Self-diffraction at a dynamic photonic crystal formed in a colloidal solution of quantum dots

Self-diffraction at a one-dimensional dynamic photonic crystal formed in the colloidal solution of CdSe/ZnS quantum dots has been discovered. This self-diffraction appears simultaneously with self-diffraction at induced transparency channels at the resonant excitation of the main electron–hole (excitonic) transition of quantum dots by two laser beams with a Gaussian intensity distribution over the cross section. It is shown that a nonlinear change in the absorption of colloidal quantum dots results in the formation of a transparency channel and an induced amplitude diffraction grating, and a significant nonlinear change in the refractive index (Δn ≈ 10^?3) in the absorbing medium is responsible for the formation of the dynamic photonic crystal. Self-diffracted laser beams are revealed propagating not only in directions corresponding to self-diffraction at the induced diffraction grating but also in directions satisfying the Laue condition.     

Chaotization and decay instability of a diffraction-catastrophe field in the presence of focusing of high-power laser radiation in a nonlinear medium

Focusing of a high-power laser beam, whose initial wave front is deformed by spherical aberration and astigmatism, in a medium with refractive-index nonlinearity is investigated by the computer experiment method. It was found that the extended formations which arise near the focus are no longer diffraction catastrophes, since they are structurally unstable. It is shown that weak disturbances of the shape of the initial wave front produce extremely strong distortions of the optical field in the focusing region. As the wave propagates in the z direction, spatial chaos in the distribution of the optical field develops in the region of focusing (from 137 to 142 mm). Optical turbulence arises in the focusing region as a result of self-diffraction of light by self-induced nonuniformities of the refractive index of the medium. After the region with the smallest cross section of the formation near the focus, the three-dimensional optical field has the form of chaotically dispersing “splashes” and extended “filamentary ejecta.” Zh. Tekh. Fiz. 68, 74–83 (September 1998)     

Theoretical analysis of hot-image effect in a high-power laser system with cascaded nonlinear medium

We present a universally applicable and quick method to forecast the intensity and location of the hot-image effects in a high-power laser system structured by cascaded Kerr medium plates. The analytical expressions for the locations and the peak intensity of the hot-images are deduced by using propagation matrix method. The results are useful for laser designers to estimate and minimize the threat of optical damage. Theoretical analysis demonstrates that a maximum of N hot-images may appear in a laser system structured by N cascaded Kerr medium plates and the distance between two adjacent hot-images is two times the interval between two adjacent Kerr medium plates. The number and locations of the hot-images are related with the number of the Kerr medium plates, the distance from the scatterer to the front of the first Kerr medium plate, and the interval between two adjacent Kerr medium plates. The peak intensity of the hot-images depends on the number of the Kerr medium plates, the B-integral of each Kerr medium plate, the amplitude and phase modulation coefficients of the scatterer and the peak intensity of the input beam. The hot-image effects in a laser system with cascaded Kerr medium plates from two to eight are discussed in detail and numerically analyzed. Numerical simulation results are in agreement with the theoretical results.     

Dissipative discrete spatial optical solitons in a system of coupled optical fibers with the Kerr and resonance nonlinearities

The propagation of monochromatic radiation in a system of weakly coupled single-mode optical fibers with saturable amplification and absorption and Kerr nonlinearity of the refractive index is analyzed. Conditions of stability and bistability of plane-wave regimes are determined. Discrete dissipative optical solitons are found and their stability is studied. The hysteresis dependences of the peak intensity of the discrete solitons on the value of the Kerr nonlinearity and the input beam intensity are demonstrated. The numerical estimates of the parameters of the spatial dissipative discrete solitons are presented.     

Stability of Bragg grating solitons in a cubic-quintic nonlinear medium with dispersive reflectivity

We investigate the existence and stability of Bragg grating solitons in a cubic-quintic medium with dispersive reflectivity. It is found that the model supports two disjoint families of solitons. One family can be viewed as the generalization of the Bragg grating solitons in Kerr nonlinearity with dispersive reflectivity. On the other hand, the quintic nonlinearity is dominant in the other family. Stability regions are identified by means of systematic numerical stability analysis. In the case of the first family, the size of the stability region increases up to moderate values of dispersive reflectivity. However for the second family (i.e. region where quintic nonlinearity dominates), the size of the stability region increases even for strong dispersive reflectivity. For all values of m, there exists a subset of the unstable solitons belonging to the first family for which the instability development leads to deformation and subsequent splitting of the soliton into two moving solitons with different amplitudes and velocities.     

Elliptic incoherent solitons in strongly nonlocal media with anisotropic Kerr nonlinearity

The propagation of elliptic incoherent beam in strongly nonlocal media with noninstantaneous anisotropic Kerr nonlinearity is systematically investigated. Using the mutual coherence function approach, we obtain the existence curve of such solitons and an interesting outcome: correlation characteristics of the elliptic incoherent solitons can be anisotropic as well as isotropic. When the existence conditions of solitons are not satisfied, the elliptic incoherent beam will undergo periodic oscillation. Nonstationary evolution behaviors of the elliptic beam are shown in detail by numerical calculation. It is also obtained that the oscillation periods of the beam in x and y direction are different and the elliptic beam will become circular at some propagation distance under special conditions.     

Solitons and collapse suppression due to parametric interaction in bulk Kerr media

We demonstrate that weak parametric interaction of a fundamental beam with its harmonic field in a Kerr medium can drastically modify the beam dynamics, giving rise to very complex bifurcation phenomena and quasi solitons. Most importantly, we reveal a novel physical mechanism of the collapse suppression in a bulk optical Kerr medium: parametric coupling to a weakly radiating harmonic field.     

Surface defect gap solitons in two-dimensional optical lattices

We investigate the existence and stability of surface defect gap solitons at an interface between a defect in a two-dimensional optical lattice and a uniform saturable Kerr nonlinear medium. The surface defect embedded in the two-dimensional optical lattice gives rise to some unique properties. It is interestingly found that for the negative defect, stable surface defect gap solitons can exist both in the semi-infinite gap and in the first gap. The deeper the negative defect, the narrower the stable region in the semi-infinite gap will be. For a positive defect, the surface defect gap solitons exist only in the semi-infinite gap and the stable region localizes in a low power region.     

Stable helical solitons in optical media

We present a review of new results which suggest the existence of fully stable spinning solitons (self-supporting localised objects with an internal vorticity) in optical fibres with self-focusing Kerr (cubic) nonlinearity, and in bulk media featuring a combination of the cubic self-defocusing and quadratic nonlinearities. Their distinctive difference from other optical solitons with an internal vorticity, which were recently studied in various optical media, theoretically and also experimentally, is that all the spinning solitons considered thus far have been found to be unstable against azimuthal perturbations. In the first part of the paper, we consider solitons in a nonlinear optical fibre in a region of parameters where the fibre carries exactly two distinct modes, viz., the fundamental one and the first-order helical mode. From the viewpoint of application to communication systems, this opens the way to doubling the number of channels carried by a fibre. Besides that, these solitons are objects of fundamental interest. To fully examine their stability, it is crucially important to consider collisions between them, and their collisions with fundamental solitons, in (ordinary or hollow) optical fibres. We introduce a system of coupled nonlinear Schrödinger equations for the fundamental and helical modes with nonstandard values of the cross-phase-modulation coupling constants, and show, in analytical and numerical forms, results of collisions between solitons carried by the two modes. In the second part of the paper, we demonstrate that the interaction of the fundamental beam with its second harmonic in bulk media, in the presence of self-defocusing Kerr nonlinearity, gives rise to the first ever example of completely stable spatial ring-shaped solitons with intrinsic vorticity. The stability is demonstrated both by direct simulations and by analysis of linearized equations.     

Mighty morphing spatial solitons and bullets

We give what we believe to be the first closed-form exact expression for the dynamic evolution of nonstationary beams of arbitrary intensity and width propagating in a uniform nonlinear medium and in both two and three dimensions. This shows that periodic and quasi-periodic (nonradiating) beams can exist in a non-Kerr nonlinear medium. The Schr?dinger equation is solved for Gaussian beams in a saturable medium. For one critical (initial) beam width, the Gaussian is a stable stationary soliton or bullet, independent of its intensity; otherwise, it breathes. New quasi-periodic beams (mighty morphing solitons) and bullets (mighty morphs) of elliptical cross section also exist whose ellipticity changes with propagation.     

Kerr非线性介质中聚焦像散高斯光束的传输特性

当高功率激光通过Kerr非线性介质传输时,Kerr效应会严重影响激光的传输特性.实际应用中常遇到像散光束.迄今为止,像散光束传输特性的研究大都局限于在线性介质中的传输,而在非线性介质中传输的研究较少,且还未涉及像散激光束通过含光学系统的Kerr非线性介质传输变换的研究.本文主要研究Kerr效应对聚焦光束像散特性和焦移特性的影响,以及聚焦像散高斯光束的自聚焦焦距和光束焦点调控.在光束扩展情况下,推导出了聚焦像散高斯光束在Kerr非线性介质中传输的束宽、束腰位置和焦移的解析公式,研究表明:在自聚焦介质中,随着自聚焦作用增强(如光束功率增强),光束像散越强,但焦移越小;在自散焦介质中,随着自散焦作用增强(如光束功率增强),光束像散越弱,但焦移越大.另一方面,在光束自聚焦情况下,推导出了自聚焦焦距的解析公式,研究表明利用光束像散可以调控光束焦点个数.     

Higher order representation of the beam cross section deformation in large displacement finite element analysis

Most existing beam formulations assume that the cross section of the beam remains rigid regardless of the amplitude of the displacement. The absolute nodal coordinate formulation (ANCF); however, allows for the deformation of the cross section and leads to a more general beam models that capture the coupling between different modes of displacement. This paper examines the effect of the order of interpolation on the modes of deformation of the beam cross section using ANCF finite elements. To this end, a new two-dimensional shear deformable ANCF beam element is developed. The new finite element employs a higher order of interpolation, and allows for new cross section deformation modes that cannot be captured using previously developed shear deformable ANCF beam elements. The element developed in this study relaxes the assumption of planar cross section; thereby allowing for including the effect of warping as well as for different stretch values at different points on the element cross section. The displacement field of the new element is assumed to be cubic in the axial direction and quadratic in the transverse direction. Using this displacement field, more expressions for the element extension, shear and the cross section stretch can be systematically defined. The change in the cross section area is measured using Nanson’s formula. Measures of the shear angle, extension, and cross section stretch can also be systematically defined using coordinate systems defined at the element material points. Using these local coordinate systems, expressions for a nominal shear angle are obtained. The differences between the cross section deformation modes obtained using the new higher order element and those obtained using the previously developed lower order elements are highlighted. Numerical examples are presented in order to compare the results obtained using the new finite element and the results obtained using previously developed ANCF finite elements.     

一种新型有机金属化合物纳秒时域饱和吸收特性研究

合成了一种新型有机金属配合物Cetyltrimethylammonium-bis(2-thioxo-1,3- dithiole- 4,5-dithiolato)-copper(简称CtCu)材料.采用单光束Z扫描测试技术,在波长为1 053 nm,脉宽为1 ns的条件下研究了该样品的三阶非线性光学性质.研究发现,该材料具有很强的饱和吸收特性,激发态的有效吸收截面为σeff＝1.10×10－19 cm2,与基态吸收截面的比值为1∶484.利用非线性透过率实验验证了材料的饱和吸收特性,并对其产生机理进行了分析.实验结果表明,该材料在近红外波段的激光脉冲压缩方面有潜在的应用前景.     

Generation and tight-focusing properties of cylindrical vector circular Airy beams

Tight-focusing properties of cylindrical vector circular Airy beams [i.e., azimuthally polarized (AP) circular Airy beam and radially polarized (RP) circular Airy beam] passing through a high numerical aperture thin lens are investigated in detail. It is found that a super long subwavelength dark channel with full width at half maximum about 0.49λ and depth of focus (DOF) about 52λ can be achieved near the focal region for the case of tight focusing of an AP circular Airy beam, and a super long needle with DOF about 27.5λ of strong longitudinally polarized field can be obtained near the focal region for the case of tight focusing of a RP circular Airy beam. Furthermore, we report experimental generation of an AP circular Airy. Our results will be useful for atom guiding and trapping, particle acceleration and fluorescent imaging.     

Thermally induced nonlinear optical response and optical power limiting of acid blue 40 dye

We report the investigations of thermally induced third-order nonlinear optical and optical limiting characterizations for various concentrations of acid blue 40 dye in N,N-Dimethyl Formamide, studied by employing z-scan technique under cw He–Ne laser irradiation at 633 nm wavelength. The samples exhibited nonlinear absorption and nonlinear refraction under the experimental conditions. For lower concentration, the samples display both saturable absorption (SA) and reverse saturable absorption (RSA); whereas with increase in concentration, RSA behaviour prevails. The estimated values of the effective coefficients of nonlinear absorption β_eff, nonlinear refraction n₂ and third-order nonlinear susceptibility χ⁽³⁾ were found to be of the order of 10^?2 cm/W, 10^?4 esu and 10^?6 esu respectively. Multiple diffraction rings were observed when the samples were exposed to laser beam due to refractive index change and thermal lensing. The effect of concentration and the laser intensity on the self-diffraction ring patterns was studied experimentally. The acid blue 40 dye also exhibited strong optical limiting properties under cw excitation and reverse saturable absorption is found to be the dominant nonlinear optical process leading to the observed nonlinear behaviour.     

Break up of bound-N-spatial-soliton in a ramp waveguide

We present an analytical and numerical investigation of the propagation of spatial solitons in a nonlinear waveguide with ramp linear refractive index profile (ramp waveguide). For the propagation of a single soliton beam in a ramp waveguide, the particle theory shows that the soliton beam follows a parabolic curve in the region where the linear refractive index increases and a straight line outside the waveguide. The acceleration of the soliton depends on the beam intensity: higher amplitude solitons experience higher acceleration. Numerical calculations using an implicit Crank–Nicolson scheme confirm the result of the particle theory. Combining these propagation properties with the theory about bound-N-soliton, we study the break up of such a bound-N-soliton in a ramp waveguide. In a ramp waveguide, a bound-N-soliton will always be splitted into N independent solitons with the higher amplitude soliton emitted first. The amplitude of the separated solitons after break up are calculated using the soliton theory as if the solitons are independent. Numerical simulations show that the results agree quite well with this theoretical prediction, indicating that the interaction during break up has only little influence.     

Nonlinear intensity-related magneto-optical Kerr effects in the planar geometry

The reflection of an electromagnetic wave at the second-harmonic frequency from a semi-infinite optically isotropic magnetic medium for the directions of uniform magnetization corresponding to the meridional and equatorial Kerr effects is considered. Using the Green’s tensor function technique, in the first approximation in magnetization, the expressions for complex amplitudes of the field are obtained for the s and p polarizations of the incident beam and their superpositions. It is shown that in the latter case, the meridional effect becomes intensity-related. Dependences of the intensity-related meridional and equatorial Kerr effects on the angle characterizing polarization of the pump wave are obtained by numerical calculations. A comparative analysis of the linear and nonlinear Kerr effects is made.     

Fission of <Superscript>232</Superscript>Th in a spallation neutron field

The spatial distributions of thorium fission reaction rate in a spallation neutron field of thick lead target bombarded by protons or deuterons with energy between 1.0 and 3.7 GeV were measured. Approximately a linear dependence of the thorium fission rate on the beam energy is observed. The mean fission cross section of ²³²Th 〈σ _f 〉 ≈ 123 mb and it does not depend on energy and type of the beam particles.     

The problem of the relation between double pomeron exchange in inclusive and exclusive experiments

The pionization region of the inclusive single-particle spectrum is accounted for by double pomeron exchange in the absorptive part of a six-point amplitude. In this paper a multiperipheral model for the six-point amplitude with double pomeron exchange is used for continuation by crossing and analyticity to the physical region of the exclusive two particle → four particle production process. The cross section for π^? p → π^?(π⁺π^?)p in the double-Regge region is then calculated and compared with the experimental analysis of Lipes, Zweig and Robertson which sets an upper bound to the strength of the double pomeron exchange coupling. This upper bound, coupled with the model for continuation to the inclusive cross section, is shown to give too small a magnitude for the double pomeron exchange in the pionization region. Further avenues for investigation are discussed.     

Cusp and Regular Ion-Acoustic Solitons

Cups and regular smooth solitons are studied using the fluid model in cylindrical geometry for parallel propagating ion-acoustic waves in a low β plasma. It is found that smooth solitons only occur in the supersonic regime, whereas cusp solitons occur both in supersonic and subsonic regimes. In the supersonic regime, the amplitude and the width of cusp solitons increase when the Mach number M increases and initial electric field E ₀ decreases. However, the amplitude of smooth regular solitons increases and their width decreases when E ₀ increases and M decreases. For the subsonic case, both the amplitude as well as the width of a cusp solitons increase when M increases and E ₀ decreases. Corresponding to these cusp and regular solitons, bipolar electric field structures are also studied. These results may be helpful in understanding the properties of ion-acoustic regular and cusp solitons in space plasmas.