soliton solutions and it is expected that the solutions obtained will play a vital role in the fields of physics and engineering.

Optical non-linearities and applications of ZnS phosphors

Optical non-linearities play a crucial role in enabling efficient and ultrafast switching applications that are essential for next-generation photonic devices. ZnS phosphor material produces the best results in terms of increased luminescence quantum yield when doped with certain impurities. Nevertheless, the investigation of the third-order non-linear optical susceptibility of the phosphor materials can be exploited for various switching applications. In this regard, we review the recent advancements in the investigation of non-linear optical properties of ZnS phosphors, where the knowledge of absorption and refraction is utilized in various optical and detector applications. Furthermore, the review highlights strategies employed to enhance the non-linear optical response of phosphor materials as well as a general discussion of an attosecond optical switching scheme which can be used to fabricate devices with petahertz speeds. Consequently, we provide a solution to the unsolved problem of the significant extension of optical limiting applications to switching applications by developing design strategies to manipulate conventional ZnS phosphor material. The potential challenges and future prospects of utilizing phosphor materials for switching applications are also addressed. The strategies for manipulating ZnS phosphor can be generalized for a broad range of other materials by minimizing linear and non-linear losses, while enhancing the values of the non-linear refractive index coefficient. We propose that the figure-of-merit of ZnS material can be enhanced by using a suitable combination of pump and probe wavelength values, which can be useful for optical switching applications.

Facile Z-scan determination of nonlinear refractive index and absorption coefficient of dye-doped polymer film

Facile Z-scan determination of nonlinear refractive index and absorption coefficient of dye-doped polymer film

Low-power Z-scan study of nonlinear refractive index and absorption coefficient of acid blue 129 dye-doped polymer thin film

Low-power Z-scan study of nonlinear refractive index and absorption coefficient of acid blue 129 dye-doped polymer thin film

Enhanced optical nonlinearity of epsilon-near-zero metasurface by quasi-bound state in the continuum

Bound states in the continuum (BICs) provide a powerful way to enhance the nonlinear properties of materials, epsilon-near-zero (ENZ) materials are considered as promising candidates with strong nonlinearities. However, the realization of BIC based on ENZ materials in the near-infrared (NIR) is very challenging due to the large loss in the NIR. Here, a high-quality quasi-BIC based on the ENZ metasurface is proposed for the first time, which is composed of patterned ENZ films embedded in a dielectric-metal hybrid structure, and realizes destructive interference between the Berreman mode and photonic mode to form the Friedrich-Wintergen BIC (FW-BIC). The electric field is strongly confined in the ENZ film, resulting in considerable field enhancement, and the nonlinear refractive index coefficient is 1.63 × 10−12 m2/W, which is three orders of magnitude larger than that of the ITO film. The instantaneous response time is 600 fs and extremely high modulation speed up to the THz level. Benefiting from the perfect absorption and narrow linewidth of quasi-BIC and the change in refractive index of the metasurface induced by Kerr nonlinearity, the absolute modulation is from near-zero to 92% with an extinction ratio of 23.2 dB. It provides a promising platform for the development of integrated ultrafast high-speed photonics.

Role of vacuum annealing on the structural, optical properties and Dc conductivity of titanium (IV) phthalocyanine dichloride thin films

The present work elucidates the significant alterations in several physical characteristics of thermally evaporated TiPcCl2 thin films resulting from vacuum annealing at 373 and 473 K. The structure, surface morphologies, and molecular structure of TiPcCl2 thin films were studied using x-ray Diffraction (XRD), Transmission Electron Microscope (TEM), Field-Emission Scanning Electron Microscope (FESEM), and Fourier Transform Infrared (FT-IR). Results confirmed nanostructure attributes of as-deposited and annealed films, as well as the phase transition in TiPcCl2 was observed during annealing. The optical constants of as-deposited and annealed films in the wavelength range of 200–2500 nm were determined using spectrophotometric techniques. The indirect optical energy gap was observed to diminish with increasing annealing temperature due to enhanced crystallinity of thin films. Using the single oscillator model, the dispersion of the refractive index at normal dispersion was investigated. The third-order nonlinear susceptibility, χ(3), the nonlinear refractive index n2 and the nonlinear absorption coefficient, βc, were calculated and then discussed for both the as-deposited and annealed films. The electrical conductivity of TiPcCl2 exhibited increased as the temperature increased, suggesting its characteristic as a conventional organic semiconductor. The parameters of Mott’s model were obtained and discussed under low-temperature conditions afterward. Conclusions derived from this research indicate that the unique properties of vacuum annealing TiPcCl2 have great promise for future use in optoelectronic systems.

Solvent-Driven Variations of Third-Order Nonlinear Thermo-Optical Features of Glutaric Acid-Directed Self-Healing Supramolecular Ni(II) Metallogels.

The generation of solvent-directed self-healing supramolecular Ni(II) metallogels of glutaric acid (i.e., Ni-Glu-DMF and Ni-Glu-DMSO) is described in this article. Polar aprotic solvents like N,N'-dimethylformamide (DMF) and dimethyl sulfoxide (DMSO) are separately entrapped into the Ni(II)-acetate salt and glutaric acid-mediated networks to attain the semisolid flexible scaffolds. The gel nature of the fabricated materials is experimentally proven through different rheological tests such as amplitude sweep, frequency sweep, and thixotropic (time sweep) measurements. The self-repairing strategy and load-bearing features of the synthesized metallogel are studied in this work. The different supramolecular noncovalent interactions working within the soft scaffold are clearly explored. The formation strategy and the microstructural features of these synthesized metallogels are scrutinized through a Fourier transform infrared (FT-IR) spectroscopy study and field-emission scanning electron microscopy (FESEM) morphological analyses. The FT-IR spectroscopy observation displays a considerable amount of shifting of the infrared (IR) peaks of the xerogel samples of both the metallogels Ni-Glu-DMF and Ni-Glu-DMSO. The electrospray ionization (ESI)-mass spectroscopy result demonstrates the plausible construction of the metallogel network. In order to examine the nonlinear optical characteristics of the two synthesized self-healing metallogels Ni-Glu-DMSO and Ni-Glu-DMF, Z-scan measurements are carried out with a continuous wave (CW) diode-pumped solid-state (DPSS) laser at 532 nm. The nonlinear refractive index, nonlinear absorption coefficient, thermo-optical coefficient, and third-order susceptibility of these metallogels were evaluated by analyzing the experimental data from the Sheik-Bahae formalism. The nonlinear thermo-optical study reveals that these solvent-dependent metallogels show negative signs of nonlinear refractive index and nonlinear absorption coefficient. The figure of merit calculated for these compounds shows good agreement for their use in nonlinear photonic devices.

Measurement of Non-Linear Optical Absorption of PVC/TiO2 Nanocomposite via Z-Scan Technique for Optical Limiting

Abstract: This research focuses on PVC/TiO2 nanocomposites in the form of thin films in order to expand our understanding of photonics technology. For fabrication of the thin films, the casting method was used with nanocomposites composite were developed by mixing TiO2 nanoparticles with Polyvinyl Chloride (PVC) as the polymer matrix. The absorbance parameters were determined using spectral analysis, and the linear absorption coefficient was computed. A single beam Z-scan technique was used to evaluate the nonlinear refractive index and nonlinear absorption coefficient via a CW diode pumped solid state (DPSS) laser (Coherent Verdi-V5, 532 nm) was employed as the excitation laser at 50mW. Peak absorption was detected at 280 nm with increasing absorption observed as the proportion of TiO2 nanoparticles increased. The nonlinear absorption coefficient was found at (0.5342, 1.3585,1.5999, and 0.0253) 1ݔ 10−5 cm/W. All of the sample morphology resulting poor structure which then affect the NLO absorption of the materials. However, with the positive value of NLO absorption, they appear to be promising candidates for optical limiting applications.

Crystal structure, DFT study, Hirshfeld analysis and optical third order nonlinear properties of new 1-naphthylaminium hydrogen fumarate salt

This study reports the crystal structure and its supramolecular framework, quantum chemical calculations and nonlinear optical properties of 1-naphthylaminium hydrogen fumarate salt. The supramolecular self-assembly of fumarate anions and 1-naphthylaminium cation of the salt is primarily stabilized by N-H…O, O-H…O and C-H…O interactions. The construction of strong hydrogen bonds such as N-H…O and O-H…O produces two-dimensional corrugated sheet parallel to (010) plane, which resembles a supramolecular grid type architecture in the crystal structure. Two weak C-H…O interactions interlink the parallel (010) supramolecular sheet generating a three-dimensional molecular network. The molecular stability of the experimentally determined structure is theoretically optimized by DFT quantum chemical calculations using 6-31G(++) basis set. The relative molecular interaction-based charge distribution and the chemical reactivity of the titled salt were identified using electrostatic potential contouring and HOMO-LUMO maps. The crystal structure is subjected to Hirshfeld surface analysis to gain better understanding on the intermolecular interactions exhibited by the molecules. The optical nonlinearities of the titled salt are examined using Z-scan experimentation, the optical nonlinear refractive index and optical nonlinear absorption coefficient is estimated by closed and open aperture Z-scan methods. The observed nonlinear values are quite comparable to the conventional optical nonlinear values.

Intensity-Dependent Optical Response of 2D LTMDs Suspensions: From Thermal to Electronic Nonlinearities.

The nonlinear optical (NLO) response of photonic materials plays an important role in the understanding of light-matter interaction as well as pointing out a diversity of photonic and optoelectronic applications. Among the recently studied materials, 2D-LTMDs (bi-dimensional layered transition metal dichalcogenides) have appeared as a beyond-graphene nanomaterial with semiconducting and metallic optical properties. In this article, we review most of our work in studies of the NLO response of a series of 2D-LTMDs nanomaterials in suspension, using six different NLO techniques, namely hyper Rayleigh scattering, Z-scan, photoacoustic Z-scan, optical Kerr gate, and spatial self-phase modulation, besides the Fourier transform nonlinear optics technique, to infer the nonlinear optical response of semiconducting MoS2, MoSe2, MoTe2, WS2, semimetallic WTe2, ZrTe2, and metallic NbS2 and NbSe2. The nonlinear optical response from a thermal to non-thermal origin was studied, and the nonlinear refraction index and nonlinear absorption coefficient, where present, were measured. Theoretical support was given to explain the origin of the nonlinear responses, which is very dependent on the spectro-temporal regime of the optical source employed in the studies.

Low-Threshold Optical Bistability Based on Photonic Crystal Fabry–Perot Cavity with Three-Dimensional Dirac Semimetal

In this paper, we investigate theoretically the tunable low threshold optical bistability (OB) in the terahertz range based on photonic crystals’ Fabry–Perot (FP) cavity with a three-dimensional Dirac semimetal (3D DSM). On the one hand, a 3D DSM with a high nonlinear refractive index coefficient creates conditions for the generation of OB. Additionally, the finite film thickness of 3D DSMs leads to significantly a enhanced interaction volume compared to graphene, which allows easier preparation and has stable properties. On the other hand, the resonance of the FP cavity plays a positive role in promoting the tunable low-threshold OB. It was found that the OB threshold and hysteresis curve can be continuously adjusted by manipulating the Fermi energy and relaxation times of a 3D DSM. Additionally, the bistable curve of the composite structure is also closely related to the angle of incident light. Through parameter optimization, OB with a threshold approaching 105 V/m can be obtained. The photonic crystal’s FP cavity with a 3D DSM structure provides a feasible way to achieve low-threshold OB and a building block for future integrated all-optical devices.

Evaluation of surface roughness, linear and nonlinear optical parameters of a mixture of sudan black b and polymer films for optical limiting application

A film of a mixture of sudan black b (SBB) dye and a poly methyl methacrylate (PMMA) is fabricated by casting. X-ray diffraction measurement proves the SBB/PMMA film's structure is amorphous. The scanning probe microscope confirmed that the SBB/PMMA film has a good quality and homogeneous surface. The SBB/PMMA film's optical constants are estimated via the transmittance, absorbance, and reflectance spectra. The indirect optical band gap is calculated and found to be 1.49 eV. The single oscillator energy, Eo, the dispersion energy, Ed, and the static refractive index, no, are computed by using Wemple and DiDomenico model. Semi-empirical relation, Z-scan, and diffraction ring patterns are three methods used to determine the film's nonlinear refractive index value. The SBB/PMMA film exhibited a high nonlinear refractive index (n2 = 7.83 × 10−7 cm2/W) and nonlinear absorption coefficient (β = 9.3 × 10−3 cm/W), calculated by the Z-scan method. Under a continuous wave laser beam, the property of the optical limiting of the film is examined. The film exhibited optical limiting properties with a limiting threshold value of 5 mW.

Harmonic-Gaussian Symmetric and Asymmetric Double Quantum Wells: Magnetic Field Effects

In this study, we considered the linear and non-linear optical properties of an electron in both symmetrical and asymmetrical double quantum wells, which consist of the sum of an internal Gaussian barrier and a harmonic potential under an applied magnetic field. Calculations are in the effective mass and parabolic band approximations. We have used the diagonalization method to find eigenvalues and eigenfunctions of the electron confined within the symmetric and asymmetric double well formed by the sum of a parabolic and Gaussian potential. A two-level approach is used in the density matrix expansion to calculate the linear and third-order non-linear optical absorption and refractive index coefficients. The potential model proposed in this study is useful for simulating and manipulating the optical and electronic properties of symmetric and asymmetric double quantum heterostructures, such as double quantum wells and double quantum dots, with controllable coupling and subjected to externally applied magnetic fields.

Quantitative analysis of the synthetic food colorants with optical nonlinearity

The self-focusing transmissions of light beams in five food dye suspensions including Red 40, Red 2, Red 4, Yellow 6, Blue 1 are studied. We qualitatively analyze the key influencing factors of the self-focusing phenomenon with five widely-used food dyes, including the concentration of suspensions, the input-beam power and the kinds of the food dyes. It is found that, the self-focusing phenomenon is mainly attributed to the shift of focus caused by thermal effects. Particularly, Red 40 presents a best nonlinear performance with a 5 cm self-focusing propagation at the wavelength of 532 nm. The significant difference of the self-focusing effects of the five food dyes are further explained by investigating their optical absorption and optical nonlinearity including nonlinear refractive index and absorption coefficient. It is found that a stronger absorption and nonlinearity, originated from the kinds of the dyes or the concentration of the dyes, leads to a stronger nonlinear self-focusing effect. Our work provides a systematic study on the quantitative analysis of the synthetic food colorants with optical nonlinearity, demonstrating a strong nonlinear self-focusing propagation and high nonlinear refractive index in red 40, red 2, red 4. This may have potential applications in nonlinear optics with soft matters.

A comparison of the crystal structure and optical properties of reduced graphene oxide and aminated graphene nanosheets for optoelectronic device applications

Optical properties of graphene transform in presence of amine or amide groups. So, the comparison of the linear and nonlinear optical (NLO) properties of reduced graphene oxide (RGO) nanosheets and aminated graphene (AMG) nanosheets will significantly accelerate the development of a flexible optoelectronic device based on this material in the future. In this paper, the structural and optical properties of RGO and AMG are investigated by TEM, XRD, Raman, and UV-Vis analysis. TEM images show the formation of the very thin layer of RGO and AMG nanosheets. The peak of XRD spectra (26.6◦) for both indicate the good quality of crystallization of RGO and AMG. Raman spectra result in ID/IG of about 0.9 and 1.1 for RGO and AMG, respectively. Also, different functional groups for RGO and AMG nanosheets are shown in FTIR spectra. Then, Kramers-Kronig (KK) method was employed to determine the dielectric function, ε̃(λ), extinction coefficient, k(λ) and refractive index, n(λ). Third-order optical nonlinearities of nanosheets dispersed in DMF are investigated with the Z-scan method. The nanosheets achieve an appropriate figure of merit (FOM) due to their high nonlinear refractive (NLR) index, n2 (10−8cm2/W) and low nonlinear absorption (NLA) coefficient, β (10−4cm/W).

Modulation of epsilon-near-zero wavelength and enhancement of third-order optical nonlinearity in ITO/Au multilayer films

We report the modulation of epsilon-near-zero (ENZ) wavelength and enhanced third-order nonlinearity in indium tin oxide (ITO)/Au multilayer films. The samples consisting of five-layer 40 nm ITO films spaced by four-layer ultrathin Au films of different thickness, i.e., ITO(40 nm)/[Au(x)/ITO(40 nm)]4, were prepared by magnetron sputtering at room temperature. The ENZ wavelength in the multilayer films is theoretically calculated and experimentally confirmed. The nonlinear refractive index and nonlinear absorption coefficient of the samples of x=0, 2, 3, 4 nm were determined using the Z-scan method at a wavelength of 1.064 µm. The large nonlinear refractive index n2=1.12×10-13 m2/W and nonlinear absorption coefficient β=-1.78×10-7 m/W in the sample of x = 4 nm are both four times larger than those in the single-layer ITO film. The large optical nonlinearity due to the ENZ enhancement and carrier concentration is discussed. The results indicate that the ITO/Au multilayer films are promising for advanced all-optical devices.

Growth, characterizations and nonlinear optical studies of dimethylamine substituted anthracene chalcone single crystals

We report the structural, thermal, linear and nonlinear optical (NLO) properties of a newly grown anthracene based chalcone single crystal, (2E)-1-(anthracen-9-yl)-3-[4-(dimethylamino)phenyl]prop-2-en-1-one (abbreviated as DA-ANC). The chalcone was synthesized by Claisen-Schmidt condensation reaction and the single crystals were grown by slow evaporation of solution growth technique. Single-crystal XRD, NMR (1H & 13C), FT-IR, UV-Vis-NIR spectroscopies, TG/DTA, and computational DFT studies were performed to characterize the crystals. The intermolecular interactions were described by Hirshfeld surface analysis (HSA). The third-order NLO properties of DA-ANC were studied by Z-scan technique using CW-DPSS laser at 532 nm. Open aperture Z-scan exhibits strong two-photon assisted reverse saturation absorption (RSA) with two-photon absorption (TPA) coefficient (β) 6.9 × 10−5 cmW−1. Closed aperture Z-scan reveals the negative nonlinear refraction arising due to self-defocusing effect with nonlinear refractive index (n2) coefficient -1.31 × 10−8 cm2W−1. The optical limiting behavior based on TPA was performed and limiting-threshold was evaluated to be 6.47 kJ cm−2. The obtained one-photon and two-photon figures of merit satisfied the conditions of all-optical switching. The results show that DA-ANC can be a potential candidate for NLO applications.

Материалы для сверхбыстрой терагерцовой фотоники

Designing of the ultrafast terahertz photonics devices requires materials with the biggest nonlinear refractive index coefficient n2 and the lowest settling time of the nonlinear response τ in the terahertz spectral range. In the present study, we show that the ratio n2/τ for media with the vibrational nonlinearity in the terahertz range is determined by the square of the medium thermal expansion coefficient and the fifth power of its dominative stretching vibrational mode frequency. These findings are based on the theory of the media vibrational nature nonlinear polarization response to incident THz radiation. We provide estimated values of the n2/τ ratio for a group of liquids and crystal materials. According to our evaluations, n2/τ value for alpha-pinene in the terahertz spectral range is about 10^6 cm^2/J and is almost the biggest one compared to materials with different nonlinearity types in various spectral ranges.

Mechanism of optical limiting in metalloporphyrins under visible continuous radiation.

Here, we present an experimental investigation on the nonlinear optical (NLO) and optical limiting properties of metalloporphyrin compounds (Cu-1-OH, Zn-1-OH, Cu-1-E and Zn-1-E) using spatial self-phase modulation (SSPM) method in the visible range. It is found that all of the samples show a large self-defocusing effect at 532 nm, which is attributed to the thermal nonlinear optical effects with negative nonlinear refractive index coefficient n2 due to the relatively high absorption at 532 nm. In contrast, at 780 nm where absorption is weak for both Zn- and Cu-porphyrins, Zn-porphyrins still exhibit visible self-defocusing while Cu-porphyrins do not show any nonlinear diffraction pattern. Such a phenomenon can be explained by the Kerr effect of Cu-porphyrins at 780 nm. As the thermal nonlinear optical effects (of negative n2) at 780 nm are reduced due to the low absorption, the Kerr effect with positive n2 becomes comparable and the overall nonlinearity is reduced. The Kerr effect of Cu-porphyrins is stronger than that of Zn-porphyrins because of the enhanced π-electron delocalization effect as Cu(II) has a variable number of valence electrons and incompletely filled d atomic orbitals. Finally, the optical limiting performance of Zn-porphyrins is demonstrated as a representative and its dependence on sample position is examined. This work not only enriches the understanding of the physical mechanism of optical limiting in porphyrin materials, but also provides a significant reference to improve the third-order NLO coefficient by adjusting the structure of compounds.

Effect of Cerium dopant on third-order nonlinear optical properties of CdS/PEG self-standing nanocomposite films

CdS/PEG, 4 and 7 mol% Ce doped CdS/PEG nanocomposite films were synthesized by in situ method. The XRD pattern confirmed the cubic structure of the CdS and the size of the CdS nanocrystallite is found to be smaller than the Bohr exciton radius for all the samples. SEM analysis shows that CdS and Ce doped CdS nanoparticles are well mono-dispersed in PEG polymer. FTIR spectra confirm the interaction of Ce-doped CdS nanoparticles with PEG polymer. UV–Vis optical absorption studies exhibit a red-shift of CdS nanoparticle with Ce doping. The photoluminescence spectra of all the films show a red emission due to the surface defects. The third-order nonlinear optical properties of all the films have been studied using the Z-scan technique. Closed and open aperture Z-scan plots show self-focusing optical nonlinearity and reverse saturable absorption with positive nonlinear coefficients. The 7 mol% Ce doped CdS/PEG nanocomposite film exhibits the highest value of nonlinear refractive index and nonlinear absorption coefficient which are about 1.649 × 10−9 m2/W and 7.149 × 10−3 m/W. The third-order nonlinear optical susceptibility and figure of merit have also been estimated for all the films and also increase with increase in Ce dopant concentrations. The maximum value of third-order nonlinear optical susceptibility and figure merit are found for 7 mol% Ce doped CdS/PEG nanocomposite film and are about 9.882 × 10−4 esu and 5.902 × 10−8 esu m. The present study strongly recommends that the Ce doped CdS/PEG nanocomposite films are worthy candidates for fabricating the future optical limiting devices.