Self-defocusing Nonlinearity Research Articles

Stability of one and two-dimensional spatial solitons in a cubic–quintic–septimal nonlinear Schrödinger equation with fourth-order diffraction and [formula omitted]-symmetric potentials

In this paper, the existence and stability of solitons in parity-time (PT)-symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with fourth-order diffraction (FOD) coefficient and higher-order nonlinearities have been investigated. For the linear case, we have demonstrated numerically that, the FOD parameter can alter the PT-breaking points. Exact analytical expressions of the localized modes are obtained respectively, in one and two dimensional nonlinear Schrödinger (NLS) equation with both self-focusing and self-defocusing Kerr, and higher-order nonlinearities for nonlinear case. The effects of both FOD and higher-order nonlinearities on the stability/instability structure of these localized modes have also been discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. Some stable and unstable solutions have been given and, it has been seen how higher-order self-focusing and self-defocusing nonlinearities can influence the stability/instability of the system.

Study of Third-order Nonlinear Optical Properties of Basic Violet 3 Dye in Polar Protic and Aprotic Solvents.

The present work aims to study of third-order nonlinear optical (TONLO) behavior of basic violet 3 dye dissolved in polar protic and aprotic solvents, namely, ethanol, 1-propanol, acetone and dimethyl sulfonate (DMSO), respectively. The polarity of the solvent used to have a substantial impact on the linear and TONLO properties of the dye sample. The dye exhibits self-defocusing nonlinearity due to thermally induced nonlinear refractive index and nonlinear absorption coefficient reveals the character of both saturable and reverse saturable absorption (RSA). The order of magnitude of nonlinear refractive index (n2) and nonlinear coefficient of absorption (β) of dye sample was determined to be 10-7 cm2/W and 10-3cm/W, respectively. The real and imaginary factors of the TONLO susceptibility of basic violet 3 dye were measured to be the power of 10-5 esu. The obtained results reveal that the dye sample seems to have the potential candidate for use in various photonics and optoelectronics applications.

Transmission of electromagnetic waves through nonlinear optical layers

The excitation of soliton states in optical layers exhibiting Kerr nonlinearities is theoretically investigated. The optical transmission coefficient is obtained as a function of the intensity of an incident light beam. The incident electromagnetic wave is considered to be monochromatic and linearly polarized in the transverse electric configuration. In materials exhibiting self-defocusing nonlinearity, soliton excitations are not observed if the product of the nonlinear dielectric coefficient of the slab and the absolute square of the incident electric-field amplitude is below a well-defined value. At such a limit, a soliton excitation with a position-independent electric field amplitude is observed within the nonlinear layer, regardless of the frequency value of the incident wave.

Thermal nonlinearities in GaSe

The nonlinear light absorption at the fundamental absorption edge under laser excitation in GaSe crystals has been investiqated experimentally. It is shown that at high excitation levels, the absorption coefficient shifted towards lower energies (red shift). The nonlinear refractive index is positive at frequencies below the absorption edge and negative on the high-energy side. The laser-induced negative index change is referred to as a selfdefocusing optical nonlinearity. The positive Δn(ω) on the high-energy side to a selffocusing optical nonlinearity. The measured parameters showed that GaSe crystals exhibits strong nonlinear properties.

4-(4,5-Diphenyl-1H-imidazole-2-yl)phenol: Synthesis and Estimation of Nonlinear Optical Properties using Z-Scan Technique and Quantum Mechanical Calculations

In this study, 4-(4,5-Diphenyl-1H-imidazole-2-yl) phenol is successfully synthesized, and its nonlinear optical properties (NLO) are investigated both experimentally and theoretically. Theoretical investigations have been done by using TD-DFT and B3LYP functional with usual 6-31+G(d,p) basis set. The results of HOMO-LUMO and NBO analysis show the low energy gap, high total dipole moment, and hyperpolarizabilities (β, g) as well as the presence of dipolar excited states with relatively significant dipole-moment changes which are linked to the nonlinearity. The z-scan technique confirmed the NLO properties of title compound. The nonlinear absorption coefficient, refractive index, and third-order susceptibility were found to be 4.044 × 10-1 cmW-1, 2.89 × 10-6 cm2W-1 and 2.2627 × 10-6 esu, respectively. The negative sign of n2 indicated the occurrence of self-defocusing nonlinearity. The results show that the title compound can been used as potential NLO material.

Dark matter-wave gap solitons in dense ultracold atoms trapped by a one-dimensional optical lattice

Optical lattices have been used as a versatile toolbox to control Bose-Einstein condensates (BECs) in recent years, and a wealth of emergent nonlinear phenomena have been found, including bright gap solitons and dark ones, among which the former has been realized in experiments. The latter, however, has only theoretical results and its fundamental properties are still not well understood. Here we theoretically and numerically explore an open issue of creating stable matter-wave dark gap solitons in a one-dimensional optical lattice, onto which the BECs with self-defocusing quintic nonlinearity are loaded. Using linear-stability analysis and direct simulations, the formation, structures, and properties of dark gap solitons in quintic nonlinearity have been compared to those upheld by cubic Kerr nonlinearity. In particular, we uncover that the dark gap solitons and soliton clusters are robustly stable in the first finite band gap of the underlying linear spectrum, and are hard to be stabilized in the second gap. The predicted dark gap solitons are observable in current experiments on dense ultracold atoms, using an optical lattice technique, and in the optics domain for nonlinear light propagation in periodic optical media with quintic nonlinearity.

Existence, symmetry breaking bifurcation and stability of two-dimensional optical solitons supported by fractional diffraction.

We study existence, bifurcation and stability of two-dimensional optical solitons in the framework of fractional nonlinear Schrödinger equation, characterized by its Lévy index, with self-focusing and self-defocusing saturable nonlinearities. We demonstrate that the fractional diffraction system with different Lévy indexes, combined with saturable nonlinearity, supports two-dimensional symmetric, antisymmetric and asymmetric solitons, where the asymmetric solitons emerge by way of symmetry breaking bifurcation. Different scenarios of bifurcations emerge with the change of stability: the branches of asymmetric solitons split off the branches of unstable symmetric solitons with the increase of soliton power and form a supercritical type bifurcation for self-focusing saturable nonlinearity; the branches of asymmetric solitons bifurcates from the branches of unstable antisymmetric solitons for self-defocusing saturable nonlinearity, featuring a convex shape of the bifurcation loops: an antisymmetric soliton loses its stability via a supercritical bifurcation, which is followed by a reverse bifurcation that restores the stability of the symmetric soliton. Furthermore, we found a scheme of restoration or destruction the symmetry of the antisymmetric solitons by controlling the fractional diffraction in the case of self-defocusing saturable nonlinearity.

Bioinspired fluorescence carbon quantum dots extracted from natural honey: Efficient material for photonic and antibacterial applications

Fluorescent carbon quantum dots were extracted from natural honey using the hydrothermal approach. The XRD and HRTEM investigations confirm the morphology of the carbon quantum dots (CQDs) are spherical shape with a diameter of 8.29 nm. The FTIR and XPS analysis indicate the effective incorporation of nitrogen and sulfuratoms into the CQDs. The sample demonstrated the blue fluorescence by the UV-light illumination (λex=365nm). When excited at 350 nm, the quantum yield of honey CQDs was found to be ∼4.192 % at the emission wavelength (431 nm). Crucially for the first time, the existing honey CQDs generates a strong nonlinear optical response relative to some semiconductor QDs. The non-linear optical characterization was investigated utilizing the Z-Scan method. These CQDs exhibit self-defocusing nonlinearity and strong nonlinear performance in the absorption. Also, the agar well diffusion method used to investigate the antimicrobial efficacy of the CQDs against the foodborne pathogens. It is inferred from the existing observations that honey CQDs have been used as effective optoelectronic devices and antimicrobial agents.

The nonlinear optical properties of graphene loaded [formula omitted] colloidal quantum dots

The effect of graphene (Gr) on the nonlinear and linear optical properties of Cadmium-Selenide (CdSe) colloidal quantum dots (QDs) is investigated using Z-scan technique (at 532 nm) and Uv–visible spectrophotometer, respectively. Graphene concentrations are 1, 2 and 3 wt % of CdSe. The values of both linear and nonlinear absorption coefficients (α and β) along with nonlinear refraction index (n2) are increased in the Gr loaded samples. The open aperture results demonstrate that like Gr free samples, a negative n2 is obtained for the Gr included samples which leads to self-defocusing nonlinearity in them.

Laser patterning induced the tunability of nonlinear optical property in silver thin films

Patterned Ag thin films were obtained through laser irradiation at ambient conditions. We investigated the effects of laser scanning rate for the structure and optical properties of patterned Ag films. XPS results show that the volume fractions of Ag and Ag2O are dependent on the laser scanning rate. The localized surface plasmon resonance was observed in the as-irradiated samples and increased with the acceleration of the scanning rate. Moreover, with the variations of laser scanning rates and excitation energy, these samples exhibit tunable self-defocusing nonlinearity caused by charge transfer and the enhanced electromagnetic field at the interface between Ag and Ag2O.

Breather Interaction Properties Induced by Self-Steepening and Space-Time Correction* *Supported by the National Natural Science Foundation of China (Grant Nos. 11705145, 11947301, 11434013, and 11425522), the Major Basic Research Program of Natural Science of Shaanxi Province (Grant Nos. 2017KCT-12 and 2017ZDJC-32), and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2018JQ1003).

We study the properties of breather interactions in nonlinear Kerr media with self-steepening and spacetime correction and with either self-focusing or self-defocusing nonlinearity, and present a new family of exact breather solutions via the Darboux transformation with a special-designed quadratic spectral parameter. In contrast to the previous results of the nonlinear Schrödinger equation (NLSE) hierarchy, we show that the relative phase of colliding breathers has a significant effect on the collision manifestation. In particular, only the out-of-phase interactions can generate small amplitude waves at the collision center, which are analogous to the NLSE super-regular breathers. Our results will deepen our understanding of the properties of breather interactions and they will offer the possibility of experimental observations of super-regular breather dynamics in systems with self-steepening and spacetime correction.

Surface-polaritonic phase singularities and multimode polaritonic frequency combs via dark rogue-wave excitation in hybrid plasmonic waveguide

Material characteristics and input-field specifics limit controllability of nonlinear electromagnetic-field interactions. As these nonlinear interactions could be exploited to create strongly localized bright and dark waves, such as nonlinear surface polaritons, ameliorating this limitation is important. We present our approach to amelioration, which is based on a surface-polaritonic waveguide reconfiguration that enables excitation, propagation and coherent control of coupled dark rogue waves having orthogonal polarizations. Our control mechanism is achieved by finely tuning laser-field intensities and their respective detuning at the interface between the atomic medium and the metamaterial layer. In particular, we utilize controllable electromagnetically induced transparency windows commensurate with surface-polaritonic polarization-modulation instability to create symmetric and asymmetric polaritonic frequency combs associated with dark localized waves. Our method takes advantage of an atomic self-defocusing nonlinearity and dark rogue-wave propagation to obtain a sufficient condition for generating phase singularities. Underpinning this method is our theory which incorporates dissipation and dispersion due to the atomic medium being coupled to nonlinear surface-polaritonic waves. Consequently, our waveguide configuration acts as a bimodal polaritonic frequency-comb generator and high-speed phase rotator, thereby opening prospects for phase singularities in nanophotonic and quantum communication devices.

Synthesis and characterization of GO doped bio-resource based composites for NLO and multifaceted applications

The objective of the present work is to synthesize three different types of cardanol based benzoxazines such as cardanol-{1,4-bis(4-aminophenoxy)ethane}benzoxazine (CBAE2Bz), cardanol-{1,4-bis(4-aminophenoxy)butane} benzoxazine (CBAE4Bz) and cardanol-{1,4-bis(4-aminophenoxy)octane}benzoxazine (CBAE8Bz) by varying aliphatic ether link chain length through solventless method. The benzoxazines obtained with varying chain length were converted in to three different types of composites using paraphenylenediamine (PPDA) functionalized gaphene oxide (f-GO) as nano-reinforcement with varying weight percentage and were characterized by different analytical techniques. The molecular structure of the monomers was confirmed from Fourier transform infrared (FTIR) spectroscopy, 1HNMR, 13C NMR and MALDI mass. Data obtained from thermal studies infer that the prepared composites possess good thermal stability and enhanced values of Tg with respect to weight percent of functionalized graphene oxide content. However, the values of thermal stability, Tg, dielectric constant and dielectric loss were marginally decreased with respect to increase in length of the spacer aliphatic chain. The SEM and TEM studies confirm the homogeneous dispersion and single layer thickness of graphene sheet, respectively. The feasibility of usage of f-GO/PCAE2Bz composite in both gram positive bacteria (Bacillus subtilis, Staphylococcus aureus) and gram negative bacteria (Pseudomonas aeruginosa, Escherichia coli) environments were checked and the results obtained were discussed. Further, third-order NLO properties of open and closed aperture Z–scan results conclude that GO doped bio-resource based composites exhibit saturable absorption and self-defocusing type optical non-linearity. The third-order NLO susceptibility (χ3) of GO doped bio-resource based composites are increased with respect to quantity of reinforcement of GO to bio-based polymer. The maximum value of 1.03X 10−4 esu was observed and this nonlinearity is thermal in nature. Thus, the prepared composites may find wide range of applications in diverse surrounding conditions.

Symmetry breaking of spatial Kerr solitons in fractional dimension

We study symmetry breaking of solitons in the framework of a nonlinear fractional Schr\"{o}dinger equation (NLFSE), characterized by its L\'{e}vy index, with cubic nonlinearity and a symmetric double-well potential. Asymmetric, symmetric, and antisymmetric soliton solutions are found, with stable asymmetric soliton solutions emerging from unstable symmetric and antisymmetric ones by way of symmetry-breaking bifurcations. Two different bifurcation scenarios are possible. First, symmetric soliton solutions undergo a symmetry-breaking bifurcation of the pitchfork type, which gives rise to a branch of asymmetric solitons, under the action of the self-focusing nonlinearity. Second, a family of asymmetric solutions branches off from antisymmetric states in the case of self-defocusing nonlinearity through a bifurcation of an inverted-pitchfork type. Systematic numerical analysis demonstrates that increase of the L\'{e}vy index leads to shrinkage or expansion of the symmetry-breaking region, depending on parameters of the double-well potential. Stability of the soliton solutions is explored following the variation of the L\'{e}vy index, and the results are confirmed by direct numerical simulations.

Conical diffraction modulation in honeycomb lattices

We investigate the generation and destruction of asymmetric conical diffraction in honeycomb lattices by adjusting rotation angle θ of the three vectors and considering nonlinearities. For θ = 0° and 60°, the modes of the Dirac cone of the honeycomb lattice are excited, symmetric conical diffraction are obtained. When 0 < θ < 60°, asymmetric conical diffraction with a dark notch appears and the dark notch moves clockwise or anti-clockwise around the outer edge of the bright ring. In addition, it is also demonstrated that both Kerr and saturation nonlinearities can cause triangular deformation of conical diffraction pattern. Under the same nonlinearity, two identical wave centered around different Dirac points can evolve to identical triangular rings pointing in opposite directions. The dark notch at a point of triangular appears and moves in a clockwise or anti-clockwise way for self-focusing and self-defocusing nonlinearity, respectively.

Facile synthesis of ZnS\u2013Ag2S core\u2013shell nanospheres with enhanced nonlinear refraction

ZnS–Ag2S core–shell nano/hetero-junctions have been synthesized by a two-step co-precipitation technique, in which thin layers of Ag2S have been successfully coated on the surface of ZnS nanospheres. Structural studies and elemental analysis have been performed using X-ray diffraction, Fourier transfer infrared spectroscopy, field emission scanning electron microscopy, energy dispersive spectroscopy, and high-resolution transmission electron microscopy. UV–Vis diffuse reflectance spectroscopy and photoluminescence spectroscopy have been employed to investigate linear optical characteristics. Nanosecond laser pulsed-based single-beam Z-scan analysis has been used to examine the magnitude and the sign of the third-order nonlinear refractive indices. Samples show negative values of nonlinear refractive indices indicating self-defocusing optical nonlinearity under 1064 nm excitation. The results have shown that the third-order nonlinear refractive index in ZnS nanospheres can reach the magnitude of 61.0 times 10^{ - 12} {text{m}}^{2} /{text{W}} by encapsulating such a nanostructure within nanometer shells of Ag2S. The enhanced nonlinearity for ZnS–Ag2S core–shells has been found to be 9 times higher than sole ZnS nanoparticles, which was estimated to be about 6.4 times 10^{ - 12} {text{m}}^{2} /{text{W}}.

Vectorial dispersive shock waves in optical fibers

Dispersive shock waves are a universal phenomenon encountered in many fields of science, ranging from fluid dynamics, Bose-Einstein condensates and geophysics. It has been established that light behaves as a perfect fluid when propagating in an optical medium exhibiting a weakly self-defocusing nonlinearity. Consequently, this analogy has become attractive for the exploration of dispersive shock wave phenomena. Here, we observe of a novel class of vectorial dispersive shock waves in nonlinear fiber optics. Analogous to blast-waves, identified in inviscid perfect fluids, vectorial dispersive shock waves are triggered by a non-uniform double piston imprinted on a continuous-wave probe via nonlinear cross-phase modulation, produced by an orthogonally-polarized pump pulse. The nonlinear phase potential imparted on the probe results in the formation of an expanding zone of zero intensity surrounded by two repulsive oscillating fronts, which move away from each other with opposite velocities.

One-dimensional gap solitons in quintic and cubic–quintic fractional nonlinear Schrödinger equations with a periodically modulated linear potential

Competing nonlinearities, such as the cubic (Kerr) and quintic nonlinear terms whose strengths are of opposite signs (the coefficients in front of the nonlinearities), exist in various physical media (in particular, in optical and matter-wave media). A benign competition between self-focusing cubic and self-defocusing quintic nonlinear nonlinearities (known as cubic–quintic model) plays an important role in creating and stabilizing the self-trapping of D-dimensional localized structures, in the contexts of standard nonlinear Schrödinger equation. We incorporate an external periodic potential (linear lattice) into this model and extend it to the space-fractional scenario that begins to surface in very recent years—the nonlinear fractional Schrödinger equation (NLFSE), therefore obtaining the cubic–quintic or the purely quintic NLFSE, and investigate the propagation and stability properties of self-trapped modes therein. Two types of one-dimensional localized gap modes are found, including the fundamental and dipole-mode gap solitons. Employing the techniques based on the linear-stability analysis and direct numerical simulations, we get the stability regions of all the localized modes; and particularly, the anti-Vakhitov–Kolokolov criterion applies for the stable portions of soliton families generated in the frameworks of quintic-only nonlinearity and competing cubic–quintic nonlinear terms.

Snakelike similaritons in tapered grating dual-core waveguide amplifiers

We present a physical model that describes bright and dark snakelike similaritons propagating in an asymmetric dual-core waveguide amplifier by considering self-focusing and self-defocusing Kerr nonlinearities. The asymmetric dual-core waveguide is composed of two adjoining, closely spaced, upper and lower cores, in which the upper one is an active tapered graded-index waveguide with a long-period grating along the medium while the lower one is a passive step-index waveguide. For different choices of tapered index profile, novel exact analytical similariton solutions undergoing a self-compression are obtained. Our results show that these optical structures can be effectively controlled by adjusting the long-period grating and amplitude of the source. Besides, the stability and interaction of two neighboring bright similaritons are discussed by means of numerical simulations. These results may simulate the possibility of experiments related to tapered grating dual-core waveguide amplifiers.

Optical generation and control of spatial Riemann waves.

We extend the concept of Riemann waves (RWs) to the spatial domain and demonstrate for the first time, to the best of our knowledge, Riemann beams with a propagation scenario allowing controllable shock formation in a nonlinear optical system. Similar to their standard counterparts, "shifted" RWs are characterized by a local propagation speed proportional to their local amplitude. Their steepening dynamics can be judiciously controlled by means of an additional phase term. In particular, RWs are generated by properly tailoring the initial phase of an optical beam propagating through a thermal solution of an m-cresol/nylon mixture that exhibits a giant self-defocusing nonlinearity. The experimental results show a controllable steepening and shock wave behavior, in good agreement with the prediction from the simple inviscid Burgers equation.