高斯涡旋光束的光束传输因子和峭度参数

基于强度二阶矩定义, 导出了高斯涡旋光束光束传输因子即M² 因子的解析表达式, 高斯涡旋光束的M² 因子唯一取决于拓扑电荷数n. 数值计算表明, 高斯涡旋光束的M² 因子随着拓扑电荷数n的增大而增大. 基于强度高阶矩, 还导出了高斯涡旋光束经傍轴ABCD光学系统传输时峭度参数的解析表达式, 高斯涡旋光束的峭度参数取决于拓扑电荷数n、参数δ、矩阵元A和矩阵元D. 在自由空间传输时, 高斯涡旋光束的峭度参数仅取决于拓扑电荷数n和参数δ. 自由空间传输时, 高斯涡旋光束峭度参数的变化规律为: 峭度参数随参数δ的增大先减小而后趋向于一最小值, 随拓扑电荷数n的增大而减小. 这一研究有助于高斯涡旋光束的实际应用.     

激光光束传输因子M2的一些问题

本文讨论与M²因子有关的一些问题,指出在近轴近似条件下由光束的二阶强度矩定义的M²因子满足M²≥1,其中只有对基模高斯光束等式才成立.由光束的功率通量值定义的M²因子(M_pc²)有可能小于1,M_pc²的大小取决于所定义的光斑半径内包含的光功率的百分数.通过计算光场的二阶矩,我们获得了轴向相干叠加的高斯光束的M²因子的解析解.     

N2O+离子A2Σ+电子态高振动能级的转动结构分析

利用一束波长为36055nm的激光，通过(3+1)共振多光子电离方法制备纯净的且处于X²Π_1/2，3/2(000)态的N₂O⁺离子，用另一束激光激发所制备的离子到第一电子激发态A²Σ⁺的不同振动能级，然后解离，通过检测解离碎片NO⁺强度随光解光波长的变化，得到了转动分辨的N₂     

厄米-高斯光束在非Kolmogorov大气湍流中的传输性质

基于广义惠更斯-菲涅尔原理和非Kolmogorov(非K)谱,推导出了厄米-高斯光束在非K大气湍流中传输的束宽、角扩展以及M²因子的解析表达式.数值计算表明,在传输距离比较远(如z≥3 km)时,厄米-高斯光束的束宽、角扩展和M²因子随广义指数参量α的增大而增加直到α=3.11时达到最大值后再随α的增大而减小;随湍流的内尺度l₀的减小而增大;随外尺度l₀的增加而增大(3.6<α<4).但是当广义指数参量α在3<α<3.6区间取值时,束宽和M²因子几乎不随外尺度的增加而变化.     

一种强度不等的新型两态叠加多模叠加态光场的等阶N次方Y压缩效应

本文构造了由多模虚共轭相干态{iZ_j^(a)*}>_q与多模虚共轭相干态的相反态|{-iZ_j^(b)*}>_q这两者的线性叠加所组成的一种强度不等的新型两态叠加多模叠加态光场 |Ψ^(ab)>_q.利用多模压缩态理论,对态|Ψ^(ab)>_q的等阶N次方Y压缩特性进行了详细研究.结果发现:该态在一定条件下可呈现出周期性变化的任意奇数阶和任意偶数阶的等阶N次方Y压缩效应,而在特殊条件下,则呈现出等阶N次方Y压缩简并现象.     

光束的空间相干性与空间质量评价

光束空间质量评价的标准应该能够反映光束的空间相干性和强度(功率或能量)分布,并主要由空间相干性的优劣来说明.本文对模式纯度(1-δ)以及空间质量评价因子-衍射极限倍数因子M²做了讨论,并对此因子的表达形式提出了我们的改进建议.     

态|Ψn(2)>q的广义非线性等阶N次方H压缩效应

构造了一种新型的多模叠加态|Ψ_n⁽²⁾>_q=C_n^(R)|{-iZ_j^*}>_q+C_n⁽⁰⁾|{O_j}>_q;并首次详细地研究了此量子态的等阶N次方H压缩特性.大量的计算和分析表明:态|Ψ_n⁽²⁾>_q是一种多模典型的非经典光场;还发现了"相似压缩"等现象.     

两种特殊四态叠加多模叠加态光场的等N次幂H压缩

根据线性叠加原理,用多模相干态|{Z_j^*}〉q,|{-Z_j^*}〉q及其复共轭|{Z_j^*}〉q和|{-Z_j^*}〉q组成了两种四态叠加多模叠加态光场|Ψ_oe⁽⁴⁾Ⅵ〉q和|Ψ(4)oeⅦ〉q,利用多模压缩态理论研究了它们的等N次幂H压缩,结果发现:态|Ψ_oe⁽⁴⁾Ⅵ〉q和|Ψ(4)oeⅦ〉q具有完全相同的等N次幂H压缩规律;当压缩幂次N与腔模总数q之积,即qN为偶数时,态|Ψ_oe⁽⁴⁾Ⅵ〉q和|Ψ(4)oeⅦ〉q恒处于等幂次N-H最小测不准态或呈现"半相干态效应";当qN为奇数时,在不同条件下,态|Ψ_oe⁽⁴⁾Ⅵ〉q和|Ψ(4)oeⅦ〉q可以呈现三种不同状态:第一正交分量呈现等N次幂H压缩;第二正交分量呈现等N次幂H压缩; 可呈现"半相干态效应".     

一种新型的两态叠加多模叠加态光场的广义非线性等阶N次方H压缩

本文根据量子力学中的线性叠加原理,构造了由多模(即 q模)相干态的相反态 | {-Z_j}〉_q及多模虚相干态的相反态 | {-iZ_j}〉_q 这两者的线性叠加所组成的一种新型的两态叠加多模叠加态光场 | ψ_msc⁽²⁾〉_q 利用新近建立的多模压缩态理论,详细研究了态 | ψ_msc⁽²⁾〉_q 的广义非线性等阶N次方H压缩特性 结果发现:1)当压缩阶数N与腔模总数q这两者之积为偶数,亦即当q·N =2p且p =2m(m =1,2,3,…,…)时,态 | ψ_msc⁽²⁾〉_q恒处于等阶N-H最小测不准态;2)当q·N =2p且 p =2m′+ 1(m′ =0,1,2,3,…,…)时,如果各模的初始相位之和 、态间的初始相位差(θ_nq^(I)-θ_nq^(R))、各多模相干态光场的总的平均光子数 以及 [(θ_nq^(I)-θ_nq^(R))+ ]等满足一定的量子化条件时,态 | ψ_msc⁽²⁾〉_q 总可呈现出周期性变化的、任意阶的等阶N次方H压缩效应;3)当压缩阶数N与腔模总数 q这两者之积为奇数时,亦即当 q·N =2p + 1时,无论 p =2m(m =0,1,2,3,…,…)还是 p =2m′ + 1(m′ =0,1,2,3,…,…),只要各模初始相位之和 满足一定的量子化条件,则当两态叠加几率幅满足r_nq^(R) =r_nq^(I) 时,态 | ψ_msc⁽²⁾〉_q 就恒处于N-H测不准态     

一种非对称多模叠加态光场的Nj次方H偶数压缩

利用多模压缩态理论研究了一种非对称多模叠加态光场|Ψ_I^(ab)〉_q的N_j次方H压缩特性.结果发现:当各模压缩幂次数之和为偶数时,态|Ψ_I^(ab)〉_q的第一或第二正交分量可分别呈现出周期性变化的N_j次方H压缩效应,进而揭示了压缩简并产生的根源.     

Characteristics of scintillations and bit error rate of partially coherent rectangular array beams in turbulence

According to the paraxial form of the extended Huygens-Fresnel principle, the analytical formulas of the on-axis average irradiance and the on-axis scintillation index for a rectangular array Gaussian Schell-model (RAGSM) beams in atmospheric turbulence have been derived. The on-axis bit error rate has been analyzed quantitatively. Their effects of the turbulence intensity, the initial correlation length, and the array parameters including the beamlet number (M and N) and the array separation distance (x₀ and y₀) have been discussed. The results show that the correlated and uncorrelated superposition RAGSM beams exhibit the different on-axis intensity distribution, the similar variation of the on-axis scintillation and the bit error rate. At the nearer propagation distance the on-axis scintillation rises against propagation distance with the increasing beamlet number and the decreasing array separation distance, whereas the situation is reversed at the farther propagation distance. The effects of array parameters on the bit error rate are similar to that on the scintillation. For a given propagation distance the scintillation index increases with the stronger coherence and the larger waist width of the array beam.     

Stokes beams formed by superposition of a completely unpolarized and a completely polarized Gaussian Schell-model beam

Analytic expressions and computed examples are given to elucidate the coherence and polarization properties of Stokes beams, i.e. beams formed by superposition of a completely unpolarized and a completely polarized electromagnetic Gaussian Schell-model beam. We found that superposition of such two beams cannot form a Stokes beam with a constant state of polarization on propagation. An additional constraint on the source plane parameters of the two Gaussian Schell-model beams is proposed. The resultant Stokes beam with a constant state of polarization on propagation is found to be a Gaussian Schell-model beam with the same variances as the two constituent Gaussian Schell-model beams. However, the modulus of the Gaussian intensity distributions across the source planes of these beams may be different.     

椭圆平顶高斯光束的聚焦特性

利用级数分解法把椭圆平顶高斯光束(EFGB)分解成多个椭圆厄密-高斯模的叠加形式,利用椭圆厄密-高斯模的传输公式导出了EFGB通过非轴对称光学系统的传输公式,该公式和直接用矢量积分得出的结果是等效的.利用导出的公式,我们计算分析了EFGB通过轴对称透镜和非轴对称透镜的聚焦特性.结果表明,EFGB聚焦后,近场光强分布变化很快,特别是焦点前后,光强分布会快速旋转.另外,EFGB的聚焦特性与阶次有关.     

多束高斯光束的相干叠加分析

采用Collins公式推导了入射高斯光束在输出场的场分布解析式，模拟了四束光在靶点相干叠加的强度分布，并分析了入射光束的位相差和离焦量对靶点光强分布的影响。     

Coherent and partially coherent twisting beams

We present coherent and partially coherent beams that exhibit transverse pattern expansion and rotation upon free propagation. Coherent twisting beams may be generated by a suitable superposition of Laguerre-Gauss modes, while a model for partially coherent twisting beams is given by a continuous incoherent superposition of lowest order modes.     

矩形分布高斯-谢尔模型列阵光束的等效曲率半径

 推导出矩形分布高斯-谢尔模型（GSM）列阵光束通过湍流大气传输的等效曲率半径的解析表达式。研究表明,等效曲率半径由湍流强度、GSM列阵光束参数及光束的叠加方式等因素共同确定。湍流使得等效曲率半径减小,但湍流对交叉谱密度函数叠加时等效曲率半径的影响要比光强叠加时大。在自由空间中,交叉谱密度函数叠加时GSM列阵光束的等效曲率半径要比光强叠加时的大。但是,随着湍流的增强,交叉谱密度函数叠加时GSM列阵光束的等效曲率半径可以大于、等于或小于光强叠加时的等效曲率半径。此外,若光束相干参数和子光束数目越大,则等效曲率半径受湍流的影响越大。GSM列阵光束的等效曲率半径受湍流的影响比高斯列阵光束要小。     

基于格林函数法的奇型Mathieu-Gaussian光束

根据光束传播的独立性和叠加性原理,引入了一组能够产生第一类(2n+2阶)奇型Mathieu-Gaussian光束的虚光源点.利用虚源点技术和格林函数法,计算得到第一类奇型Mathieu-Gaussian光束的严格解析积分表达式.利用该表达式得到了轴上光场分布的积分解析解.以三阶非旁轴修正为例,得到了第一类奇型Mathieu-Gaussian光束保留到三阶非旁轴修正项的轴上光场分布精确解.     

Intensity distribution and coherence property for the broadband Gaussian Schell-model array beams in free space

The intensity distribution and the equal-time complex degree of coherence for the broadband Gaussian Schell-model array beams with different bandwidth propagating in free space are analyzed by the numerical calculation. Results show that the intensity distribution for the broadband Gaussian Schell-model array beams by uncorrelated superposition is rarely affected by the bandwidth; the intensity distribution in the far field for the broadband Gaussian Schell-model array beams by correlated superposition is affected by the bandwidth more obviously than that in the near field. With the increasing of the propagation distance, differences in the equal-time complex degree of coherence for the broadband Gaussian Schell-model array beams with different bandwidth become prominent.     

Specular and vortical Airy beams

A new kind of truncated Airy beams is investigated and discussed. These beams are a superposition of shifted and truncated Airy functions and its specular counterparts, where zeroes or extremal points of the Airy function are chosen as a truncation point. The specular Airy beams are smooth at the truncation point and produce a diffraction pattern similar to Hermite-Gaussian modes. Under propagation in Fresnel zone, specular Airy beams demonstrate a symmetrical acceleration in opposite sides and the beam divergence is proportional to the traveled distance squared. The astigmatic mode converter transforms a two-dimensional specular Airy beam into a quasi-annular field with a nonzero orbital angular momentum. Vortical Airy beams based on truncated Airy functions are also discussed. These beams are similar to Laguerre-Gaussian modes, while their annular structure is changed during propagation.     

Composite coherence vortices and their propagation in free space

Taking Gaussian Schell-model (GSM) background vortex beams as an example of partially coherent vortex beams, the composite coherence vortices resulting from the superposition of the cross-spectral density function of two parallel, noncollinear partially coherent vortex beams and their propagation in free space are studied, and the main attention is paid to the effect of relative off-axis distance, coherence parameter and propagation distance on the composite coherence vortices. The number and location of composite coherence vortices vary by changing the relative off-axis distance, coherence parameter or propagation distance. In the coherent limit, the composite coherence vortex becomes the composite optical vortex.