【作者】 朱兴；

【导师】 吴庭万； 陈武喝；

【作者基本信息】 华南理工大学 ， 光学， 2010， 硕士

【摘要】 本论文研究光孤子的传输特性,对时间孤子和空间孤子都进行了研究。研究时间光孤子的传输特性对于设计和实现高速光孤子通信系统具有重要的理论意义和现实意义。光学空间孤子在全光开关、光波导、光显示、光计算等方面有应用潜力,同时也在相关的物理理论的研究、验证等方面有重要的意义。在研究时间孤子时,详细讨论了一种解光纤中非线性薛定谔方程的数值方法—对称分步傅里叶法。研究了三阶色散效应对基态孤子传输的影响,发现正、负三阶色散都会使基态孤子在传输过程中产生畸变。针对研究高阶孤子情况较少的情况,研究了高阶孤子对间的相互作用,发现高阶孤子对与一阶孤子对的传输特性不同,高阶孤子对会在中间周期性的产生衍生孤子,在相同的传输距离内,三阶孤子对产生的衍生孤子多于二阶孤子对。本论文在研究光学格子中的带隙光孤子时,获得一维、二维光学格子的布洛赫带结构都是用平面波展开法,在计算孤子形状时,一维情况用打靶法,二维情况用改进的平方算子迭代法,模拟孤子传输时,都是用分步傅里叶法。研究了饱和非线性介质中一维超晶格光学格子中的带隙空间光孤子,对其传输特性进行了详细的研究。发现带隙孤子只存在于半无穷带隙,而且只能在低功率区域稳定传输。研究了饱和介质中正方形的二维光学格子中的空间缺陷带隙孤子,研究发现对于负缺陷,孤子可以存在于第一带隙,随着负缺陷的增大,缺陷孤子不再是在第一带隙都能稳定传输,而是只能在中等功率范围内稳定传输;而在半无穷带隙,随着缺陷深度的增加,孤子在整个半无穷带隙都不能稳定传输。对于正缺陷,缺陷孤子只存在于半无穷带隙,而且只能在低功率范围内稳定传输。本论文还对三角形格子中的缺陷孤子进行了研究,研究发现,对于正缺陷,孤子只存在于半无穷带隙,而且只能在低功率范围内稳定传输。而对于负缺陷,孤子不但能存在于半无穷带隙,而且能存在于第一带隙,随着负缺陷的加深,孤子将在整个半无穷带隙内不稳定,在第一带隙内,将经历低功率不稳定,高功率和低功率不稳定,直至整个第一带隙不稳定的过程。最后对克尔介质中正方形二维光学格子中的带隙空间光孤子的稳定性进行了讨论。发现,在半无穷带隙内离散孤子和涡旋孤子在靠近带边时都不能稳定传输。更多还原

【Abstract】 The paper has researched the transmission characteristics of solitons. Time solitons and spatial solitons have been studied. Researching for time solitons has theoretical and practical significance for designing and implementing high-speed optical solitons communication. Spatial optical solitons have the potential applications in all-optical switching, optical waveguide, optical display, optical computing, etc. At the same time,the spatial optical solitons also have the important significance in related theoretical researching and validation of physicsWhen researched the time solitons, A form of symmetric split-step Fourier method is carefully discussed. Researched the influence of third-order dispersion on state-ground solitons transmission, found the state-ground solitons pulse will be distorted by the third-order dispersion. The case of researching the two high-order solitons are less, We have studied the interaction between two high-order solitons, found that the transmission characteristics of the two second-order solitons and the two third-order solitons are significantly different from the two first-order solitons, the two second-order solitons and the two third-order solitons will not attract and collide periodically, the interaction between the two second-order solitons and the two third-order solitons will periodically produce ramification solitons in the middle, in same transmission distance, the third-order soliton-pair produce more derivative solitons than the second-order soliton-pair.When researched gap solitons in optical lattices, get the blouch band structures of one-dimensional and two-dimensional lattices both by the plane wave expansion method. To calculate the numerical gap solitons solution of one-dimension optical lattices, used the shooting method, and used The modified squared-operator method to calulate the numerical gap solitons solution of two-dimension optical lattices. When simulated spatial optical solitons transmit, used symmetric split-step Fourier method.The paper has researched gap solitons in superlattice, the propagation characteristics of these solitons were carefully discussed. It is found that these gap solitons only transmit stably in low power region.Gap solitons in two-demensional square lattices in focusing saturable nonlinearity have been researshed, we constructed a defect in the square lattices. It is found that for the negative defect, the defect gap solitons not only exist in the semi-infinite gap, but also exist in the first gap, increasing the defect depth, the stable region only in the moderate power region in the first gap; In the semi-infinite gap, with the increasing of defect depth, defect solitons will unstably transmit in the entire gap. Forpositive defect, gap solitons only exist in semi-infinite gap, and these solitons only can stably transmit in low power region and unstably transmit in high power region. The paper also has researshed the defect gap solitons in triangular optical lattices.For the negative defect, solitons only exist in semi-infinite gap, and it can stably transmit only in the lower power region. For the negative defect, solitons not only exist in the semi-infinte gap, but also exist in the first gap, with the increasing of thedefect depth, the solitons will unstable in the whole semi-infinte gap, and in the first gap, it will be unstable in lower power region, high power region and lower power region, untill the whole first gap region.Finally, the paper has researched the gap solitons’stability in kerr nonlinearity, it is found that in the semi-infinite gap, vortex and discrete solitons near the band can not stably transmit.更多还原