Propagation properties of a non-paraxial hollow Gaussian beam

Based on the non-paraxial vectorial moment theory of beam propagation, the analytical expressions of the M² factors for a non-paraxial hollow Gaussian beam (HGB) have been derived. The analytical formulae are further simplified for paraxial and highly non-paraxial cases. The beam waists, the divergence angles and the beam propagation factors are also depicted as functions of the parameter w₀. The divergence angles will not exceed the maximum value of 90°. When w₀ is within the scale of one time of light wavelength, the TE polarization results in the different beam propagation factors in the two transverse directions and the beam propagation factors first increase and then decrease. When w₀ is large enough, the beam propagation factors are determined only by the beam order.     

Propagation characteristics of TM Gaussian beam

The propagation characteristics of TM polarized Gaussian beam, which is the rigorous solution of an eigenfunction problem for a confocal resonator, have been investigated using the nonparaxial vectorial moment theory of light beam propagation. The analytical expressions of the beam propagation factors are given by means of Fourier transform. Both the transversal second-order moment beam widths follow a simple hyperbolic variational law. For nonparaxial case, however, beam has different propagating features in the two transversal directions. As to paraxial case, its propagation approximately reduces to that of scalar Gaussian beam TEM₀₀ mode.     

M 2-factor of a partially coherent Lorentz–Gauss beam in a turbulent atmosphere

Based on the second-order moments of partially coherent beams in atmospheric turbulence, the analytical beam propagation factor of a partially coherent Lorentz–Gauss beam in a turbulent atmosphere is derived. As a special case of the general formula, the beam propagation factor of a partially coherent Lorentz beam in a turbulent atmosphere is also presented. By using the derived analytical expression, the beam propagation factor is illustrated and analyzed with numerical examples, and the influences of the beam parameters a _j and w _0j , the coherent parameter τ _j , the axial propagation distance z, the structure constant C_n²C_{n}^{2}, and the inner scale turbulence l ₀ on the beam propagation factor are also discussed in detail.     

Analysis of non-linear refractive index influences on four-wave mixing conversion efficiency in semiconductor optical amplifiers

In this paper, we have analyzed the influences of non-linear refractive index on the four-wave mixing (FWM) characteristics in semiconductor optical amplifiers (SOAs). It has been shown that the generated FWM signal characteristics can be modified due to the variation of non-linear refractive index of the SOA's medium. The wave propagation in the SOA has been modeled using the nonlinear propagation equation taking into account gain spectrum dynamics, gain saturation, which depends on carrier depletion, carrier heating, spectral hole-burning, group velocity dispersion, self-phase modulation and two photon absorption. Simulation of optical wave evolution in the SOA has been carried out using the finite-difference beam propagation method (FD-BPM) both in time and spectral domains. Our simulation results confirm that higher FWM conversion efficiency and lower time bandwidth product are achieved for higher absolute values of non-linear refractive index. Moreover, non-linear refractive index is more efficacious for high power propagated waves in SOAs. Finally, we have studied the modification of waveguide refractive index due to the propagation of optical pulses. We have also shown that when |n₂|=1 cm²/TW, refractive index variation is in the order of 10^?4 to 10^?7 for high and low power input pulses, respectively.     

LD泵浦的Nd:YVO_4激光器被动式产生近似无衍射绿光

使用连续式输出的砷化镓半导体激光器泵浦的掺钕钒酸钇激光器作为光源,利用磷酸氧钛钾晶体腔内倍频产生波长为532nm的绿光,通过轴棱锥产生了近似无衍射贝塞尔光束。推导了倍频产生的绿光的场分布,并模拟了倍频绿光经过轴棱锥产生的近似无衍射光束的轴向光强分布图和截面光强分布图。通过实验拍摄了距离轴棱锥不同位置的截面光强分布,测量了无衍射贝塞尔绿光的最大无衍射距离和中心光斑直径,实验数据与理论模拟基本吻合。实验结果说明所述方法产生的倍频无衍射绿光具有良好的光束质量,具有应用价值。     

Generalized beams in ABCDGH systems

For a generalized beam at the source plane passing through co-located aperture and a propagation path consisting of an off-axis x-y asymmetric ABCDGH system, the receiver plane irradiance expression is derived using the Collins integral. A collection of source beam profiles that are obtainable from the generalized beam formulation are illustrated. Plots are given for viewing the progress of selected generalized beam types along the propagation axis, containing a single thin lens, co-centric and misaligned in the x-direction. The received power falling onto a finite aperture surface is calculated for various misalignment situations.     

双轴棱锥产生长距离近似无衍射光的新技术

提出了一种利用会聚透镜、轴棱锥等简单光学元件产生长距离近似无衍射光的新技术. 分别利用几何光学和衍射理论分析了该方法产生长距离近似无衍射光束的原理, 通过软件模拟了长距离近似无衍射光束的形成过程,得出了该光束在不同距离处的横向光强分布. 模拟结果显示该光束在较长距离处的横向光强分布满足Bessel分布. 从实验上获得了传播距离长达80 m、中心光斑发散角约为0.12 mrad的近似无衍射光束, 相比于国外学者最近的研究成果(Belyi et al. 2010 Opt. Exp. 18 1966)将传播距离延长了50多米,而光束发散角压缩了22倍.实验中, 对光束沿光轴传播时在不同距离处的光斑进行了拍摄,所得实验结果与理论分析基本符合.     

Evolution of a finite Olver beam propagating in a right handed and double negative index slab system

In this work, we investigate the evolution of a first order finite Olver beam and a zeroth order one (finite Airy beam) propagating in a right handed and double negative index cascaded slab system based on the transfer matrix and generalized Huygens-Fresnel integral equation. It is discovered that the incident finite Olver beam could reappear on the output cross section by using a periodic slab system with a negative index material as long as n_l=??n_r, L?=?R; for n_l≠?n_r, the bigger abs(n_l) is, the longer the needed unit length L to achieve an original beam intensity reproduction, and vice versa; the relations between the negative refractive index and the double negative material unit length are also quantitative explored by using the Origin Lab. It is expected that the derived analytical formulae and conclusions can provide a convenient and effective way for studying the evolution of a finite Olver beam propagating in multilayered structures, especially for periodic and quasi-periodic slab systems.     

Theoretical study of the time-resolved photoelectron spectrum of Na 2F: effects of thermal initial conditions

The excited state dynamics of the Na₂F cluster initiated by a femtosecond laser pulse is studied considering a thermally excited initial sample. Within a pump-probe set-up, the time-dependent photoelectron spectrum is calculated, which is shown to be a sensitive tool to study intramolecular motion of the cluster. Temperature effects are taken into account through thermal averaging over the time-dependent spectra obtained from different initial vibrational states of the cluster. The nuclear motion upon laser excitation is described by full-dimensional quantum wavepacket propagation using explicit, realistic pump and probe pulses. The characteristic features of the time-resolved photoelectron spectra of the Na₂F cluster, identified as due to periodic bending motion of the cluster as well as to the excitation of the stretching mode, are found to be robust against increasing vibrational temperature of the cluster beam. This finding is important for possible future experiments.     

Propagation of cosh Gaussian laser beam in plasma with density ripple in relativistic – ponderomotive regime

Self-focusing of cosh Gaussian laser beam in plasma with periodic density ripple has been investigated. The pondermotive force on electron and the relativistic oscillation of the electron mass causes periodic self-focusing/defocusing of the cosh Gaussian laser beam. The beam converges in the region of high plasma density due to dominance of self-focusing effect over diffraction effect and diverges in the low density region. Non-linear partial differential equation governing the evolution of complex envelope in slowly varying approximation is solved using paraxial ray approximation. The variation of beam-width parameter is studied with distance of propagation for different values of ripple wave number d and decentred parameter b. In order to get strong self-focusing, wavelength and intensity parameters of cosh Gaussian laser beam are optimized.     

聚片多畴LiNbO3晶体的倍频效应

通过对聚片多畴LiNbO₃晶体倍频效应的研究,从实验上对Bloembergen等人所提出的准位相匹配理论进行了细致的检验。首先运用Maker条纹法在实验上直接测定了单畴LiNbO₃晶体在e^ω·e^ω→e^2ω非位相匹配下的倍频光强,并采用角度扫描和温度扫描方法,以获得满足准位相匹配条件时的不同片数的聚片多畴晶体的最大倍频强度,从而验证了聚片多畴晶体倍频相对光强与片畴数N成平方关系。在N<200时,取得 关键词：     

Self-activated Nd:Ba2NaNb5O12 optical super-lattices: Micro characterization and non-collinear laser light generation

Czochralsky grown Nd³⁺-ion doped barium sodium niobate (Ba₂NaNb₅O₁₂, “banana”) optical super-lattices have been characterized by a combination of chemical etching, optical microscopy, micro-Raman and micro-photoluminescence experiments. The presence of ferroelectric domains, induced during growth process, is accompanied by a periodic modulation of Nd³⁺-ion concentration as well as by a small lattice distortion. When Nd³⁺-ion laser action at ≈1.06 μm is achieved under 0.808 μm laser diode pumping, the singularities of refractive index caused by opposed ferroelectric domains lead to non-collinear intra-cavity propagation.     

Nonparaxial propagation of a super-Lorentz－Gauss SLG01 mode beam

Based on the vectorial Rayleigh--Sommerfeld integral formulae, this paper derives the analytical nonparaxial propagation equation of a super-Lorentz--Gauss (SLG) SLG₀₁ mode beam in free space. The far field expression and the scalar paraxial result are treated with special cases of the general formulae. According to the obtained analytical representation, the nonparaxial propagation properties of the SLG₀₁ mode beam are illustrated and analysed with numerical examples. This research provides an approach to investigate the propagation of the SLG₀₁ mode beam within the framework of the nonparaxial regime.     

Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor

In this paper, propagation of a Gaussian laser beam through turbulent atmosphere is evaluated numerically. The beam quality factor for the propagated beam has been estimated for different turbulent conditions that are characterized by parameter C_n. The calculations show that the beam quality can be affected dramatically by atmospheric turbulence and the laser beam size and wavelength have major role in the results. Furthermore, the propagation of laser beam in longer distance results in more spatial perturbation of the beam. The results of these calculations and evaluation of beam quality factor M² can be used for estimating the refractive index structure parameter (or atmosphere turbulent parameter) C_n.     

Potential Images of Ferroelectric Domain Structures Formed by Electron Beam in Lithium Niobate Crystals

Ferroelectric domain structures formed by an electron beam in lithium niobate crystals are studied using low-voltage SEM microscopy. The structures are formed in crystals with different conductivity, including samples with high-resistance congruent composition (CLN) and samples with conductivity increased by reductive annealing (RLN). The potential nature of the contrast of the domain structures observed in the secondary electron mode depending on the conductivity of the samples and the direction of spontaneous polarization of the domains is analyzed. It is assumed that the domain contrast in CLN crystals is associated with long-lived charges localized near domain walls and in the irradiated areas. The recorded domain structures in the CLN crystals are visualized on polar and nonpolar cuts. In the RLN crystals with improved conductivity compared to CLN, the potential contrast of the periodic domain structures is found only on the polar cuts, where vector P_s of the domains is perpendicular to the irradiated surface. This contrast is likely because the field of the spontaneous electric polarization charges influences the secondary electrons.     

Regular domain structures fabricated by an electron beam in stoichiometric LiNbO3 crystals

Electron beam writing of regular domain structures in Z-cuts 0.75 mm thick of stoichiometric and close to stoichiometric LiNbO₃ crystals has been carried out. Crystals have been grown by the Czochralski method from a melt with excess Li₂O (58.6 mol %) and from a congruent-composition melt in the presence of 6 wt % K₂O alkali solvent (flux). In both crystals, threshold charge doses required to form individual domains have been determined, and the optimal conditions of periodic structure patterning by sequential local irradiations have been found. Domain gratings of similar type (with periods of 6.5, 7, and 10 ??m) are formed in both types of stoichiometric crystals.     

Transmission of an X‐ray beam through a two‐dimensional photonic crystal and the Talbot effect

Results of computer simulations of the transmission of an X‐ray beam through a two‐dimensional photonic crystal as well as the propagation of an X‐ray beam in free space behind the photonic crystal are reported. The photonic crystal consists of a square lattice of silicon cylinders of diameter 0.5 µm. The amount of matter in the path of the X‐ray beam rapidly decreases at the sides of the cylinder projections. Therefore the transmission is localized near the boundaries, and appears like a channeling effect. The iterative method of computer simulations is applied. This method is similar to the multi‐slice method that is widely used in electron microscopy. It allows a solution to be obtained with acceptable accuracy. A peculiarity in the intensity distribution inside the Talbot period z_T in free space was found when the intensity is approximately equal to the initial value at a distance 0.46z_T, and it is shifted by half a period at distance 0.5z_T. The reason for this effect is the existence of a periodic phase of the wavefunction of radiation inside the intensity peaks. Simulations with zero phase do not show this effect. Symmetry rules for the Talbot effect are discussed.     

Surface relief diffraction gratings written on <Emphasis Type="BoldItalic">β</Emphasis> -BaB<Subscript>2</Subscript>O<Subscript>4</Subscript> crystal by femtosecond pulses

Surface relief diffraction gratings were written at the entrance surface of a β-BaB₂O₄ (BBO) crystal under irradiation with femtosecond laser pulses. Probe–beam diffraction and atomic force microscopy (AFM) were employed to characterize the diffraction properties and the microstructures of the gratings. The maximal first-order diffraction efficiency of these gratings is approximately 63%. The surface periodic structure of the material induces noncollinear propagation of the fundamental input beam in the crystal. Using this diffractive optical element, efficient generation of multiple second-harmonic beams was achieved. PACS 42.79.Dj; 42.40.Lx; 42.65.–k     

大气湍流中光束束宽扩展和角扩展的比较研究

以厄米-双曲余弦-高斯（H-ChG）光束为例,对H-ChG光束通过大气湍流传输时的束宽扩展和角扩展做了详细研究.用相对束宽和相对角扩展代替束宽和角扩展来研究湍流对光束影响的灵敏程度.研究表明,折射率结构常数C²_n越小,光束束宽扩展和角扩展越小.有较大阶数m,n,较小参数Ω₀和束腰宽度w₀ H-ChG光束的角扩展受湍流影响较小.当传输距离足够远时,这一结论对H-ChG光束的束宽扩展也成立.当传输距离不长时,对H-ChG光束相对束宽随Ω₀和w₀的变化规律做了分析.用数值计算例做了说明,并对结果的正确性做了物理解释.厄米-高斯,双曲余弦高斯和高斯光束在大气湍流中的扩展可作为H-ChG光束的特例来处理. 关键词： 束宽扩展和角扩展 大气湍流 厄米-双曲余弦-高斯光束     

单口径相干合成系统激光光束的M2因子研究

单口径相干合成系统激光光束的光束质量是一个亟待解决的重要问题.基于二阶矩定义, 文中给出了单口径TEM₀₀, TEM₀₁及TEM₁₀两两相干光束M²因子的解析表达式, 并比较分析了束腰宽度、传输距离、振幅之比,以及源场位置矢量对相干光束M²因子的影响, 得到了诸如源场位置参量d₁<100λ时,各相干光束M²因子恒定,反之, 其随位置参量d₁的增大而增大等一些结论.最后,文章对两TEM₀₀模相干光束M²因子的 部分理论进行了实验验证.