Quasi-fractional Talbot effect of resonant diffraction grating

The Fresnel diffraction of resonant diffraction grating is studied on the basis of the modal method, and it shows that the conventional fractional Talbot effect can still occur by choosing appropriate parameters. The Fresnel diffraction distributions of the resonant diffraction gratings with periods between λ and 4λ are analyzed, and the diffraction fields exhibit periodicity in both grating direction and the propagating direction. The experiment is carried out to verify the simulation results of the quasi-fractional Talbot effect of the resonant diffraction grating. This effect has potential application in lithography for high-resolution patterning.     

部分相干光照明下光栅的塔尔博特效应

首先利用部分相干光理论详细地分析了在部分相干光照明下光栅的菲涅耳衍射,给出了观察面上衍射光强分布的一般公式,并就光源的发光面积对光栅塔尔博特效应的影响进行了讨论,得到了光栅衍射光强的分布随着照明光源的发光尺寸的增加而逐渐变得平滑这一结论．并且,当光源发光尺寸增加到毫米量级时,光栅的塔尔博特效应将完全消失。在实验上埘不同发光尺寸的扩展作相干光源照明光栅时的菲涅耳衍射光强进行了测量,实验结果与理论分析得出的结论相符合。     

Unveiling Talbot Effect under Fresnel Diffraction at a Fork-Shaped Grating

The near-field effect of diffraction image self-reproduction or self-imaging of a periodic grating illuminated by quasi-monochromatic wave is well-known as the Talbot effect. Introducing a dislocation to a periodic structure provides a fork-shaped modulation of the phase/amplitude, which produces discrete diffraction pattern in a far-field consisting of optical vortices. In this paper, Fresnel diffraction at amplitude fork-shaped grating is theoretically and experimentally studied. The coexistence of spatial ordering and local violation of translational symmetry of the structure manifests itself in a strict diffraction pattern consisting of optical vortices in the far-field, which is shown to be accompanied by formation of a spatially ordered intensity distribution in the near-field, reminiscent the Talbot carpets for periodic structures. These results demonstrate the first evidence of Talbot effect occurred under light diffraction at fork-shaped gratings, being promising for deep understanding of near-field singular optics phenomena.     

畴腐蚀掺镁铌酸锂可调阵列光分束器的研究

研究了不同畴腐蚀深度的掺镁铌酸锂二维六角可调阵列光分束器的分数Talbot效应.对不同Talbot分数β和不同畴腐蚀深度的阵列光分束器Talbot衍射像进行了数值模拟理论研究.模拟结果表明,Talbot分数β可以改变Talbot衍射像的周期及结构分布,而畴腐蚀深度可有效调制衍射像的光强分布.在理论研究的基础上,设计并制备了具有不同畴腐蚀深度的掺镁铌酸锂二维六角阵列光分束器,对其在不同Talbot分数β条件下的分数Talbot效应进行了通光实验研究,实现了畴腐蚀阵列光分束器对近场Talbot衍射光强分布的调制,实验结果与理论研究结果一致.     

任意发光类型的多色光照明下光栅塔尔博特效应的研究

利用部分相干光理论对多色光源照明下光栅的菲涅耳衍射进行了理论分析,得到了适用于任意发光类型(脉冲或连续发光)的多色光源的衍射光强的一般公式,理论结果表明菲涅耳衍射区的平均衍射光强的形式只与光源的频谱分布有关,这对借助于连续发光光源来研究脉冲光源照明下光栅的塔尔博特效应以及用来确定脉冲光源的性能参量提供了有力的参考依据。此外,详细讨论了光源的频谱分布对光栅塔尔博特效应的影响并进行了相应的数值计算。实验中通过选用不同频率的激光分别照明光栅,拍摄到对应于不同频率的衍射光强分布图像,从而间接获得多色光同时照明光栅时总的衍射光强分布。实验结果表明,理论和实验符合较好。     

Observation of the Talbot effect for ultrasonic waves

The diffraction of ultrasonic radiation on an amplitude diffraction grating in the near-field area (Fresnel diffraction) has been studied. The effect of self-imaging of the grating (Talbot effect) has been detected for ultrasonic radiation at distances from the grating in the range from z = 0 to z = 2L _T, where L _T is the Talbot length. The fractional Talbot effect, i.e., the ultrasonic image of the grating with the period d/2, has been observed.     

分析光栅分数塔尔博特效应的一组新方程

对一维开口比为1/M(这里M为大于1的正整数)的短形光栅,建立了一组新 在分数塔尔博特(Talbot)距离上计算其菲涅 法射光场分布的简单方程.在该方程中考虑了光栅结构与分数塔尔博特距离的联系,显然比迭代方程和基于距离的方程更方便地描述分数塔尔博特效应.给出了一种研究光栅分数塔尔博特铲应的新途径.     

啁啾超短脉冲光波照射下光栅Talbot效应的研究

应用傅里叶频谱分析法，给出了光栅在啁啾超短脉冲光波照射下菲涅耳衍射方程并分析了其Talbot效应. 数值计算表明，在Talbot距离处的衍射光强不仅与照射的超短脉冲光波的宽度有关，而且与脉冲光波的啁啾有关. 根据光栅在Talbot距离处衍射光强的变化，给出了一种检验超短脉冲光波是否含有啁啾的简单方法. 关键词： 光栅 菲涅耳衍射 Talbot效应 啁啾超短脉冲激光     

光栅衍射像的反差,位相和周期的分析

本文从理论上导出了相干光照明了菲涅耳衍射场中离开泰伯自成像平面时光栅像的反差、位相和周期的变化。得到了球面波和平面波照明下,光栅的傅里叶像生成的条件,从而定量地说明了泰伯效应与Lau效应的某种一致性。理论结果被实验验证。     

光栅在超短脉冲激光照射下的塔尔博特效应

首先导出了光栅在短脉冲激光照射下的菲涅耳衍射光场的方程 ,利用该方程分析了一个开口比为 1∶4的光栅的衍射光场。数值计算结果表明当激光脉冲的半极大值全宽 (FWHM)Δτ在皮秒数量级时 ,可以得到塔尔博特自成像。当激光脉冲的 Δτ从皮秒逐渐减小时 ,塔尔博特自成像现象逐渐消失。而当激光脉冲的Δτ小于几十个飞秒时在第一个塔尔博特距离处光栅的衍射光强的最大值随Δτ的减小而减小     

相位光栅分离双波长宽角度光线的理论分析

使用衍射光栅的分色分光方式一般以平行光入射情况为讨论基础,对于非平行光入射的情况讨论较少.本文基于菲涅尔衍射理论和角谱理论,将球面波与平面波的衍射波场联系起来,从而在传播函数中引入角度参量,结合分数泰伯效应的理论基础,推导出双波长宽角度入射光线经相位光栅衍射后的波场分布函数,并对推导出的函数进行数值模拟,得到像面不同位置衍射波场分布.与平行光入射时的标准波场分布相比较,得到宽角度入射时的衍射波场的横向展宽量和偏移量.通过调节光栅台阶的宽度,改变衍射场的展宽和偏移,使各个单一波长的衍射波场宽度小于光栅周期的一半,从而减少双波长光衍射波场的混叠.同时本文给出波场宽度与光栅台阶宽度的变化关系,选取光栅面上多个位置作为台阶宽度的计算点,并对整个光栅的台阶宽度进行曲线拟合,得到可以使双波长宽角度入射光实现良好空间分离的光栅参量.该结果可用于各类宽角度入射光线的光谱分离场合,如双波长成像、液晶显示和液晶投影等.     

一般多值相位光栅菲涅耳衍射光场的分析

基于光栅结构与距离的关系,给出了一种求解一般多值相位光栅菲涅耳衍射光场的解析表达式利用该表达式可以直接分析一般多值相位光栅的分数泰伯数效应及在阵列照明中的应用,克服了间接分析法只能分析某些类型的泰伯阵列照明器的不足之处.     

利用保角变换实现环形光栅的Talbot效应

Talbot效应是一种近场自成像效应,通常只有周期光栅可以产生Talbot效应,而环形光栅无法产生.本文通过引入保角变换,发现可以在环形光栅外部设计适当的折射率渐变层介质,使得其中也能够产生严格的Talbot效应,并计算了对应的自成像半径表达式.本文利用FDTD软件分别将一个环形光栅放置在真空中以及人工设计的折射率渐变层中进行了模拟,并对二者的结果进行了比较分析,发现这种折射率渐变层介质确实对点光源入射的环形光栅的自成像情况有着很好的改善.希望这一工作能够推广Talbot效应的应用范围.     

Talbot Images of Two-Dimensional Gaussian Beam Arrays with Amplitude Fluctuation

Talbot images constructed in the Fresnel diffraction region due to two-dimensional Gaussian beam arrays with amplitude fluctuation are statistically investigated using a mathematical model based on the propagation law of a Gaussian beam. The average intensity distribution of Talbot images is analyzed theoretically, and the corresponding simulation is conducted by computer. The relative fluctuation of the peak intensity to the mean with respect to Talbot images is found to be less than that of the source by approximately 1/4. Furthermore, the effect of the finite size of source arrays on the formation of Talbot images is revealed throughout the simulation as well as the effect of the amplitude fluctuation.     

在超短脉冲照射下光栅的瞬时Talbot效应的研究

本文给出了光栅在超短脉冲照射下其瞬时Fresnel衍射光场的解析解.对该解析解的数值计算表明:当脉冲光波的半极大值全宽Δτ在几十个fs内,光栅的瞬时Talbot自成象现象消失,且Δτ越小或距离越远,瞬时光强波形与初始波形差异较大.而当Δτ达到ps的数值级时,瞬时Talbot自成象现象是存在的.     

Observation of the High-Order Fractional Talbot Effect in the Optical Range

The Talbot effect in the diffraction of light on the amplitude diffraction grating has been investigated experimentally. A high-order fractional Talbot effect up to d/102, where d is the grating period, has been discovered and studied. Possible applications of this phenomenon have been mentioned.     

基于泰伯效应的高斯光束尺寸测量

光栅用在高斯光束参数测量中的突出优点是方法简单，成本较低，全息光栅由于其制备容易，无周期误差而比一般光栅具有更多的优点。在用光栅进行光斑测量的实验中，观察到由全息光栅引起的泰伯（Ｔａｌｂｏｔ）效应携带有关光斑参数的有用信息，本文提出了一种基于泰伯效应的测量方法，只需测定条纹间隔就能确定高斯光束尺寸，因此降低了对光源或光栅定位精度，电路和光源稳定性的要求，文中聚焦高斯光束照明全息光栅时光场分布，及其     

基于Talbot效应的掺镁铌酸锂二维六角位相阵列光栅的研究

本文系统研究了基于泰伯效应(Talbot) 的位相可调掺镁铌酸锂二维六角位相阵列光栅及其光衍射成像, 对光栅占空比D、不同位相差Δφ、及泰伯分数β条件下的光栅近场光衍射强度分布进行了理论研究, 结果表明当光栅占空比D=52%、位相差Δφ=0.75 π、 泰伯分数β=0.2时, 光栅近场衍射光图像效果最佳. 实验设计与 制备了掺镁铌酸锂二维六角位相阵列光栅, 并对其进行了Talbot衍射光成像实验研究, 得到了不同位相差和不同泰伯分数β条件下光栅近场衍射 光图像, 实验结果与理论研究结果相符. 关键词： 二维六角位相阵列光栅 掺镁铌酸锂晶体 泰伯效应     

Partially coherent Fresnel diffraction by a slit aperture. IV. Effect of the phase term in the coherence function

A formula was derived in paper 1 of the this series for investigating the Fresnel diffraction field of a slit aperture when the mutual coherence function of the illumination contains a quadratic phase term. That formula is applied to study the intensity distribution in the Fresnel diffraction field of a slit aperture illuminated by a quasi-monochromatic incoherent slit source. The phase term has a big effect on the features of Fresnel diffraction.