Self-defocusing Nonlinearity Research Articles

Saturation and absorption effects on the transmission properties of Kerr-type nonlinear layers

The effects of absorption and saturation on soliton states in Kerr-type nonlinear layers are theoretically investigated. In addition to the usual gray and bright soliton structures observed in nonlinear slabs, a flat soliton, i.e., a particular soliton excitation with electric field amplitude independent of the position within the layer, is researched in cases of self-defocusing and self-focusing nonlinearities. Effects caused by the combination of absorption and saturation, such as the shift and extinction of the flat soliton peak, the decrease in the amplitude of the electric field within the nonlinear layer, and the suppression of the multistable behavior of the transmission coefficient in the vicinity of the soliton peaks, are discussed. The present theoretical results are compared and found in good quantitative agreement with previous experimental measurements.Graphical

Enhanced optical third-harmonic generation in phase-engineered nanostructured Zn1−x Cd x S thin films for optoelectronic device applications

A polycrystalline nanostructured thin film of zinc cadmium sulfide was meticulously fabricated on a glass substrate using the thermal evaporation method physical vapor deposition within a vacuum chamber. Different doping concentrations were introduced by varying the cadmium (Cd) content, resulting in Zn1-x Cd x S films with Cd concentrations ranging from x = 0.00–0.20 wt %. The impact of Cd doping on the third-order nonlinear optical (TONLO) properties of these films was thoroughly studied using the Z-scan method, employing a diode-pumped solid-state continuous-wave laser. To gain insight into the structural characteristics, the Zn1-x Cd x S thin films underwent analysis through x-ray diffraction. Optical studies confirmed the tunability of the optical band gap (Eg) in the Zn1-x Cd x S films, ranging from 3.88 eV for undoped ZnS to 2.80 eV for the film fabricated with 20 wt. % of Cd-content. This significant reduction in ‘Eg’ renders the films highly suitable for use as absorbing layers in applications such as solar cells and optoelectronics. Surface morphology analysis, performed via field emission scanning electron microscopy, revealed noticeable alterations with increased Cd doping. Significantly, the doped films exhibited a substantial redshift in the band edge and an increase in transmittance within the visible and near-infrared regions. The investigation of TONLO properties, including the nonlinear absorption coefficient (β), nonlinear refractive index (n 2) and susceptibility χ(3), yielded values ranging from 3.15 × 10−3 to 8.16 × 10−3 (cm W−1), 1.65 × 10−8 to 7.45 x 10–8 (cm2 W−1), and 3.12 × 10−5 to 7.86 × 10−5 (esu), respectively. These results indicate the presence of self-defocusing nonlinearity in the films. Overall, the outcomes underscore the potential of Cd-doped ZnS nanostructures in modifying surface morphology and enhancing NLO characteristics. Zn1-x Cd x S thin films exhibit promise for applications in nonlinear optical devices, as evidenced by these encouraging findings.

Solitons supported by a self-defocusing trap in a fractional-diffraction waveguide

We introduce a model which gives rise to self-trapping of fundamental and higher-order localized states in a one-dimensional nonlinear Schrödinger equation with fractional diffraction and the strength of the self-defocusing nonlinearity growing steeply enough from the center to periphery. The model can be implemented in a planar optical waveguide. Stability regions are identified for the fundamental and dipole (single-node) states in the plane of the Lévy index and the total power (norm), while states of higher orders are unstable. Evolution of unstable states is investigated too, leading to spontaneous conversion towards stable modes with fewer node.

Stationary states and switching dynamics of the self-defocusing nonlinear coupled system with PT-symmetric [formula omitted]-wavenumber Scarf II potential

The stationary states and switching dynamics of the parity-time (PT) symmetric coupled system with k-wavenumber Scarf II potential in the self-defocusing nonlinear regime have been analysed. The eigenmodes with central peaks are evolved in the linear regime, whereas those with central dips are evolved in the defocusing nonlinear regime, for ground, 2nd, and 4th excited states. The threshold condition of the PT-symmetry breaking and the effect of coupling, self-defocusing nonlinearity, and width of the potential on the high and low-frequency modes of the ground and excited states have been analysed. The stability of the eigenmodes is verified using the linear stability analysis. The power-switching dynamics between the gain and lossy channels of the system has been analysed. The input power-dependent switching and the effects of gain/loss and potential width on the switching are discussed.

Nonlinear optical properties of methyl green investigated by the femtosecond Z-scan technique

The third-order optical nonlinearities of methyl green in aqueous solution are studied by the Z-scan technique using a femtosecond laser at 800 nm. The valley shape in the open aperture measurements reveals the presence of reverse saturable absorption effect, which is ascribed to the three-photon absorption process. The closed aperture Z-scan traces demonstrate a negative sign for the nonlinear refractive coefficient, indicating the self-defocusing optical nonlinearity. Furthermore, the magnitudes of the nonlinear refractive index n 2, the three-photon absorption coefficient α 3, and the real part of the third-order nonlinear optical susceptibility Re χ (3) are determined and found to be linearly proportional to the dye concentration within the investigated range. Our results suggest that methyl green may be a hopeful candidate for applications in nonlinear optics.

Using dark solitons from a Bose–Einstein condensate necklace to imprint soliton states in the spectral memory of a free boson gas

A possible use of matter-wave dark-soliton crystal produced by a Bose–Einstein condensate (BEC) with ring geometry, to store soliton states in the quantum memory of a free boson gas, is explored. A self-defocusing nonlinearity combined with dispersion and the finite size of the BEC, favor the creation of dark-soliton crystals that imprint quantum states with Jacobi elliptic-type soliton wavefunctions in the spectrum of the free boson gas. The problem is formulated by considering the Gross–Pitaevskii equation with a positive scattering length, coupled to a linear Schrödinger equation for the free boson gas. With the help of the matter-wave dark soliton-crystal solution, the spectrum of bound states created in the free boson gas is shown to be determined by the Lamé eigenvalue problem. This spectrum consists of quantum states whose wave functions and energy eigenvalues can be unambiguously identified. Among these eigenstates some have their wave functions that are replicas of the generating dark soliton crystal.

Self-defocusing nonlinear coupled system with PT-symmetric super-Gaussian potential.

The stationary solutions of the coupled nonlinear Schrödinger equation with self-defocusing nonlinearity and super-Gaussian form of parity-time (PT) symmetric potential in an optical system have been analyzed. The stationary eigenmodes of the ground and excited states and the influence of the gain/loss coefficient on the eigenvalue spectra are discussed. The threshold condition of the PT-symmetric phase transition of the high and low-frequency modes has been studied. Also, the variation of the threshold values with the coupling constant and the effect of the nonlinearity on the eigenmodes are analyzed. The stability of the solution is verified using the linear-stability analysis. In addition, the power distribution of the fundamental solutions with the propagation, in the two channels of the system, is analyzed in the PT and broken PT regimes.

Generation of multiple ultrashort temporal solitons in a third-order nonlinear composite medium with self-focusing and self-defocusing nonlinearities

Generation of multiple ultrashort temporal solitons in a third-order nonlinear composite medium with self-focusing and self-defocusing nonlinearities

Controllable nonlinear propagation of partially incoherent Airy beams.

The self-accelerating beams such as the Airy beam show great potentials in many applications including optical manipulation, imaging and communication. However, their superior features during linear propagation could be easily corrupted by optical nonlinearity or spatial incoherence individually. Here we investigate how the interaction of spatial incoherence and nonlinear propagation affect the beam quality of Airy beam, and find that the two destroying factors can in fact balance each other. Our results show that the influence of coherence and nonlinearity on the propagation of partially incoherent Airy beams (PIABs) can be formulated as two exponential functions that have factors of opposite signs. With appropriate spatial coherence length, the PIABs not only resist the corruption of beam profile caused by self-focusing nonlinearity, but also exhibits less anomalous diffraction caused by the self-defocusing nonlinearity. Our work provides deep insight into how to maintain the beam quality of self-accelerating Airy beams by exploiting the interaction between partially incoherence and optical nonlinearity. Our results may bring about new possibilities for optimizing partially incoherent structured field and developing related applications such as optical communication, incoherent imaging and optical manipulations.

Discrete solitons in competitive zigzag waveguide arrays with cubic-quintic nonlinearity

In this paper, we study one-dimensional discrete solitons in zigzag waveguide arrays with competitive cubic-quintic nonlinearity and competitive linear mixing between the nearest-neighbor (NN) and next-nearest-neighbor (NNN) couplings. The competitive nonlinearity features a cubic self-focusing associated with a quintic self-defocusing nonlinearities. The competitive linear mixing between the NN and NNN couplings is induced by making the two coefficients opposite of each other, which is assumed to be induced by the embedding synthetic gauge phase within the coupling constants. The combination of these two types of competition, linear mixing and nonlinearity can create four types of soliton: multipeak bell-shaped solitons, multipeak flat-top solitons, staggered bell-shaped solitons, and staggered flat-top solitons. The stability and dynamics of these types of solitons are verified systematically through the paper. The total power and the types of competition between the linear mixing play important roles in tuning these solitons.

Triangular bright solitons in nonlinear optics and Bose-Einstein condensates.

We demonstrate what we believe to be novel triangular bright solitons that can be supported by the nonlinear Schrödinger equation with inhomogeneous Kerr-like nonlinearity and external harmonic potential, which can be realized in nonlinear optics and Bose-Einstein condensates. The profiles of these solitons are quite different from the common Gaussian or sech envelope beams, as their tops and bottoms are similar to the triangle and inverted triangle functions, respectively. The self-defocusing nonlinearity gives rise to the triangle-up solitons, while the self-focusing nonlinearity supports the triangle-down solitons. Here, we restrict our attention only to the lowest-order fundamental triangular solitons. All such solitons are stable, which is demonstrated by the linear stability analysis and also clarified by direct numerical simulations. In addition, the modulated propagation of both types of triangular solitons, with the modulated parameter being the strength of nonlinearity, is also presented. We find that such propagation is strongly affected by the form of the modulation of the nonlinearity. For example, the sudden change of the modulated parameter causes instabilities in the solitons, whereas the gradual variation generates stable solitons. Also, a periodic variation of the parameter causes the regular oscillation of solitons, with the same period. Interestingly, the triangle-up and triangle-down solitons can change into each other, when the parameter changes the sign.

One-dimensional -symmetric eigenmodes in k-wave number Scarf II potential with defocusing nonlinearity

The stationary states and dynamical evolution of one-dimensional eigenmodes in self-defocusing nonlinear Kerr medium under transverse parity-time () symmetric k-wave number Scarff-II potential have been analysed. We study the effect of the coefficient of the imaginary component of the -symmetric potential on the eigenvalue spectra of the ground and first excited states in linear and nonlinear models. Symmetric eigenmodes with real eigenvalues are obtained in the unbroken regime in both models. The linear stability analysis shows that the solutions are stable in the unbroken regime. The stable propagation of the solutions in linear and nonlinear media supported by -symmetric k-wave number Scarff-II potential is also investigated. The comparison of the solutions in the presence and the absence of nonlinearity reveals that in the self-defocusing Kerr medium nonlinearity suppresses the region of -symmetry. The influence of the width of the complex k-wave number Scarff-II potential and the depth of the real potential function on the -symmetry breaking have also been analysed.

Multiple-peak and multiple-ring solitons in the nonlinear Schrödinger equation with inhomogeneous self-defocusing nonlinearity

Multiple-peak and multiple-ring solitons in the nonlinear Schrödinger equation with inhomogeneous self-defocusing nonlinearity

Two-dimensional lattice soliton and pattern formation in a cold Rydberg atomic gas with nonlocal self-defocusing Kerr nonlinearity

We propose a Rydberg-dressed atomic gas under the condition of electromagnetically induced transparency (EIT) to realize two-dimensional (2D) optical lattices and achieve nonlocal giant Kerr nonlinearity. We obtain the formation of stable 2D bright lattice solitons that result by the balance of diffraction with negative effective mass and nonlocal self-defocusing Kerr nonlinearity. Moreover, extended optical pattern formations are observed based on the modulation instability (MI). It is interesting to note that the solitons and patterns obtained are strongly influenced by the depth of the potential, the degree of nonlocality, and the strength of the Kerr nonlinearity. The results of our work provide a route for versatile control of laser patterns and solitons, which may have potential applications in optical communications and information processing.

Optical Pattern Formation in a Rydberg-Dressed Atomic Gas with Non-Hermitian Potentials

Spontaneous pattern formation from a spatially homogeneous background of nonlinear systems driven out of equilibrium is a widespread phenomenon in nature. However, similar phenomena and their physical realization in nonlinear systems with external potentials of gain and loss remain a challenge. We propose a scheme to realize a new type of spatial pattern formation through the self-organization of laser light in a Rydberg-dressed atomic gas with self-defocusing Kerr nonlinearity as well as non-Hermitian optical potentials. We show that by a suitable design of control and assistant laser fields, non-Hermitian optical potentials with or without parity-time (PT) symmetry for the probe laser field can be created. We find that through the nonlocal Kerr nonlinearity contributed by the long-range atom–atom interaction, a constant-intensity wave (CIW) may undergo modulation instability and induce spontaneous symmetry breaking, resulting in the emergence of various self-organized optical structures, which can be actively manipulated by tuning the nonlocality degree of the Kerr nonlinearity and by designing the non-Hermitian optical potentials. The results reported here open a door for developing non-Hermitian nonlinear optics.

Families of fundamental solitons in the two-dimensional superlattices based on the fractional Schrödinger equation

We investigate the existence and stability of fundamental solitons in the optical superlattices with self-defocusing and self-focusing nonlinearity based on the fractional Schrödinger equation. With the self-defocusing nonlinearity, fundamental solitons exist in the first gap, and the stability of solitons is in accordance with the anti-Vakhitov–Kolokolov criterion. However, for the self-focusing nonlinearity, the fundamental solitons exist in the semi-infinite gap, and the stability of solitons is in accordance with the Vakhitov–Kolokolov​ criterion. Moreover, the power, integral form factor, and peak value of fundamental solitons versus propagation constant, Lévy index, and relative strength of superlattice are illustrated. It is necessary to mention that the soliton becomes more and more localized by decreasing the Lévy index in both self-defocusing and self-focusing media. It is due to the fact that small Lévy index leads to weak diffraction. It should be pointed that the solitons can also exist with α<1.

Influence of structural and morphological features of zinc (II)-tetraphenylporphyrin thin film on its third order optical nonlinearity at pico and nano second regimes

Implications of laser pulse width on the third-order nonlinear optical properties of Zinc(II) 5, 10, 15, 20-Tetraphenyl-21H, 23H-Porphine (ZnTPP) thin films is investigated. Thin films of ZnTPP are developed on glass substrate by means of thermal vapor deposition technique. X-ray diffraction analysis illustrates polycrystalline nature of these films. Atomic force microscopy and field emission scanning electron microscope images confirm the homogeneous film surface with mean surface roughness value of 8.45 nm. UV–Visible absorption spectrum depicts signature peaks attributable to π-π* orbital transitions. Photoluminescence spectrum illustrates fluorescence emission in the wavelength range of 590 nm–650 nm from S1 state. Nonlinear optical investigations are carried out using single-beam Z-scan technique. ZnTPP thin-film at pico-second regime depicts saturable nonlinear absorption nature, attributable to the collective effect of singlet excited state absorption and filling effect of localized defect states. Whereas, at nanosecond timescale the film exhibits reverse saturable nonlinear absorption, sensitive to triplet excited state absorption. Closed aperture Z-scan measurements at pico and nano second regime highlight self-defocusing optical nonlinearity. Enhanced nonlinear optical coefficient (βeff and n2) values are strongly influenced by the heavy zinc metal ion and modified excited state dynamics due to the strong intermolecular interactions through J-aggregation.

Modulation instability in fractional Schrödinger equation with cubic–quintic nonlinearity

In this paper, we investigate the properties of modulation instability (MI) in the fractional Schrödinger equation with cubic–quintic nonlinearity (SECN), particularly focusing on some novel dynamical behaviors different from those in the conventional SECN. First, we apply the linear-stability theory to derive an analytical expression for instability gain in such novel fractional physical system. Just like the case of the conventional SECN, our analysis shows that the dynamical behavior of MI in the fractional SECN still depends on the various combinations of the signs of cubic and quintic nonlinearities. In particular, MI is found to still occur even in the fractional Schrödinger equation (SE) with self-defocusing cubic nonlinearity if the quintic nonlinearity is positive. Moreover, we further find that the Lévy indices related to the fractional effects mainly act to increase not only the fastest growth frequency but also the bandwidth, when compared to the case in the conventional SECN. However, the corresponding maximum gain is completely independent on such Lévy indices. The theoretical predictions are confirmed by the numerical results from the split-step Fourier method. Our findings suggest that the novel fractional systems with cubic–quintic nonlinearity provide some possibilities to control the dynamical behavior of MI and new solitary waves.

Unique Features of Nonlocally Nonlinear Systems with Oscillatory Responses

We review the recent investigation of a new form of nonlocally nonlinear system with oscillatory responses. The system has various new features, such as the nonlocality-controllable transition of self-focusing and self-defocusing nonlinearities, a unique modulational instability and new forms of solitons. We also discuss the propagation of the optical beam in a nematic liquid crystal with negative dielectric anisotropy and demonstrate theoretically that propagation can be modelled by the system.

Carrier-envelope offset frequency dynamics of a 10-GHz modelocked laser based on cascaded quadratic nonlinearities.

Cascaded quadratic nonlinearities from phase-mismatched second-harmonic generation build the foundation for robust soliton modelocking in straight-cavity laser configurations by providing a tunable and self-defocusing nonlinearity. The frequency dependence of the loss-related part of the corresponding nonlinear response function causes a power-dependent self-frequency shift (SFS). In this paper, we develop a simple analytical model for the SFS-induced changes on the carrier-envelope offset frequency (fCEO) and experimentally investigate the static and dynamic fCEO dependence on pump power. We find good agreement with the measured dependence of fCEO on laser output power, showing a broad fCEO tuning capability from zero up to the pulse repetition rate. Moreover, we stabilize the relative intensity noise to the -157dBc/Hz level leading to a tenfold reduction in fCEO-linewidth.