非均匀偏振光束通过环状光阑像散透镜的聚焦特性

借助于光束相干偏振矩阵和广义惠更斯－菲涅耳衍射积分公式,研究了非均匀偏振(NUP)光束通过环状光阑像散透镜的聚焦特性,并将圆孔光阑作为环状光阑内径为零的特例处理.数值计算结果表明,实际焦点位置、光强和偏振度分布与透镜的像散、环状光阑的菲涅耳数和遮拦比以及NUP光束参量有关.     

Dynamic pulsed-beam shaping using a TAG lens in the near UV

The ability to dynamically shape the spatial intensity profile of an incident laser beam enables new ways to modify and structure surfaces through pulsed laser processing. Here we describe a method to generate doughnut-shaped beams from an input Gaussian source using a tunable acoustic gradient index (TAG) lens. The TAG lens is capable of modulating between focused beams and annular rings of variable size, using sinusoidal driving frequencies. Laser micromachining is accomplished by synchronizing the TAG lens to a 355 nm pulsed nanosecond laser. Results in polyimide demonstrate the ability to generate adjacent surface features with different shapes and sizes.     

Focusing of flattened Gaussian beams by an annular lens

Focusing properties of flattened Gaussian beams (FGBs) passing through an annular lens is studied based on the Collins formula. It is found that the on-axis irradiance distributions of focused FGBs are unsymmetrical with respect to the geometrical focal plane even for large values of Fresnel number F_w associated with the beam, so that there exist focal shifts in general. Detailed numerical results show the dependence of focal shifts on the beam and system parameters. Focal shifts of FGBs by a lens without central obscuration and focal shifts of Gaussian beams by an annular lens can be treated as special cases of the obscure ratio =0 and beam order N=0, respectively. Furthermore, focal shifts of plane waves by an annular lens can also be treated as a special case of N=0 and F_w→∞.     

Phase-locking resonator with annular gain media

A new type of laser resonator that is designed to extract good phase coherence and circular beams from an annular gain region is developed. We also calculated the parameters theoretically by applying the resonator to a CO₂ laser. And the transfer characteristics of the output beam from the phase-locking laser resonator through a lens are also discussed.     

Focusing properties of a general-type beam in turbulent atmosphere

Based on the generalized Huygens–Fresnel integral, analytical propagation formulas for a general-type beam propagating through aligned or misaligned ABCD optical systems in turbulent atmosphere are derived. The derived formulas provide a convenient way for studying the focusing properties of a variety of laser beams, such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams in turbulent atmosphere. As an application example, the focused intensities of cos-Gaussian, Hermite-sine-Gaussian and flat-topped beams in turbulent atmosphere are studied numerically. Focal shift of a flat-topped beam in turbulent atmosphere is investigated. Effect of the misalignment of the thin lens on the focusing properties of a cos-Gaussian beam is also explored. Our results will be useful for the applications of the general-type beam in LIDAR systems and remote sensing operating in turbulent atmosphere, where optical elements such as aligned or misaligned thin lens are commonly encountered.     

Effect of annular obstruction on tight focusing of partially coherent radially polarized Vortex beam

Based on vectorial Debye theory, the effect of annular apodization of tightly focused partially coherent radially polarized vortex beams in the focal field of high NA lens is studied. The intensity distribution in the focal region is illustrated by numerical calculations. It is found that the focal depth of the generated focal segment strongly dependent on the source coherence length for unobstructed case and the presence of annular aperture reduces the variation of focal depth with source coherence length.     

Diffractionless beams and their use for harmonic generation

Use of diffraction-free beams to generate low-order harmonics in xenon jets has been investigated. Nearly diffractionless beams have been generated from a Ti : sapphire, 100 fs, laser system by focussing ring-type radiation, which has been produced in two different ways: either, by inserting an annular slit into the incident Gaussian beam, or by placing a doublet of axicons in a vertex-to-vertex configuration before the focussing lens. The results obtained with the first scheme are discussed and interpreted in terms of a simple perturbative model of the harmonic generation (HG) process. The first measurements performed with the doublet of axicons are also reported and discussed.     

环状平顶光束的传输特性研究

利用偏心高斯光束相干叠加方法，建立了柱坐标系下环状平顶光束模型.采用广义强度二阶矩定义，推导出环状光束广义M2因子的解析表达式.利用广义衍射积分理论，给出环状光束经过近轴ABCD光学系统的传输公式，并进一步给出了环状平顶光束修正的菲涅耳数定义.分析了环状平顶光束在自由空间的传输规律.研究结果表明，该模型可统一描述基模高斯光束、环状高斯光束以及环状平顶光束.环状平顶光束的广义M2因子和环状平顶光束的传输特性与其阶数及遮拦比有关.     

Fresnel phase retrieval method using an annular lens array on an SLM

Wavefront aberrations play a major role when focusing an ultrashort laser pulse to a high-quality focal spot. Here, we report a novel method to measure and correct wavefront aberrations of a 30-fs pulsed laser beam. The method only requires a programmable liquid-crystal spatial light modulator and a camera. Wavefront retrieval is based on pupil segmentation with an annular lens array, which allows us to determine the local phase that minimizes focusing errors due to wavefront aberrations. Our method provides accurate results even when implemented with low dynamic range cameras and polychromatic beams. Finally, the retrieved phase is added to a diffractive lens codified onto the spatial light modulator to experimentally demonstrate near-diffraction-limited femtosecond beam focusing without refractive components.     

Propagation of a general-type beam through apertured aligned and misaligned ABCD optical systems

By expanding the hard-aperture function into a finite sum of complex Gaussian functions, analytical formulae for the electric field of a general-type beam propagating through apertured aligned and misaligned ABCD optical systems are derived using the generalized Collins formulae, which provide a convenient way of studying the propagation of a variety of laser beams, such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams, through such optical systems. As numerical examples, the propagation properties of a cos-Gaussian beam through an apertured aligned or misaligned thin lens are studied.     

Changes in the intensity distribution and polarization of non-uniformly polarized beams focused by a spherically aberrated lens with annular aperture

Based on the generalized Huygens-Fresnel diffraction integral and beam coherence polarization (BCP) matrix formulation, the focusing properties of a type of non-uniformly polarized (NUP) beam through a spherical aberrated lens with annular aperture are studied. The dependence of focal shift, intensity distribution, power in the bucket (PIB) and degree of polarization on the spherical aberration coefficient, obscure ratio and polarization parameters is illustrated numerically. The focusing of NUP beams by a spherically aberrated lens with circular aperture is treated as a special case, where the inner radius of the aperture is equal to zero.     

Scintillation index of astigmatic annular beams in a turbulent atmosphere

The scintillation properties of astigmatic annular beams in a weak turbulent atmosphere are investigated. Expression for the on-axis scintillation index of an astigmatic annular beam is derived. It is found that the scintillation index of an astigmatic annular beam can be smaller than that of a Gaussian beam, an elliptical Gaussian beam and a stigmatic annular beam in a weak turbulent atmosphere under certain conditions. The scintillation properties of astigmatic annular beams are closely controlled by its beam parameters.     

Propagation characteristics of flattened Gaussian beams through a misaligned optical system with a misaligned annular aperture

The approximate analytical formula for flattened Gaussian beams through a misaligned optical system with a misaligned annular aperture was derived by the extended Huygens–Fresnel principle. Some numerical simulations are illustrated to the effects on the propagation of flattened Gaussian beams by the misaligned annular aperture. To compare the difference between annular apertured system and circular apertured system, the circular apertured system is also studied. The results show that angle misalignments and lateral displacements of aperture create asymmetrical average intensity distribution at receiving plane z = 500. The effects on intensity distribution by angle misalignments of annular aperture were small. In annular aperture case, the smooth of intensity distribution was worse with escalating obscure ratio ? in near-field; the side-lobes increased and the central lobe decreased with escalating obscure ratio ? in far-field. At receiving plane z = 500: for circular aperture, the side-lobes decreased, even to be neglected, with the increasing of truncation parameter δ; for annular aperture, the side-lobes increased with the increasing of truncation parameter δ. In addition, it is found that the aligned thin lens can fix asymmetry of intensity distribution which was caused by the misaligned annular aperture.     

环状光束通过透镜的聚焦特性研究

给出了环状光束在柱坐标系下的一种描述模型,并利用广义衍射积分理论,推导出环状光束经过近轴ABCD光学系统的传输公式.在此基础上,通过数值模拟方法定量分析了环状光束的聚焦光强分布以及焦面处的桶中功率.研究结果表明,环状光束的聚焦特性与光束阶数以及系统菲涅耳数有关;环状光束在实际焦面和几何焦面上的桶中功率均随着遮拦比的增大而降低,而随着系统菲涅耳数的增大而增大.在实际工作中,通过合理地选取系统菲涅耳数和光束遮拦比可以有效地控制环状光束聚焦后的光束质量.     

光束自聚焦的矢量理论研究

基于矢量非傍轴非线性Schr-dinger方程,利用调制理论研究了光束的自聚焦特性,比较了非零电场散度项和非傍轴项在消除自聚焦崩塌方面的贡献。结果表明,引入两项之一都可使光束聚焦到一有限宽度后开始散焦,然后又自聚焦,如此作聚焦-散焦的周期性循环。但是,在光束自聚焦点附近,非零电场散度项的作用要强于非傍轴项。     

Propagation of vectorial nonparaxial Gaussian beams through an annular aperture

Starting from the vectorial Rayleigh diffraction integrals, the nonparaxial propagation of vectorial Gaussian beams through an annular aperture is studied. The analytical propagation expressions are derived, which permit us to treat the on-axis field and far field of vectorial nonparaxial Gaussian beams diffracted at the annular aperture, the nonparaxial diffraction at a circular aperture and a circular disc as our special cases in a unified way. The validity of our treatment is confirmed by direct numerical integration of the Rayleigh formulae. It is shown that the f-parameter and annular obscuration affect the beam nonparaxiality in the case of diffraction at the annular aperture.     

Annular, cosh and cos Gaussian beams in strong turbulence

For the strong atmospheric turbulence regime, the asymptotic on-axis scintillation behavior of annular, cosh and cos Gaussian beams is theoretically derived and illustrated with numerical examples. It is observed from the plots that annular Gaussian beams exhibit more scintillations than a Gaussian beam, regardless of the amplitude coefficient and source size settings. For small source sizes, cosh Gaussian beams seem to have an advantage over Gaussian beams in terms of reduced scintillation, but for large source sizes a switchover occurs where cos Gaussian beams assume the advantage. Analysis of the effect of inner scale value shows that scintillations increases for all beams as the inner scale increases.     

Field correlations of annular beams in extremely strong turbulence

The field correlations of annular beams are formulated when the atmosphere assumes extremely strong turbulence. Thicker and larger ring sized annular beams are found to exhibit larger absolute field correlations. For the same transverse distance at the receiver plane, annular beams attain larger field correlations if the transverse distance starts from the receiver origin. Comparisons of the annular beam absolute field correlations in extremely strong turbulence with the no turbulence results show that the absolute field correlation variations follow similar trends, except that the magnitudes of the absolute field correlations are much smaller in extremely strong turbulence and the annular fields become decorrelated at very short transverse distances. When the inner scale of turbulence becomes smaller, the absolute field correlations of the annular beams in extremely strong turbulence become smaller.     

部分相干光被环形透镜聚焦而产生的焦移

 从理论上研究部分相干光被一环形透镜聚焦，在焦点附近的轴上点的光强分布。研究结果表明，当部分相干光被一环形透镜聚焦时，最大聚焦光强不在几何焦点，而是位于透镜与几何焦点之间，出现焦移现象。并且，焦移量不仅依赖于透镜外半径的菲涅耳数，还依赖于部分相干光的空间相干度和中心拦截比。透镜的菲涅耳数越小，焦移越大；部分相干光的空间相干度越低，焦移越大。当菲涅耳数一定时，环形透镜的中心拦截比越大，焦移越大；当空间相干度很小时，情况就变得比较复杂。     

Effects of extremely strong turbulent medium on scintillations of partially coherent annular and flat-topped Gaussian beams

Scintillation index of partially coherent annular and partially coherent flat-topped Gaussian beams propagating in horizontal links is found at the receiver origin when these beams propagate in extremely strong atmospheric turbulence. Scintillation index of coherent versions of such beams attain unity saturation value whereas the decrease in the degree of source coherence results in the decrease of the scintillations. At a fixed degree of partial coherence, thin ring sized annular beams possess smaller scintillations than thick ones. For partially coherent flat-topped Gaussian beams, higher flatness yields smaller intensity fluctuations. In extremely strong turbulence, partially coherent annular and partially coherent flat-topped Gaussian beams have smaller scintillations when compared to partially coherent single Gaussian beam scintillations.