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Longitudinal super-resolution spherical multi-focus array based on column vector light modulation
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摘要:
激光多焦点阵列以兼具更高的光场操控自由度和焦斑单元高空间分辨率的特点，被广泛应用在光学诱捕以及飞秒激光微纳制造等领域。然而由于阵列中焦斑的纵向分辨率弱于横向分辨率，在激光加工应用中限制了其对各向同性结构的加工能力。因此，本文提出一种基于柱矢量光调控生成纵向超分辨准球形多焦点阵列的方法。利用对柱矢量光的两组基径向偏振光和角向偏振光分别进行聚焦调控，结合环形衰减调制可形成纵向超分辨焦斑，再将两种偏振光场以适当的振幅比例在焦区叠加，从而合成准球形多焦点阵列。实验结果表明，10×10的多焦点阵列中各焦斑尺寸均一，具有近球形光强分布。其中，阵列中所有焦点的纵向半高全宽的平均值为0.76
λ 、标准差为0.005λ ，横向半高全宽的平均值为0.76λ 、标准差为0.019λ 。该具有高尺寸均一性的准球形多焦点阵列可为激光微纳加工精准制备微纳器件提供新的途径。Abstract:Featured by the capability of multi degree-of-freedom light-field manipulations while reserving high spatial resolution, multifocal laser arrays have been widely applied in femtosecond laser micro/nanofabrication, optical trapping, and so forth. Yet, due to the relatively lower axial resolution of single focuses within the array in comparison with the lateral resolution of their own, multifocal laser array has been refrained from isotropic 3D nanofabrication. Herein, we propose a feasible method for generation of axially super-resolved multifocal array with quasi-spherical focal spots. In particular, quasi-spherical multifocal array is optically synthesized via precise modulation on the coherent superposition of the orthogonal radially polarized beam (RPB) and azimuthally polarized beam (APB) states in the focal region based on annular amplitude modulation. We show theoretically the generation of quasi-spherical multifocal array with a high uniformity up to 99%. The average axial and lateral full-width-half maximum (FWHM) of the focal array are measured to be 0.76
λ with the standard deviations in the axial and lateral directions being 0.005λ and 0.019λ , respectively. The presented strategy for synthesis of quasi-spherical multifocal array with high uniformity paves the way for high-precision laser fabrication of 3D micro/nano devices. -
Overview: Featured by the capability of multi degree-of-freedom light-field manipulations while reserving high spatial resolution, multifocal laser arrays have been widely applied in femtosecond laser micro/nanofabrication, optical trapping, etc. However, for lens diffraction, the smaller momentum spread along the optical axis with respect to that in the transverse direction could introduce a larger position spread in real space, which in turn leads to lower axial resolution than the transverse resolution. The anisotropy of the focused laser beam, inherent regardless of paraxial or tight-focusing cases, has been a great hurdle for laser printing of functional microdevices with precise control on feature size and improved mechanical performances. To this end, in this research, a feasible method for generation of isotropic focused laser beam with quasi-spherical 3D point spread function (PSF) is developed based on vectorial light field modulation. We demonstrate that through simultaneous implementation of phase modulation and amplitude modulation, homogeneous multifocal array with quasi-spherical focal spots can be generated. Particularly, with the use of a well-designed annular mask, the suppression on the axial spread of field is accomplished via accurate control on the coherent superposition of the orthogonal radially polarized beam (RPB) and azimuthally polarized beam (APB) in the focal region since the depolarized axial component of the AP beam vanishes in vicinity of the gaussian focus even under tight focusing condition. Using the proposed method, isotropic 3D PSF with identical axial and transverse FWHM of 0.71λ is achieved. Meanwhile, based on iterative phase retrieval algorithm, phase-only holograms are designed and employed transforming the incident wavelet as the summation of sub-wavelets, yielding multiple converging sites in 3D space, thereby generating the multifocal array. We further present the synthesis of quasi-spherical multifocal array. A high uniformity up to 99% for a 10-by-10 multifocal array, in which the single focus elements share near-identical axial and transverse FWHM, being 0.76λ on average. The standard deviation of the axial and transverse FWHM of the multifocal array are evaluated be 0.005λ and 0.019λ, respectively, highlighting the features of high uniformity and isotropy. The reported strategy renders precise control on the axial feature size and is potential for the application in high-precision parallel laser printing technique.
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图 1 基于柱矢量光调控实现纵向超分辨率准球形多焦点阵列的原理示意图
Figure 1. Schematic diagram of the principle of synthesizing longitudinal super-resolution quasi-spherical multifocal arrays based on the superposition principle of cylindrical vector light modulation
图 2 (a) 在角向偏振光和径向偏振光的不同振幅比下合成焦点的五个方向上的半高全宽的标准差；(b) 合成焦点的强度分布沿不同方向的场强曲线； (c)~(e) 角向偏振光叠加径向偏振光生成合成焦点的二维强度分布
Figure 2. (a) The standard deviation of the full width at half maximum in the five directions of the composite focus under different amplitude ratios of angularly polarized beam and radially polarized beam; (b) Field strength curves of the intensity distribution of the synthetic focus along different directions; (c)~(e) Azimuthal polarized beam superimposed on radially polarized beam to generate a two-dimensional intensity distribution of the composite focus
图 3 (a)~(b) x-z平面上叠加生成的球形焦点的二维光场强度分布，以及在不同阈值和不同物镜NAs下的横向和纵向尺寸大小，虚线是纵向尺寸、实线是横向尺寸；(c) 在不同的阈值强度和数值孔径下的角向偏振光与径向偏振光焦点的纵向和横向半高全宽的比值
Figure 3. (a)~(b) Two-dimensional light field intensity distributions of spherical foci generated by superposition in the x-z plane, as well as lateral and longitudinal dimensions at different thresholds and different objective NAs, where the dotted line is the longitudinal dimension and the solid line is the transverse dimension; (c) The ratio of the longitudinal and transverse full width at half maximum of the focal point for angularly polarized light to radially polarized light at different threshold intensities and numerical apertures
图 4 (a) 不同焦点个数的径向偏振光多焦点阵列；(b) 均一性和迭代次数随不同焦点个数的变化图
Figure 4. (a) Radial polarized beam multifocal array with different number of focal points; (b) The variation of uniformity and iteration number with the number of different foci
图 5 (a)，(d) 调制角向偏振光(a)和调制径向偏振光(d)聚焦叠加得到的准球形多焦点阵列x-y面剖面图(g)；(b)，(e) 调制角向偏振光(b)和调制径向偏振光(e)聚焦得到的准球形多焦点阵列x-z面剖面图(h)；(c)，(f)，(i) 分别是(b)，(e)，(h)中标记焦点的放大图
Figure 5. (a), (d) The x-y cross-section (g) of the quasi-spherical multifocal array obtained by focusing and stacking the modulated angularly polarized light (a) and the modulated radially polarized light (d); (b), (e) The x-z profile (h) of the quasi-spherical multifocal array obtained by focusing the modulated angularly polarized light (b) and the modulated radially polarized light (e); (c), (f), (i) are magnifications of the marked foci in (b), (e), (h), respectively
图 6 (a) 合成准球形多焦点阵列焦点横向光场强度分布；(b) x-y面的最大焦点与最小焦点的光场强度曲线对比；(c) x-z面的最大焦点与最小焦点的光场强度分布沿不同方向的场强曲线；(d) 合成纵向超分辨率的准球形多焦点阵列的三维光场强度分布
Figure 6. (a) The lateral light field intensity distribution at the focal point of the synthetic quasi-spherical multifocal array; (b) Comparison of the light field intensity curves of the maximum focus and the minimum focus on the x-y plane; (c) The field intensity curves of the light intensity distribution of the maximum focus and the minimum focus in the x-z plane along different directions; (d) Three-dimensional light intensity distribution of synthetic longitudinal super-resolution quasi-spherical multifocal arrays
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