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利用零邻域的马克劳林展开对归一化非线性薛定谔方程的频域差分形式进行分析,得出一个能够同时考虑光学媒质的色散作用以及非线性克尔作用的时域快速数值差分递推公式.选取若干算例,将运用该公式的数值计算结果与已知的解析结果和传统分步傅里叶方法所得的计算结果做了相应的比较,结果表明这种快速数值差分递推公式不但拥有相当快的计算速度,也有很高的计算精度,而且在物理上符合光脉冲在光学媒质中传输时色散和非线性作用同时施加影响的客观实际,这说明它是研究非线性光学媒质中光脉冲传输的一种科学、合理而快速有效的数值计算方法.
关键词:
快速数值差分递推公式
零邻域马克劳林展开
非线性薛定谔方程
光脉冲传输 相似文献
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铜、溴化铜、铅激光光脉冲的形状和瞬时发散度 总被引:1,自引:1,他引:0
本文报道了一种简单的测量光脉冲强度的时空分布方法。用此方法得到Cu/CuBr和Ph激光的具有立体感的光脉冲形状,它包括了光脉冲结构的一些细节,以及光脉冲的瞬时发散度。 相似文献
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波长共享的WDM无源光网络媒质接入控制算法及其性能分析 总被引:2,自引:2,他引:0
结合波长分配和前跳虚时钟算法,提出了一个基于连接的WDM无源光网络媒质接入控制算法.通过理论和仿真,分析了此算法的延时保证和公平性. 相似文献
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光子晶体中缺陷的色散导致的群速度降低 总被引:8,自引:4,他引:4
利用传输矩阵方法计算了包含色散媒质缺陷的一维光子晶体的复透射系数,其中色散媒质用洛仑兹振子模型描述。计算了由复透射系数定义的等效复折射率并由此研究了频谱位于缺陷模频率附近的光脉冲的群速度。结果发现,由于缺陷模附近的透射谱敏感地依赖于缺陷层的光学厚度,而缺陷层的色散使缺陷层光学厚度随频率变化而改变,从而使包含缺陷的光子晶体的等效色散性质明显地依赖于缺陷的色散行为。由于光脉冲是由多种频率成分的单色场迭加构成的,透射脉冲由各单色场透射后重新迭加构成,因此波包的传播由介质的等效色散性质决定。与包含无色散缺陷的光子晶体相比,缺陷的色散可导致极慢的群速度。通过改变振子强度,群速度可从极慢光速转变为超光速(superluminal)。 相似文献
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脉冲在时域二次折射率介质中的传播 总被引:3,自引:1,他引:2
从空域与时域的相似性出发,把克尔介质近似为时域二次折射率介质,从而得到了脉冲在该介质中的解析形式,并给出了相应的时域传输矩阵。 相似文献
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Review on second-harmonic generation of ultrasonic guided waves in solid media (I):Theoretical analyses
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Considering the high sensitivity of the nonlinear ultrasonic measurement technique and great advantages of the guided wave testing method, the use of nonlinear ultrasonic guided waves provides a promising means for evaluating and characterizing the hidden and/or inaccessible damage/degradation in solid media. Increasing attention on the development of the testing method based on nonlinear ultrasonic guided waves is largely attributed to the theoretical advances of nonlinear guided waves propagation in solid media. One of the typical acoustic nonlinear responses is the generation of second harmonics that can be used to effectively evaluate damage/degradation in materials/structures. In this paper, the theoretical progress of second-harmonic generation (SHG) of ultrasonic guided wave propagation in solid media is reviewed. The advances and developments of theoretical investigations on the effect of SHG of ultrasonic guided wave propagation in different structures are addressed. Some obscure understandings and the ideas in dispute are also discussed. 相似文献
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Review on second-harmonic generation of ultrasonic guided waves in solid media(Ⅰ): Theoretical analyses
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《中国物理 B》2017,(11)
Considering the high sensitivity of the nonlinear ultrasonic measurement technique and great advantages of the guided wave testing method, the use of nonlinear ultrasonic guided waves provides a promising means for evaluating and characterizing the hidden and/or inaccessible damage/degradation in solid media. Increasing attention on the development of the testing method based on nonlinear ultrasonic guided waves is largely attributed to the theoretical advances of nonlinear guided waves propagation in solid media. One of the typical acoustic nonlinear responses is the generation of second harmonics that can be used to effectively evaluate damage/degradation in materials/structures. In this paper, the theoretical progress of second-harmonic generation(SHG) of ultrasonic guided wave propagation in solid media is reviewed. The advances and developments of theoretical investigations on the effect of SHG of ultrasonic guided wave propagation in different structures are addressed. Some obscure understandings and the ideas in dispute are also discussed. 相似文献
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In this paper the propagation of Lorentz-Gaussian beams in strongly nonlinear nonlocal media is investi- gated by the ABCD matrix method. For this purpose, an expression for field distribution during propagation is derived and based on it, the propagation of Lorentz-Gaussian beams is simulated in this media. Then, the evolutions of beam width and curvature radius during propagation are discussed. 相似文献
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Propagation of a Gaussian beam in an absorbing waveguide is analyzed for cubic-quintic and saturable media taking into account both linear and nonlinear absorption. A “collective variable approach” technique, based on trial functions, is used to solve the general nonlinear Schrodinger equation. In the absence of losses, we construct a diagram which defines regions of oscillatory and diffractive beam propagation for both types of media, and also a diagram that compares bistable behavior in such media. We show that if the linear and nonlinear absorption coefficients are small, the behavior of the oscillations of the beam width on propagation allows one to distinguish between cubic-quintic and saturable media. By reversing the sign of the linear absorption, we analyze the behavior of the beam propagation in media with gain and nonlinear absorption. In cubic-quintic media, the energy reaches a plateau for certain ratios of gain to losses, whereas for saturable media, the energy increases throughout the beam propagation. 相似文献
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研究得到了偏离束腰入射的复宗量Laguerre-Gauss光束在强非局域非线性介质中传输的解析表达式,并且得到了其二阶矩束宽的解析解.通过例子研究了偏离束腰入射的复宗量Laguerre-Gauss光束在强非局域非线性介质中传输性质.结果表明:非(0, m)模的复宗量Laguerre-Gauss光束的光束形状随着传输而发生改变,并以Δz=πzc为周期做周期性演化.而(0,m)模复宗量Laguerre-Gauss光束在演化过程中则形状保持不变,仅改变光束宽度;不论功率多大,在偏离束腰入射条件下总是表现为呼吸子;只有当其为束腰入射,并且入射功率等于临界功率时才能形成孤子.
关键词:
强非局域非线性
复宗量Laguerre-Gauss光束
二阶矩束宽
空间光孤子 相似文献
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A three-dimensional model of the forward propagation of nonlinear sound beams in inhomogeneous media, a generalized Khokhlov-Zabolotskaya-Kuznetsov equation, is described. The Texas time-domain code (which accounts for paraxial diffraction, nonlinearity, thermoviscous absorption, and absorption and dispersion associated with multiple relaxation processes) was extended to solve for the propagation of nonlinear beams for the case where all medium properties vary in space. The code was validated with measurements of the nonlinear acoustic field generated by a phased array transducer operating at 2.5 MHz in water. A nonuniform layer of gel was employed to create an inhomogeneous medium. There was good agreement between the code and measurements in capturing the shift in the pressure distribution of both the fundamental and second harmonic due to the gel layer. The results indicate that the numerical tool described here is appropriate for propagation of nonlinear sound beams through weakly inhomogeneous media. 相似文献
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In the framework of nonlinear wave optics,we report the evolution process of a dipole breathing wave in lossy nonlocal nonlinear media based on the nonlocal nonlinear Schr?dinger equation.The analytical expression of the dipole breathing wave in such a nonlinear system is obtained by using the variational method.Taking advantage of the analytical expression,we analyze the influences of various physical parameters on the breathing wave propagation,including the propagation loss and the input power on the beam width,the beam intensity,and the wavefront curvature.Also,the corresponding analytical solutions are obtained.The validity of the analysis results is verified by numerical simulation.This study provides some new insights for investigating beam propagation in lossy nonlinear media. 相似文献
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研究了1+1维高斯型双光束在含小损耗的强非局域非线性介质中的传输特性。通过对该介质中光束传输遵循的非局域非线性薛定谔方程进行近似简化,得到了含小损耗强非局域非线性介质中1+1维高斯型双光束传输模型。在此基础上运用解析的方法研究了双光束传输的演化规律,得到了准双孤子解。经过进一步分析发现,在传输过程中两光束中心的轨迹为艾里函数;两光束会准周期性地碰撞、分离;随着传输距离的增大,两光束中心之间的最大距离会越来越大。另一方面,当损耗逐渐增大时,两光束的碰撞空间周期将变短,同时两光束中心之间的最大距离也越来越大。 相似文献