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Nonlinear Talbot self-healing effect



Illustrating Talbot self-healing, where the initially missing point (#3) is restored in the first Talbot image plane.

Nonlinear Talbot effect is a near-field nonlinear diffraction phenomenon in which the self-imaging of periodic object is formed by the second harmonic of the incident laser beam. Different from its conventional linear analogue, the periodic object here is made with spatially modulated second-order nonlinear coefficient of the medium, and the spatial resolution in Talbot self-imaging is improved by a factor of 2 thanks to frequency doubling. Consequently, the nonlinear Talbot effect is superior in applications that require high resolution imaging and processing, such as nonlinear optical microscopy, lithography, spectrometry, and material characterization.The nonlinear Talbot effect was first observed in periodically poled LiTaO3 crystals, which are also known as nonlinear photonic crystals. The self-imaging of 1D periodically and 2D hexagonally poled ferroelectric domain structures was observed by using the second harmonic generated in the crystals. Following this pioneering work, the dependence of nonlinear Talbot distance on parameters of nonlinear photonic crystals and the fractional nonlinear Talbot effects were also investigated. Despite of these recent achievements, the fundamental properties and capabilities of nonlinear Talbot effect have not been thoroughly studied so far. For instance, very useful characteristic of Talbot effect is its capability to produce defect-free images from imperfect structures, property known as self-healing. While such capability of image restoration has been well studied in linear Talbot effect, it has never been investigated in the regime of nonlinear optics.

The research group led by Prof. Yan Sheng and Prof. Wieslaw Krolikowski from Ningbo University and Australian National University provided the first observation of nonlinear Talbot self-healing, i.e. the capability of creating defect-free images from faulty nonlinear optical structures. The research results are published in Chinese Optics Letters, Vol. 19, No. 6, 2021 (Bingxia Wang, et al., Nonlinear Talbot self-healing in periodically poled LiNbO3 crystal).

The research group led by Prof. Yan Sheng and Prof. Wieslaw Krolikowski from Ningbo University and Australian National University provided the first observation of nonlinear Talbot self-healing, i.e. the capability of creating defect-free images from faulty nonlinear optical structures. The research results are published in Chinese Optics Letters, Vol. 19, No. 6, 2021 (Bingxia Wang, et al., Nonlinear Talbot self-healing in periodically poled LiNbO3 crystal).

In this work the tightly focused femtosecond infrared optical pulses were used to fabricate LiNbO3 nonlinear photonic crystals by periodically inverting its spontaneous polarization. With the inversion of spontaneous polarization, the second-order nonlinear coefficient changes its sign. In this way the nonlinear periodic pattern was obtained in experiment. However, instead of producing a perfect periodic structure a few points were randomly removed from the 2D square and hexagonal lattices. The near-field nonlinear diffraction experiments show the missing elements are restored in the second harmonic images at the first nonlinear Talbot plane.

The observed nonlinear Talbot self-healing opens up new possibilities for defect-tolerant optical lithography and printing. As the photoelectronic industry continues to shrink the device size in integrated circuits, optical lithography will require higher resolution and accuracy. Any scratch or defects over a periodic mask will limits the resolution and accuracy of the lithographed feature. Fortunately, this problem can be overcome by nonlinear Talbot self-healing, which is a promising way to develop high resolution and defect-tolerant lithography by combining with extreme ultraviolet light source.


Nonlinear Talbot self-healing: the capability of creating defect-free images from faulty nonlinear photonic structures by the second harmonic of the incident laser beam.

The nonlinear Talbot self-healing also offers a new way to realize information encryption. In fact, the capability of nonlinear Talbot self-healing depends critically on the severity of defects, i.e. high quality self-healing can only be obtained at a moderate level of structure's defects. Then by controlling the degree of these defects one may hide the information into the units that can self-heal via the nonlinear Talbot imaging. Similarly, the nonlinear Talbot effect works perfectly with periodic χ(2) structures, but is incapable of dealing with disordered patterns. Therefore, utilizing such different responses of periodic and disordered structures in the nonlinear Talbot self-imaging, similar effects of information encryption may be achieved too.

It has been widely accepted that the nonlinear Talbot self-imaging can be used as an efficient technique for diagnostic of the surface distributions of the second-order nonlinear coefficient of the nonlinear photonic crystals. This also offers a good way to analyze antiparallel ferroelectric domains in LiTaO3, LiNbO3, and many other ferroelectric crystals. However, according to the research results presented in this work, the nonlinear Talbot self-healing has to be accounted for in analysis of the nonlinear optical structures, as the minor defects or scratches cannot be detected.

The resolution of nonlinear Talbot imaging is defined by the diffraction limit at the second harmonic frequency in this work. In order to improve the resolution, one of the future research directions will be the extension of nonlinear Talbot self-imaging to the cascaded third harmonic generation. In this cascading nonlinear process, the incident fundamental wave is converted into the second harmonic at first, and then the generated second harmonic frequency mix with the rest fundamental beam to generate the third harmonic. In this way, the resolution of nonlinear Talbot self-imaging can be further improved by 1.5 times. Meanwhile, one may consider to study the nonlinear Talbot effects and associated new phenomena in other nonlinear optical parametric processes, such as the spontaneous parametric down conversion, which may inspire new applications in quantum optical technologies as an efficient way to generate entangled photon pairs.



非线性Talbot自修复为实现信息加密提供了新途径



传统Talbot效应(图片源自网络)

非线性Talbot效应是一种近场光学非线性衍射现象,其中周期物体的自成像由入射激光的二次谐波再现。与传统线性Talbot效应不同,这里的周期性物体由介质中二阶非线性系数的空间调制构成,并且倍频过程使非线性Talbot自成像的空间分辨率相比线性情况提高了2倍。因此,非线性Talbot效应在高分辨成像和加工等领域更具优越性,如非线性光学显微镜、现代光刻技术、光谱分析和材料表征等。

非线性Talbot效应首次在周期极化的钽酸锂非线性光子晶体中观测到。利用晶体中产生的二次谐波,观察到了一维周期和二维六角阵列排布的极化铁电畴结构的自成像。在这一开创性工作的基础上,非线性光子晶体参数对非线性Talbot距离的影响以及分数阶非线性Talbot效应也得到了研究。尽管当前已经取得了一些成果,但是非线性Talbot效应的基本性质和实际应用迄今尚未得到全面的研究。例如,Talbot效应非常有用的特征之一是能够从带有缺陷的周期结构中生成无缺陷的图像,这种特性被称为自修复。虽然这种图像的自修复能力在线性Talbot效应中已经得到了很好的研究,但在非线性光学领域还没有涉及。


线性Talbot自修复效应示意图,初始缺失点(#3)在Talbot图像平面中得到恢复

宁波大学盛艳教授和澳大利亚国立大学Wieslaw Krolikowski教授领导的研究小组在实验中首次观测到了非线性Talbot自修复效应,即从有缺陷的非线性光学结构中获得自修复的无缺陷结构图像的能力。研究结果发表在Chinese Optics Letters,2021年第19卷第6期上(Bingxia Wang, et al., Nonlinear Talbot self-healing in periodically poled LiNbO3 crystal)。


周期性结构下,二维六方晶格中随机缺失的点阵在非线性Talbot效应下得到修复

该工作利用强聚焦的近红外飞秒激光脉冲,实现了铌酸锂晶体自发极化的周期性反转,也就是铌酸锂非线性光子晶体的全光制备。随着自发极化的反转,铌酸锂晶体的二阶非线性系数符号也发生反转。采用这种方式,非线性周期结构在实验上得以实现。不同于先前报道的完美周期结构,我们从二维正方晶格和六方晶格中随机地去掉一些格点,制备出具有缺陷的非线性光子结构。近场光学非线性衍射实验表明,在第一非线性Talbot平面处的二次谐波完美再现了周期结构中缺失的格点。该工作中所观测到的非线性Talbot自修复效应为容错光刻和光学打印开辟了新的可能性。光电子工业中集成电路元器件尺寸的不断减小,对光刻技术分辨率和制备精度提出了更高的要求。周期掩模板上的任何划痕或缺陷都会限制光刻形貌的分辨率和精度。幸运的是,利用非线性Talbot自修复技术可以克服这一问题,并且将此技术与极端紫外光源相结合是发展高分辨率容错光刻技术的有效途径。

非线性Talbot自修复也为实现信息加密提供了新的途径。事实上,非线性Talbot自修复能力关键取决于缺陷的严重程度,即只有在适度的结构缺陷下才能获得高质量的自修复。因此,通过控制缺陷程度,可以将信息隐藏到通过非线性Talbot成像实现自修复的缺陷单元中。类似地,非线性Talbot效应很好地适用于周期性非线性结构,但不适用于无序的结构。因此,利用非线性Talbot自成像对周期结构和无序结构的不同响应,也可以获得类似的信息加密效果。


非周期性结构的向日葵图案中,随机缺失的点阵无法通过非线性Talbot效应修复

通常非线性Talbot自成像可以作为诊断非线性光子晶体表面二阶非线性系数分布的一种有效技术,也为分析铌酸锂、钽酸锂和许多其它铁电晶体中反平行铁电畴提供了一种很好的方法。但是根据本文的研究结果,在分析非线性光学结构时必须考虑非线性Talbot自修复效应,因为自修复效应使得非线性光子晶体中微小的缺陷或划痕无法实验检测。

该工作所研究的非线性Talbot成像的分辨率是由二次谐波的衍射极限决定的。为了提高分辨率,将来的研究方向之一是将非线性Talbot自成像技术拓展至级联三次谐波成像。在这种级联三次谐波产生过程中,入射的基频波首先转换为二次谐波,然后二次谐波与剩余的基频波再通过光学和频过程产生三次谐波。通过这种方式,非线性Talbot自成像的分辨率可进一步提高1.5倍。与此同时,研究其它非线性光学参量过程中的非线性Talbot效应及其相关的新现象也具有重要的意义。例如光学自发参量下转换是产生纠缠光子的有效途径,研究自该过程中非线性Talbot效应将激发量子光学技术的新概念和应用。

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