Breathing and beating dynamics of Gaussian beam in planar graded-index absorbing nonlinear waveguides

The spatial dynamics of laser beams in absorbing planar waveguides with a parabolic index profile in a saturable or cubic-quintic medium are calculated using the “collective variable approach” technique. In the absence of losses, we construct diagrams which define regions of self-focusing and self-diffractive beam propagation for both types of media. It is found that propagating pulses exhibit an oscillatory pattern, similar to breathing behavior in homogeneous media. If the incident pulse spatial profile and the center of the index profile are not aligned, the pulse oscillates around the index origin with a “beat” frequency that depends on the graded index. Both the breathing and the beat frequencies are also calculated for other graded-index profiles, such as those with additional higher-power terms, and are found to be extremely sensitive to the index profile. In media with linear and nonlinear absorption, we demonstrate the difference between the breathing behavior in graded-index and homogeneous waveguides.     

Self tapering and uptapering of a self guided laser beam in an absorbing/gain medium with nonlinearity

The absorption/gain induced self tapering and uptapering of a self guided Gaussian laser beam when the beam propagates in a saturable nonlinear medium has been discussed. Using the WKBJ and abberationless paraxial ray approximation a beam width equation has been derived. Conditions for tapering/uptapering for both cases i.e., for absorption and gain have been discussed. The beam width of tapered/uptapered beam depends on the rate of absorption/gain, and the length of absorption/gain region along the beam propagation direction. The importance of the present study is pointed out.     

Modeling interaction of ultrashort pulses with ENZ materials

In this work, the split-step Fourier method for beam propagation is used to investigate the interaction of ultra-short pulses with epsilon-near-zero materials. The propagation of pulses is governed by the nonlinear Schrödinger equation (NLSE) containing dispersion, gain-bandwidth, self-phase modulation, self-steepening, and absorption parameters. It is found that the intensity profile of the pulse is broadened and the phase of the pulse is shifted by dispersion phenomena. The gain/loss related to the imaginary part of the refractive index causes an increase or decrease in intensity and pulse edge effects. These effects do not favor the steady propagation of the pulse. The self-phase modulation is not noted to appreciably affect the intensity pulse profile. The self-steepening modifies the phase and energy of the pulse during propagation, as well as absorption, which influences the losses by both the linear and nonlinear effects.     

Stability, dynamics, and the onset of multi-pulsing in a mode-locked laser cavity using phase-sensitive amplification

An averaged evolution equation is presented and its dynamics studied for a mode-locked laser where the intensity discrimination (saturable absorption) in the cavity is provided by phase-sensitive amplification. The phase-sensitive amplifier acts as a phase-filter for selecting the specific intensity-dependent phase-rotation of the mode-locked pulse that locks the phase to the amplifier pump phase. The resulting averaged equation is a Swift-Hohenberg type model which is a fourth-order diffusion equation with cubic-quintic nonlinearities. Additionally, the governing evolution has a new linear growth term which couples to the nonlocal cavity energy. This parameter is a standard bifurcation parameter in Swift-Hohenberg models and is controlled by the cavity saturable gain. Such a modification to the governing evolution is the first of its kind to be considered theoretically in the context of the Swift-Hohenberg equation, and its significant impact on the mode-locked pulse dynamics and multi-pulsing behavior is explored.     

非局域高次非线性介质中的多极暗孤子

研究一维非局域三-五次非线性模型下,暗孤子和多极暗孤子的新解和传输特性.发现非局域程度和非线性参量变化对暗孤子的峰值和束宽产生影响,并且在特定的竞争非局域非线性参数下存在稳定基态暗孤子和多极暗孤子的束缚态.另外,讨论了在局域自聚焦三次和非局域自散焦五次非线性介质中暗孤子和两极暗孤子的传输特性,发现孤子比在自散焦三次和自聚焦五次的非线性介质中传输更加稳定.进一步研究了单暗孤子和三极暗孤子的功率与传播常数和非局域程度的关系,并讨论了不同类型暗孤子的线性稳定性问题.     

Nonautonomous Solitons in the(3+1)-Dimensional Inhomogeneous Cubic-Quintic Nonlinear Medium

We have constructed explicit nonautonomous soliton solutions of the generalized nonlinear Schrdinger equation in the(3+1)-dimensional inhomogeneous cubic-quintic nonlinear medium.The gain parameter has no effects on the motion of the soliton's phase or their velocities,and it affects just the evolution of their peaks.As two examples,we discuss the propagation of nonautonomous solitons in the periodic distributed amplification system and the exponential dispersion decreasing system.Results show that the presence of the chirp not only makes the intensity of solitons weaken more promptly,but also broadens their width.     

Temporal response of nonlinear transmission in optically thick saturable absorbers and determination of saturable absorption parameters

The temporal response of nonlinear transmission in saturable absorbers is theoretically investigated on the basis of a four-energy-level model including an excited-state absorption, and is experimentally employed for determining saturable absorption parameters in saturable-dye-doped films. The approximation of optically thin absorbers is shown to be inadequate to this end. In theoretical calculations, optically thick saturable absorbers are treated by a set of simultaneous partial differential equations: a rate equation governing the dynamics of population densities of energy levels and a propagation equation governing the propagation of optical fields in the optically thick absorbers. By comparing experimental results with numerical ones, the saturable absorption parameters can be determined on the basis of the intensity dependence of response time. In numerical calculations, the effect of random orientation is also considered for optically anisotropic molecules rigidly fixed in saturable absorbing media. The characterization of the saturable absorption parameters is conducted by using uranine-doped poly(vinyl alcohol) films.     

Spatiotemporal self-similar waves for the (3 + 1)-dimensional inhomogeneous cubic-quintic nonlinear medium

Spatiotemporal self-similar waves of the (3 + 1)-dimensional generalized nonlinear Schrödinger equation, describing propagation of optical pulses in a cubic-quintic nonlinear medium with inhomogeneous dispersion and gain, are derived. A one-to-one correspondence between such self-similar waves and solutions of the constant-coefficient cubic-quintic nonlinear Schrödinger equation exists when two certain compatibility conditions are satisfied. Under these conditions, we discuss dynamical behaviors of self-similar waves in dispersion decreasing fiber.     

Dark–bright optical solitary waves and modulation instability analysis with (2 + 1)-dimensional cubic-quintic nonlinear Schrödinger equation

This paper addresses the (2+1)-dimensional cubic-quintic nonlinear Schrödinger equation (CQNLS) that serves as the model to study the light propagation through nonlinear optical media and non-Kerr crystals. A dark–bright optical solitary wave solution of this equation is retrieved by adopting the complex envelope function ansatz. This type of solitary wave describes the properties of bright and dark optical solitary waves in the same expression. The integration naturally lead to a constraint condition placed on the solitary wave parameters which must hold for the solitary waves to exist. Additionally, the modulation instability (MI) analysis of the model is studied based on the standard linear stability analysis and the MI gain spectrum is got. Numerical simulation and physical interpretations of the obtained results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CQNLS.     

非束缚态空间亮孤子的传输稳定性

从理论上研究了主克尔型介质中非束缚态空间亮孤子的传输行为。数值计算结果表明：在主克尔型χ＾（６）＋χ＾（５）介质中可以传输非束缚态空间亮孤子。传输稳定性与其背景平面波的横向渐近传播常数ｑ和χ＾（３）,χ＾（５）系数有关,非平凡位相因子在三、五阶效应竞争中的平衡作用,是获得非束缚态空间亮孤子稳定传输的关键。     

Nonlinear tunneling effect in the (2+1)-dimensional cubic-quintic nonlinear Schrödinger equation with variable coefficients

By means of the similarity transformation, we obtain exact solutions of the(2+1)-dimensional generalized nonlinear Schrödinger equation, which describes thepropagation of optical beams in a cubic-quintic nonlinear medium with inhomogeneousdispersion and gain. A one-to-one correspondence between such exact solutions andsolutions of the constant-coefficient cubic-quintic nonlinear Schrödinger equation existswhen two certain compatibility conditions are satisfied. Under these conditions, wediscuss nonlinear tunneling effect of self-similar solutions. Considering the fluctuationof the fiber parameter in real application, the exact balance conditions do not satisfy,and then we perform direct numerical analysis with initial 5% white noise for the brightsimilariton passing through the diffraction barrier and well. Numerical calculationsindicate stable propagation of the bright similariton over tens of diffraction lengths.     

Optical characterization of semiconductor saturable absorbers

Semiconductor saturable absorber mirror (SESAM) devices have become a key component of ultrafast passive mode-locked laser sources. Here we describe in more detail how the key SESAM parameters such as saturation fluence, modulation depth, and nonsaturable losses are measured with a high accuracy. These parameters need to be known and controlled to obtain stable pulse generation for a given laser. A high-precision, wide dynamic range setup is required to measure this nonlinear reflectivity of saturable absorbers. The challenge to measure a low modulation depth and key measures necessary to obtain an accurate calibration are described in detail. The model function for the nonlinear reflectivity is based on a simple two-level travelling wave system. We include spatial beam profiles, nonsaturable losses and higher-order absorption, such as two-photon absorption and other induced absorption. Guidelines to extract the key parameters from the measured data are given. PACS 07.60.Hv; 42.65.Re; 42.70.Nq     

Non-quantum liquefaction of coherent gases

We show that a gas-to-liquid phase transition at zero temperature may occur in a coherent gas of bosons in the presence of competing nonlinear effects. This situation can take place in atomic systems like Bose-Einstein condensates in alkali gases with two-body and three-body interactions of opposite signs, as well as in laser beams which propagate through optical media with Kerr (focusing) and higher order (defocusing) nonlinear responses. The liquefaction process takes place in the absence of any quantum effect and can be formulated in the framework of a mean field theory, in terms of the minimization of a thermodynamic potential. We study from a thermodynamic point of view all the stationary solutions of the cubic-quintic nonlinear Schrödinger equation which describes our system. We show that solitonic localized solutions connect the gaseous and liquid phases. Furthermore, we also perform a numerical simulation in the presence of linear gain and three-body recombination where a rich dynamics, including the emergence of self-organization behavior, is found.     

时空非相干光孤子的传播和相干特性

研究了时空非相干椭圆形高斯光束在饱和对数型非线性介质中的自陷行为,得到了孤子的形成条件并分析了其相干特性,讨论了光束自陷的变化形式,发现光束的初态和材料非线性对其有决定性的影响, 并进一步获得了光束半径和光束相干半径的解析表达式,发现光束的相干特性不但会随传播距离产生周期性的变化,且随组份频率的增大而减弱.     

强非线性吸收下Z扫描衍射模型及实验研究

根据光的衍射理论,建立了非线性光学介质对高斯光束的开孔Z 扫描理论模型.数值计算表明,当相移比值Γ≤0.15,出射光功率随入射光功率的增加出现振荡衰减现象;当Γ>0.15,在输入光强低于某一个值时,输出随输入的增加而线性增加;当输入光强超过该值后,输出功率不再增加甚至趋于零.实验采用Nd∶YAG脉冲激光,在波长为532 nm,脉宽8 ns条件下,对含3.5%和7.0%碳纳米管的聚苯胺/碳纳米管复合体薄膜（PANI/MWCNT）的非线性吸收特性进行了研究.计算表明,该类化合物的激发态吸收截面积远大于其基态吸收截面积,具有很强的反饱和吸收.     

χ3+χ5介质中非束缚态空间亮孤子的传输行为

本文从理论上研究了主克尔型介质中非束缚态空间亮孤子的传输行为。数值计算结果表明:在主克尔型χ⁽³⁾+χ⁽⁵⁾介质中可以传输非束缚态空间亮孤子。传输稳定性与其背景平面波的横向渐近传播常数q和χ⁽³⁾,χ⁽⁵⁾系数有关,非平凡相位因子在三、五阶效应竞争中的平衡作用,是获得非束缚态空间亮孤子稳定传输的关键。     

Full-vectorial analysis of optical vortex propagation in anisotropic cubic-quintic non-linear optical medium

This paper presents for the first time a full-vectorial analysis of optical vortex propagation in anisotropic cubic-quintic (CQ) non-linear medium. The purpose is to investigate the energy transfer mechanism and stability between orthogonal field components and how they are affected by the presence of material anisotropy in CQ materials. The numerical simulations were carried out via a three-dimensional finite difference based beam propagation method (3D-FD-BPM) which is capable of handling variations in any of the permittivity tensor components. Therefore, in this work we allowed all tensor components to vary independently and simulate vortex propagation for distances several times longer than the diffraction length. We expect that this work can provide new and important information regarding the behavior of these objects that may become valuable for the design of new photonic devices.