Talbot effect in metallic gratings under Gaussian illumination

Metallic gratings can be found in applications such as optical metrology. Due to their fabrication process, the surface presents a certain roughness. In this work, the effect of roughness on Talbot effect has been analyzed when the grating is illuminated with a Gaussian beam. A model based on Fresnel regime is used in order to determine the intensity distribution in the near field. Contrast of the self-images is obtained and it is found that it decreases in terms of the distance between the grating and the observation plane. When the autocorrelation function of roughness presents a Gaussian behaviour, the diffracted beams are still Gaussian although some of their properties change. For example, the width of the diffracted beams increases with respect to the case of the standard chrome on glass gratings. On the other hand, the power of each diffracted beam is independent on the roughness properties of the surface.     

Self-imaging with curved gratings

We analyze the near field behavior of binary amplitude gratings which present a curved profile. This configuration has an important application in rotary optical encoders. This kind of encoders is used to measure the angular displacement between two different parts of the devices. To our knowledge, its behavior in the near field has not been analyzed yet. We have found that Talbot effect is produced but the period of the self-images and Talbot distances change as we separate from the grating. We have fabricated a curved grating and have performed the experiment to corroborate the behavior theoretically found. This fact could be useful in systems that use Talbot effect to measure displacements, since the mechanical tolerances grow.     

Double grating systems with one steel tape grating

Steel tape gratings are used in different metrology applications. As the period of these gratings was large (around 100μm,), its analytical study has been performed, up to date, using a geometrical approach. Nowadays, steel tape gratings can be manufactured with lower periods, around 20-40 μm, and diffractive effects must be taken into account. Also, due to the roughness of the surface, statistical techniques need to be considered to analyze their behavior. In this work, an analysis of the pseudo-imaging formation in a double grating system including one steel tape grating is performed. In particular Moiré and Lau configurations are analyzed. We have found that roughness significantly affects to Moiré configuration. However, its effect is negligible in Lau configuration. Generalized grating imaging configuration is also studied in depth. It is shown that roughness does not affect to the contrast of pseudoimages, but it modifies their depth of focus.     

Talbot effect of a high-density grating under femtosecond laser illumination

The Talbot effect of a high-density grating under femtosecond laser illumination is analyzed with rigorous electromagnetic theory which is based on the Fourier decomposition and the rigorous coupled-wave analysis (RCWA). Numerical simulations show that the contrast of the Talbot images steadily decreases as the transmitted femtosecond laser pulses propagate forward and with wider spectrum width of the femtosecond laser pulses. The Talbot images of high-density gratings have much higher sensitivity of the spectrum widths of the incident laser pulses than those of the traditional low-density gratings. In experiments, the spectrums and the pulse widths of the incident pulses are measured with a frequency-resolved optical grating (FROG) apparatus. The Talbot images are detected by using a Talbot scanning near-field optical microscopy (Talbot-SNOM) technique, which are in coincidence with the numerical simulations. This effect should be useful for developing new femtosecond laser techniques and devices.     

Self-imaging of gratings with two roughness levels

In previous works, the authors have analyzed diffraction gratings with surface roughness on their strips. Appl. Opt. 46 (2007) 3668 determined the near field of a grating whose strips present two kinds of roughness, one of them so rough that the grating acts as an amplitude grating. On the other hand, in J. Opt. Soc. Am. A 25 (2008) 2390, a grating with roughness only in one of the grating levels is studied. In the present work, we extend our analysis to the general case where the strips of the grating present two finite roughness levels. As a consequence, the periodic modulation is only generated by random micro-topography of the strips. A statistical analysis is developed to obtain equations that predict the average intensity distribution after the grating. This general case presents differences with the previous works. For example, the maximum contrast of the self-images is given at a certain distance from the grating, that is, the contrast of the self images firstly increases with the distance of the observation plane and after, it decreases. Numerical simulations, based on Rayleigh–Sommerfeld approach, are performed which confirm the theoretical predictions.     

基于X射线塔尔博特效应的纳米光栅制作模拟研究

沿纳米多层膜生长方向切割可制成周期只有几纳米而厚度几十微米的切片多层膜光栅. 基于该切片多层膜光栅塔尔博特自成像效应的X射线光刻是一种新型的纳米图样制作方法. 已有学者用该方法完成了百纳米结构光栅的制作. 采用严格耦合波方法, 本文模拟计算了切片多层膜光栅在满足塔尔博特自成像条件下的后表面光场分布, 详细讨论三个影响光栅后表面成像质量的重要参数:光栅厚度、材料厚度所占比例和多层膜周期. 模拟结果表明, 光栅厚度不仅影响X射线透射率, 还会改变像面条纹衬比度. 材料厚度比的大小直接决定像面是否存在清晰条纹, 选取合适的材料厚度比, 得到了前人实验中近场反常成像现象. 计算还表明, 在一定条件下, 采用周期更小的多层膜光栅有望获得更高分辨率的纳米图形, 这说明使用塔尔博特效应制作更加精细的纳米结构图形具有可行性.     

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.     

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.     

基于塔尔博特效应的分波器和分束器

给出一个单一器件同时具有分波器和大规模分束器功能的实验结果，其设计原理基于塔尔博特自成像效应。以两波长为例，通过改变分数塔尔博特距离和光栅周期等参量，实验上实现了两波长光信号在空间上的交叉分离。     

The influence of the polarization effect in Talbot self-imaging of high-density gratings

The Talbot self-imaging of high-density gratings with different period at half Talbot distance for different polarization is analyzed with the finite-difference time-domain (FDTD) method. The numerical results indicate that the Talbot self-imaging of high-density gratings is obviously different for different polarization when the period d of the grating between 2λ and 3λ, which is verified through experimental results with the scanning near-field optical microscopy (SNOM) technique. Furthermore, the Fourier spectrum (far field) generated by the gratings is also given with the rigorous coupled-wave method, which is in agreement with the near field.     

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.     

Quasi-Talbot effect of the sub-wavelength Ag grating

When a TM-polarized beam incidents normally on a thick sub-wavelength Ag grating with small opening ratio, self-images form in the transparent dielectric layer due to contributions not only from waves radiating from the slits, but also from the Surface Plasmons (SPs) created on Ag surface. These two contributions make the self-images connect together along the propagation direction and form continuous stripes with period equal to half of that of the grating. We define this phenomenon as quasi-Talbot effect. For a thin sub-wavelength Ag grating or a grating with large opening ratio, its intensity distribution conforms to the conventional Talbot effect. Investigation on quasi-Talbot effect of sub-wavelength metal grating can develop new applications in nano-scale devices.     

Integration of optical pulses by resonant diffraction gratings

The possibility of integrating optical pulses by resonant diffraction gratings has been considered. It has been shown that a diffraction grating provides integration of the pulse envelope in the vicinity of quasiguided-mode resonances. The integration is performed with an exponential weight function, whose decay rate is deter-mined by the quality factor of the resonance. Metallic diffraction gratings for integration of picosecond pulses have been computed. The calculation of the grating eigenmodes with the use of the scattering-matrix method has shown that the integration is performed in the vicinity of the resonances corresponding to the excitation of surface plasmon polaritons at the grating boundary. According to the results of numerical simulation, the integration quality is quite high.     

Variable Wavelengths Fiber Bragg Gratings Written with A Phase Mask and Four Prisms

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Variable Wavelengths Fiber Bragg Gratings Written with A Phase Mask and Four Prisms

Using only one diffractive element, the Talbot interferometer provides a robust and inherently stable method for reproducing fiber Bragg gratings with variable wavelengths, and reduces the complexity of the fiber grating fabrication system. However, the usable length of the grating is limited by the practical length of the mirrors. This paper presents a phase mask with two fixed prisms and two rotational prisms to inscribe fiber Bragg gratings with variable Bragg wavelengths. In this system, the fiber Bragg grating is inscribed by UV interference stripes of 193 nm derived from two rotational prisms and two fixed prisms, where phase mask is used as a beam splitter of ±1 order diffraction light. It is noteworthy that the tunable phase mask interferometer decreases the demand of the length of prism evidently.     

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.     

具有消像差和光程补偿功能的新型取样光栅

 在惯性约束聚变(ICF)终端光学聚焦系统中,采用取样光栅将透射的高功率三倍频光按约0.5%的效率进行聚焦采样,送入能量计中进行诊断。提出了用取样光栅对结构取代单取样光栅,通过合理选择系统参数,包括两块光栅的距离、光栅倾斜角度等,设计出的消像差取样光栅可同时进行能量诊断、光脉冲响应测量、以及远场光斑质量的检测。计算结果显示：光程差从8.3 cm降低到8.7 mm,像点的均方根半径为0.777 μm,达到衍射极限和使用要求。这为ICF系统中激光能量、波前畸变的诊断提供了一种可供选择的新诊断装置。     

部分相干同步辐射照射下光栅分数塔尔博特效应

基于高斯谢尔光束的相干模式分解理论和波动光学,建立了部分相干同步辐射硬X射线光束通过光学器件的传播模型。模拟了微聚焦X射线光束照射下光栅的分数塔尔博特效应,得到了聚焦光束的光强分布和相干特性变化,并分析了散焦光束入射下的光栅自成像。然后通过模拟准直光束入射下的光栅塔尔博特效应,得到了不同传播距离处自成像条纹的变化情况,分析了影响光栅自成像条纹形状的因素。通过光栅衍射条纹测量同步辐射相干度,发现对矩形相位光栅来说,应该对衍射图样进行傅里叶分解,求出各级傅里叶系数随传播距离的变化曲线,从而得到入射光束相干特性。     

X-ray Bragg diffraction on periodic surface gratings

We report on the X-ray Bragg diffraction analysis of periodic surface gratings on (100) GaAs crystals. We show that the X-ray Bragg diffraction is a very powerful method to investigate ultrafine surface gratings and allow us to determine not only the grating period but, in particular, the width of the grooves and to characterize the quality of the sidewalls, which is not easily possible with optical methods. The X-ray diffraction on surface crystal gratings is analogue to the Fraunhofer diffraction of multiple slits or reflection gratings.