非线性分数薛定谔方程中高斯光束的传输动力学

Propagation Dynamics of Gaussian Beams in Nonlinear Fractional Schr?dinger Equation

基于包含竞争非线性效应的分数薛定谔方程,通过分步傅里叶变换方法,详细地研究了单高斯光束和双高斯光束在三次-五次竞争非局域非线性介质中的传输动力学。结果表明:光束的振幅和宽度对于高斯光束演化为束缚态孤子具有一定的影响。在局域和非局域介质中,单高斯光束和同相双高斯光束均具有一定的衍射现象,并且在非局域介质中衍射现象更为明显。此外,三次和五次非局域非线性之间的平衡,对于孤子的稳定性也至关重要。在传输过程中,同相双高斯光束表现为强烈的吸引作用,但随着间隔的增大,光束间的吸引力逐渐减弱;而反相双高斯光束则表现为排斥作用,光束间隔越大,排斥力越小,且光束在局域和非局域介质中规律相似。

Based on the competitive nonlinear fractional Schr?dinger equation,the propagation dynamics of single Gaussian beam and double Gaussian beams in nonlocal nonlinear media with cubic-quintic competition are numerically simulated by the split-step Fourier transform method.The results show that the amplitude and width of the beam have a certain effect on the evolution of the Gaussian beam into a bound soliton.For the single Gaussian beam,when the beam amplitude or width decreases,the pulse power of the bound soliton also decreases.When other conditions are the same,the peak power of the soliton in the local medium is obviously greater than the peak power in the nonlocal medium.When the amplitude of double Gaussian beams decrease or the width increase,the soliton changes from respiratory like state to bound state,and the diffraction phenomenon increase.In local and nonlocal media,both single Gaussian beam and in-phase double Gaussian beams have certain diffraction phenomena,and the diffraction phenomenon is more obvious in nonlocal media.Moreover,the balance between the cubic and quintic nonlocal nonlinearities is also crucial to the stability of the soliton.For the interaction between double Gaussian beams,the interval between the two beams also has a certain influence on the stable transmission of the soliton.In the transmission process,the in-phase double Gaussian beams show a strong attraction.The smaller the beam interval,the greater the interaction force,the weaker the diffraction phenomenon and the smaller the respiratory cycle.And affected by the interaction force,the beam has a certain distance interval in the transmission process.The pulse width and period in nonlocal media are larger than those in local media.While out-of-phase double Gaussian beams exhibit repulsion,the larger the beam spacing,the smaller the repulsive force.The pulse width in local media is wider than that in nonlocal media,and other phenomenan are consistent.