PT对称复数势光学格子中空间光孤子传输特性的研究

发布时间：2018-04-11 18:12

本文选题：PT对称复数势 + 涡旋光孤子　；参考：《华南理工大学》2016年博士论文

【摘要】：由于光束自然衍射效应、介质非线性效应和复数势增益/损耗效应之间的相互平衡,光束可以在非线性介质中保持形状不变地进行传输,进而形成空间光孤子。由于空间光孤子所具有的这种独特属性,其在实现全光通信和全光器件方面具有巨大的应用价值,尤其是携带角动量的涡旋光孤子在光学微操纵、粒子捕获、信息传输领域有着重要应用。另一方面,空间光孤子的研究可以为相邻学科的发展提供理论指导,具有重要的学术价值。本文从描述光束传输特性的非线性薛定谔方程出发,采用数值模拟、数值计算及数值分析的方法,研究了PT对称复数势光学格子中空间光孤子的传输特性。具体研究成果如下:1.研究了PT对称正方形光学格子中的涡旋光孤子和同相位四极孤子的存在性、稳定性以及传输特性。涡旋光孤子和同相位四极孤子存在于PT对称复数势布洛赫能带第一带隙且可以在一定的参数范围内稳定。由不携带角动量环形光束形成的同相位四极孤子比涡旋光孤子更稳定。PT对称复数势势深的减小或增益/损耗系数的增大都会导致涡旋光孤子稳定范围的缩小。当涡旋光孤子不稳定时,其功率在传输过程中随传输距离发生振荡,而在实数势光学格子中涡旋光孤子功率在传输过程中始终保持不变。PT对称复数势增益/损耗系数对涡旋光孤子形成有着重要影响,当其取值接近临界阈值时,涡旋光孤子发生相变。2自聚焦饱和非线性介质PT对称光学格子中饱和系数以及PT对称复数势对涡旋光孤子都有着重要影响。只有当非线性饱和系数大于某个临界阈值时涡旋光孤子才可以稳定存在。随着饱和系数的增大,涡旋光孤子的存在范围逐渐缩小,但其稳定范围先扩大后缩小。当饱和系数足够大时,模型中的非线性项可以近似为线性项,此时涡旋光孤子不存在。保持饱和系数不变,随着PT对称复数势增益/损耗系数的增大,涡旋光孤子的存在范围和稳定区间都会缩小。当PT对称复数势增益/损耗系数等于其临界阈值时,涡旋光孤子仍然可以存在,但是它在传输过程中发散很快。在同一饱和系数下,异相位四极孤子比涡旋孤子稳定范围更大,而同相位四极孤子稳定范围最小。3.具有单点缺陷的PT对称三角格子可以支持缺陷基本孤子和缺陷涡旋孤子的稳定传输。三角格子缺陷深度对缺陷基本孤子的存在性有着重要影响;当负缺陷深度绝对值足够大时,负缺陷基本孤子不存在。无缺陷和正缺陷以及负缺陷基本孤子的稳定性符合anti-Vakhitov-Kolokolov准则。然而负缺陷涡旋孤子在整个存在范围内不稳定,而正缺陷和无缺陷涡旋孤子可以在一定的范围内稳定存在,正缺陷在一定程度上可以抑制缺陷涡旋孤子的不稳定性。最后,以正缺陷基本孤子为例,发现增大PT对称复数势增益/损耗系数不仅会使缺陷孤子的存在范围缩小,而且会使缺陷孤子变得更不稳定。4.两维混合线性非线性PT对称复数势可以支持空间光孤子的稳定传输。非线性调制深度对孤子的形成和存在有着重要影响。在非线性调制深度的一个确定范围内,孤子随传播常数的变化会发生形变。孤子形变和PT对称非线性调制深度和非线性虚部相对强度之间有着重要关系。不同的非线性调制深度会致使系统呈现自聚焦和自散焦两种非线性效应。在两种非线性效应下,空间光孤子的稳定范围在非线性调制虚部相对强度不变的情况下随着非线性调制深度的增大先扩大后缩小;而当PT对称非线线性调制深度不变时,其稳定范围随着虚部相对强度的增大逐渐缩小。非线性PT对称光学格子周期的改变也会对空间光孤子的传输特性产生重大影响。当光束的入射角较小时,孤子在传输过程中保持形状不变,但是孤子的质心随传输距离发生周期性振荡,其振荡幅度随入射角的增大而变大。但是,当光束入射角足够大时,孤子在传输过程中形状发生改变,并且孤子质心随传输距离发生无规则振荡。5.自散焦Kerr非线性介质虚部为准一维的两维PT对称复数势光学格子中非PT对称多峰孤子。发现具有峰数为偶数和奇数的多峰孤子均存在于第一带隙,并且可以同相位非PT对称多峰孤子在第一带隙的某些范围内稳定。但是对一些同相位非PT对称的多峰孤子它们的稳定区间是分段的,这和实数势中的情况有很大不同。随着复数势的增益/损耗系数的增大,同相位非PT对称多峰孤子的存在范围和稳定范围都逐渐缩小。详细分析了孤子的非对称性。异相位非PT对称多峰孤子在其存在范围内不稳定。复数势中具有PT对称性对称性的单峰、双峰、菱形四峰和五峰孤子均存在于第一带隙。单峰、双峰和菱形五峰孤子可以在很大的范围内稳定传输,而菱形四峰孤子不能稳定存在。
[Abstract]:Because of the natural balance beam diffraction effect, nonlinear dielectric effect and complex potential gain / loss effect, can keep the shape of beam in nonlinear media constantly for transmission, and the formation of spatial optical solitons. Because of the spatial optical soliton has unique properties, it has great application value in optical communication and optical implementation the device, especially the vortex solitons carry angular momentum capture in optical micromanipulation, particle field, information transmission has important applications. On the other hand, providing theoretical guidance for the research of optical spatial solitons can be adjacent to the subject of development, which has important academic value. This paper from the nonlinear Schrodinger equation describing propagation properties starting with numerical simulation, numerical calculation and numerical analysis method, studied the transmission characteristics of PT space of complex symmetric solitons in optical lattice potential. Research results are as follows: 1. the existence of PT symmetric square optical lattice of optical vortex solitons and soliton phase with quadrupole, stability and transmission characteristics. Vortex solitons and the same phase soliton exists in PT complex symmetric quadrupole potential Bloch can take the first gap and can be stable in a certain range of the parameters is not. With stable.PT complex symmetric potential depth or the decrease of gain / loss coefficient increases will lead to stable vortex solitons in the narrowing of the scope more than optical vortex solitons with soliton phase quadrupole angular momentum annular beam is formed. When the vortex soliton is stable, its power in the process of transmission with transmission distance oscillation, and in the real potential of optical vortex solitons in optical lattice in the power transmission process remains the same.PT complex symmetric potential gain / loss coefficient of optical vortex soliton formation has important effect, when the The value is close to the critical threshold, vortex soliton phase.2 self focusing nonlinear medium saturation saturation coefficient PT symmetric optical lattice and PT complex symmetric potential on the optical vortex solitons have a significant impact. Only when the nonlinear coefficient is larger than a critical threshold value of optical vortex solitons can exist stably. With the increase of the coefficient of saturation the existence range, vortex solitons are gradually reduced, but the stable range of expanding shrink. When the saturation coefficient is large enough, the nonlinear model can be approximated as linear, the vortex solitons do not exist. Keep the saturation coefficient unchanged, with the increase of PT complex symmetric potential gain / loss coefficient, vortex solitons the existence of range and stable range will be reduced. When the PT of complex symmetric potential gain / loss coefficient is equal to the critical threshold, vortex solitons can still exist, but it is in the process of transmission The divergent soon. At the same saturation coefficient under different phase is greater than the quadrupole soliton stable vortex solitons, stable transmission and PT symmetric triangular lattice with single point defects in phase with the stable range of the minimum.3. quadrupole soliton can support the defects of basic soliton and vortex solitons. The triangular lattice defect defect depth of defects of basic soliton there have an important impact; when the absolute value of the negative defect depth is large enough, the negative defect fundamental soliton does not exist. No defects and defects and defects of basic stability of negative soliton accords with anti-Vakhitov-Kolokolov rule. However, the negative defect in the whole vortex solitons exist unstable range, and is defective and defect free vortex solitons can exist stably in a certain range, it can inhibit the defect defects of vortex solitons in a certain degree of instability. Finally, the positive defect soliton as an example, the increase of PT complex symmetric potential gain / loss coefficient will not only cause the defect of soliton existence range is narrow, and the defects become more unstable and stable soliton transmission.4. two dimensional mixed linear nonlinear PT complex symmetric potential can support spatial solitons. The nonlinear modulation depth of the soliton formation and plays an important role in a. A determined range of nonlinear modulation depth, with the changes of soliton propagation constant deformation will occur. There is important relationship between soliton deformation and PT symmetric nonlinear modulation depth and nonlinear imaginary relative intensity. Different nonlinear modulation depth will cause the system presents a self focusing and self defocusing nonlinear effect. Two in two kinds of nonlinear under the effect of the stable range of spatial solitons in the imaginary part of the relative intensity of nonlinear modulation unchanged with the increase of nonlinear modulation depth expanding shrink; and when PT Non symmetric linear modulation depth is constant, the stability range with the increase of the imaginary part of the relative strength gradually reduced. Nonlinear PT symmetric optical lattice periodic change will have a significant impact on the transmission characteristics of optical spatial solitons. When the beam incident angle is small, the soliton shape remains unchanged in the transmission process, but the centroid of the soliton with the propagation distance periodic oscillation, the oscillation amplitude with the increase of the incident angle becomes larger. However, when the incident angle is large enough, the soliton shape change during transmission, transmission distance and centroid with the soliton has no regular oscillations in self defocusing nonlinear media.5. Kerr virtual PT for non symmetrical multi peakons two dimensional PT complex symmetric quasi one-dimensional optical lattice potential. It was found that the multi peak soliton with peak number is even or odd exist in the first gap, and the same phase non symmetrical multi peak solitary PT In certain range of the first band gap in the stable. But for some stable interval phase with non PT symmetric multi peak soliton are segmented, and the real potential situation is very different. With the increase of the complex potential gain / loss coefficient, there is the same phase non symmetrical multi peak soliton PT and the range of stability is gradually narrowing. A detailed analysis of the non symmetry of the soliton phase. PT non symmetric multi peak soliton in the unstable range. With PT symmetry symmetry is unimodal, the complex potential in Shuangfeng, diamond four and five peaks were solitons exist in the first gap. A single peak, and Shuangfeng Five Diamond Peak soliton can be stable transmission in a large range, and there are four Diamond Peak solitons can not be stable.

【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O437

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