利用空问诱导色散补偿介质色散

研究了超短脉冲贝塞尔光束在色散介质中的传输特性，指出空间诱导色散效应可以用来补偿介质色散作用，从而可以在色散介质中实现无衍射无色散的类时空孤子波的传输。用理论推导和数值模拟的方法得到的具有反常色散性质的空间诱导色散可以有效地补偿介质色散。数值模拟的结果表明，由于超短脉冲贝塞尔光束的无衍射无色散传输距离受到高阶色散效应和贝塞尔光束空间受限两方面的限制，无衍射无色散传输只能在有限距离内近似实现。通过增加脉冲长度可以减小高阶色散效应的影响。在传输距离小于衍射距离时，空间诱导色散效应可以很好地描述脉冲演化和色散补偿过程。     

利用空间诱导色散补偿介质色散

研究了超短脉冲贝塞尔光束在色散介质中的传输特性 ,指出空间诱导色散效应可以用来补偿介质色散作用 ,从而可以在色散介质中实现无衍射无色散的类时空孤子波的传输。用理论推导和数值模拟的方法得到的具有反常色散性质的空间诱导色散可以有效地补偿介质色散。数值模拟的结果表明 ,由于超短脉冲贝塞尔光束的无衍射无色散传输距离受到高阶色散效应和贝塞尔光束空间受限两方面的限制 ,无衍射无色散传输只能在有限距离内近似实现。通过增加脉冲长度可以减小高阶色散效应的影响。在传输距离小于衍射距离时 ,空间诱导色散效应可以很好地描述脉冲演化和色散补偿过程     

超短脉冲贝塞尔-高斯光束在自由空间的传输特性

 使用复解析信号法研究了束宽与频率无关的超短脉冲贝塞尔-高斯光束在自由空间的传输特性。研究表明：在无衍射长度内，超短脉冲贝塞尔-高斯光束的横向光强分布几乎不变并集中在传输轴附近，轴上脉冲随传输距离增加而展宽。在无衍射长度外，横向光强分布显著扩展。随传输距离增加，轴上光谱蓝移先增加，达到极大值后逐渐减小，最后在远场趋于一渐近值。对单周期的超短脉冲贝塞尔-高斯光束的轴上光谱蓝移先增加，达到极大值0.50 fs^-1。然后逐渐减小，在远场蓝移趋于渐近值0.16 fs^-1。     

贝塞尔-高斯脉冲光束在色散介质中的时间和光谱特性

 对等衍射长度贝塞尔-高斯脉冲光束在色散介质中的时间和光谱特性作了研究，结果表明，通过选择适当的空间参数，贝塞尔-高斯脉冲光束沿轴上传输时，脉冲宽度不变。传输距离小于无衍射长度时，随衍射角增加，功率谱形状未变，脉冲波形保持不变；传输距离大于无衍射长度时，随衍射角增加，光谱由蓝移变为红移，脉冲展宽。     

类贝塞尔脉冲光束传输中的空间诱导色散效应

利用空间诱导色散概念,从理论上研究了等束腰宽度的类贝塞尔脉冲光束在自由空间中传输性质.在一阶近似的情况下,类贝塞尔脉冲光束的空间和时间部分可以做分离变量,空间部分在传输过程中保持类贝塞尔光束传输的特性,而时间波形部分的传输遵循空间诱导色散理论.利用数值模拟方法模拟了 Bessel-Gauss 脉冲光束和elegant Laguerre-Gauss脉冲光束的传输.结果证实,只要传输距离小于类贝塞尔光束的无衍射距离,空间诱导群速度色散理论能够很好地描述类贝塞尔脉冲光束脉冲形状的演化过程.     

矢量效应对超短脉冲光束非傍轴传输的影响

从严格的矢量非傍轴传输方程出发,并通过傅里叶变换及角谱分析的方法,分析了在超短脉冲光束中,矢量效应对其在自由空间中的非傍轴传输的影响。结果表明,矢量效直对脉冲光束的标量傍轴解的修正有着重要的影响,当对脉冲光束进行非傍轴传输处理时,必须考虑它的矢量特性。基于上述分析,得到了支配超短脉冲光束传输的矢量非傍轴方程的一个完整积分解。从这个积分解出发,通过对电场进行泰勒级数展开的方法,得到了一种相对简单的方法,通过这种方法,可以从脉冲光束的已知标量傍轴解来求出矢量非傍轴波动方程的相对精确解。     

自由空间中超短脉冲光束的非傍轴效应分析

在应用时间与空间傅里叶变换的基础上, 运用泰勒展开的方法, 得出了一种对多周期超短脉冲光束进行非傍轴修正的方法, 并将其应用于脉冲高斯光束．与数值结果的比较表明, 对于束宽在波长量级的脉冲光束, 二阶修正已经很接近非傍轴精确解, 并在例子中观察到：由于超短脉冲光束中时空耦合效应的存在, 脉冲的时间分布将会影响修正的空间分布．     

5PW超短脉冲空间滤波器色差对时间信噪比的影响

研究了大口径级联空间滤波器中色差造成的离焦色散与传输时间延迟对超短脉冲波形与时间信噪比的影响。针对神光-5PW高功率超短脉冲系统,通过数值模拟,定量分析了光束口径、色差等因素与近远场脉冲波形畸变和时间信噪比退化的关系。从脉冲波形和时间信噪比的角度,给出了大口径空间滤波器消色差后残余色差的容忍范围,为高功率超短脉冲系统中空间滤波器的设计与优化提供了理论依据。     

带宽对脉冲贝塞尔光束传输的影响

从惠更斯-菲涅耳衍射积分公式出发得到具有高斯型频谱分布的脉冲贝塞尔光束频率域的传输表示式,并使用傅里叶变换最后推导了脉冲贝塞尔光束时间域的传输公式。根据得到的公式通过具体数值计算对脉冲贝塞尔光束在自由空间中的传输进行了研究。计算结果表明脉冲光束的带宽对脉冲贝塞尔光束传输中的脉冲时间延迟和脉冲宽度产生影响。具体表现为脉冲光束带宽的增宽使脉冲时间延迟增大,并使脉冲时间波形的后沿拖长,从而导致脉冲宽度增宽。脉冲时间延迟和脉冲宽度还随传输距离发生变化。脉冲光束传输距离越大,脉冲时间延迟越大,脉冲宽度变得越宽。     

贝塞尔高斯光束在各向异性湍流中的传输特性

采用随机相位屏仿真方法模拟了各向异性大气湍流及贝塞尔高斯涡旋光束在其中的强度分布、在轴闪烁指数和抖动效应,分析了各向异性湍流参数和波源参数对涡旋光束传输质量的影响.结果表明,在各向异性大气湍流中,贝塞尔高斯涡旋光束的强度分布随传输距离的变化情况与离轴距离有关,仅一级圆环处强度值单调递减,其余次级圆环处强度值均呈现先增后降的趋势.在近距离处,贝塞尔高斯涡旋光束的在轴闪烁指数随波形参数的增大而减小,随光束宽度的增大呈现先上升后下降再上升的趋势,该现象与贝塞尔高斯光束的光斑尺寸大小相关;其抖动效应随波形参数、拓扑荷数量、波长和束腰半径的增大而减弱.但在远距离处贝塞尔高斯涡旋光束的闪烁效应和抖动效应随波形参数的影响与近距离处相反,这与贝塞尔高斯光束的展宽突然增大的现象一致.贝塞尔高斯涡旋光束在各向异性湍流大气中的抖动效应小于在各向同性湍流大气中的情况,并且在远距离处大于拉盖尔高斯涡旋光束的抖动效应.     

脉冲厄米高斯光束的载波相位分析

采用复q参量法对脉冲厄米高斯光束在自由空间中的传输进行了分析.在振幅O阶和位相一阶近似条件下,得到其传播过程中载波位相近似公式.运用数值方法和近似公式进行对比研究,发现在脉宽大于5 fs或在远场情况下,两者符合较好.采用近似办法,分别研究了厄米函数阶次、束宽与位置对载波相位的影响.研究表明,在光轴上远场,载波相位趋近于-(m+n+1)π/2,其变化快慢与厄米函数阶次(m+n+1)成正比;束腰宽度越大,则载波相位变化越慢;另外,离光轴距离越远,其导致的载波相位越大,且最大位置都出现在z=Z_R(ω_0)/3处.     

Paraxial and nonparaxial polynomial beams and the analytic approach to propagation

We construct solutions of the paraxial and Helmholtz equations that are polynomials in their spatial variables. These are derived explicitly by using the angular spectrum method and generating functions. Paraxial polynomials have the form of homogeneous Hermite and Laguerre polynomials in Cartesian and cylindrical coordinates, respectively, analogous to heat polynomials for the diffusion equation. Nonparaxial polynomials are found by substituting monomials in the propagation variable z with reverse Bessel polynomials. These explicit analytic forms give insight into the mathematical structure of paraxially and nonparaxially propagating beams, especially in regard to the divergence of nonparaxial analogs to familiar paraxial beams.     

Application of the Wigner distribution function to complex-argument Hermite– and Laguerre–Gaussian beams beyond the paraxial approximation

The Wigner distribution function (WDF) is applied to study the propagation of complex-argument Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) beams beyond the paraxial approximation. The analytical expressions for their intensity distributions in free-space propagation are derived, which are expressed in terms of Hermite polynomials for nonparaxial complex-argument HG beams and in terms of the sum of finite Hermite polynomials for nonparaxial complex-argument LG beams. A detailed comparison of the WDF approach, series expansion method and paraxial expressions is made, which shows that in the paraxial regime the WDF approach and series expansion method deliver consistent results with that of paraxial expressions. Beyond the paraxial approximation, the WDF approach offers convergent results, whereas the series expansion method has a limited applicable range, within which it gives consistent results with that of WDF approach but beyond which it gives unrealistic and divergent results.     

经光阑衍射的高阶贝塞耳光束位相奇点演化特性

推导出了高阶贝塞耳光束通过有光阑近轴ABCD光学系统传输的解析公式,用以研究了高阶贝塞耳光束被光阑衍射位相奇点的演化特性.结果表明:高阶贝塞耳光束经光阑系统衍射后,中心光涡旋始终存在,拓扑电荷守恒,但涡旋核大小会随光阑半径、传输距离和光束阶数而变化;随光阑半径和传输距离变化,圆刃型位错会消失或产生.     

非傍轴矢量异常空心光束的传输特性

 将Cai提出的异常空心光束的理论模型推广到非傍轴范畴,推导出非傍轴矢量异常空心光束传输的解析表达式,用以研究它在自由空间中的传输特性。研究表明,异常空心光束在传输过程中光束形状会发生变化。与高斯光束不同,非傍轴异常空心光束傍轴近似成立条件依赖于传输距离,这与异常空心光束光强分布随传输距离的变化有关。非傍轴异常空心光束远场的光束质量可用桶中功率来描述,桶中功率随f参数(波长与束腰宽度的比值)的增大而减小。     

真空中线性啁啾时空高斯脉冲传输特性的分析

利用稳态相位点的方法研究了线性啁啾时空高斯脉冲传输过程中的相位特性，并在二阶近似的情况下讨论了其传输过程中的时空特性，两种方法从不同侧面得出了相同的结论，即：时空高斯脉冲在传输的过程中，在无穷远处交退化为球面波，或者在旁轴近似的情况下退化为平面波。     

Spatial optical solitons in inhomogeneous elliptic core saturating nonlinear fiber

We have investigated the propagation characteristics of spatial optical solitons in saturating nonlinear waveguide employing JWKB and paraxial ray approximation. We have obtained two second-order coupled nonlinear differential equations for transverse soliton widths of solitons. Threshold power for stable propagation of the beam has been calculated from these coupled equations. We have undertaken stability analysis, which predicts robustness of these solitons. Both guiding as well as antiguiding cases have been considered and shown that stable spatial soliton propagation is possible in both cases.     

Photonic band gap of three dimensional magnetized photonic crystal with Voigt configuration

We study Bessel beams of two-level atoms that are driven by a linearly polarized laser field. Starting from the Schrödinger equation, we determine the states of two-level atoms in a plane-wave field respecting propagation directions both of the atom and the field. For such laser-driven two-level atoms, we construct Bessel beams beyond the typical paraxial approximation. We show that the probability density of these atomic beams obtains a non-trivial, Bessel-squared-type behavior and can be tuned under the special choice of the atom and laser parameters, such as the nuclear charge, atom velocity, laser frequency, and propagation geometry of the atom and laser beams. Moreover, we spatially and temporally characterize the beam of hydrogen and selected (neutral) alkali-metal atoms that carry non-zero orbital angular momentum (OAM). The proposed spatiotemporal Bessel states (i) are able to describe, in principle, twisted states of any two-level system which is driven by the radiation field and (ii) have potential applications in atomic and nuclear processes as well as in quantum communication.     

Propagation of ultrashort pulsed beams in dispersive media

Starting from the Rayleigh diffraction integral, the propagation equation of ultrashort pulsed beams in dispersive media is derived without making the paraxial approximation and slowly varying envelope approximation (SVEA). The spatiotemporal properties of ultrashort pulsed beams in dispersive media, such as spectrum redshifting, narrowing and pulse distortion are illustrated with pulsed Gaussian beams. It is stressed that the “antibeam“ behaviour of ultrashort pulsed beams can be avoided, if a suitable truncation function is chosen.     

Second harmonic generation with noncollinear focusing

The propagation of off-axis Gaussian beams through an optical system is described in the paraxial approximation. The formulae for the second harmonic power for stationary focused noncollinear SHG is given. Numerical results and analytical approximations for limiting cases are provided. The theory is applied to the problem of background of noncollinear SHG in pulse duration measurement techniques.