Formation of optical fields of stimulated Raman scattering with a resolution beyond the Abbe diffraction limit by spherical microlens cavities with whispering gallery modes: Near-field approximation

We consider a significant lowering of the threshold of stimulated Raman scattering in solid fused silica spherical microlenses cavities that is caused by an increase in the integral overlap factor of whispering gallery modes. The structure of focal regions of a microlens is shown to have the shape of honeycombs, forming a photonic crystal or a photonic nanojet. We show that, at comparatively small numerical apertures NA = 0.7–0.8, which correspond to hemispherical microlenses, a spherical microlens cavity exhibits the possibility of focusing laser radiation beyond the Abbe diffraction limit. This enables the possibility of wide practical applications of microspheres as a focusing element the resolving power of which exceeds the Abbe diffraction limit in the near field. The whispering-gallery-mode spherical microlens cavity makes it possible to perform laser generation with a duration of a coherent pulse in the subfemtosecond range and to form a subwavelength focal region of the near field. This ensures the possibility of detecting single molecules of a substance in the subwavelength range in the near field and can be used to increase the sensitivity of intracavity spectroscopy methods and as microlasers for excitation of molecules in metal molecular nanoswitches and semiconductor heterostructures. From an array of microlens cavities, metamaterials with a negative refractive index can be formed.     

Analysis of closed-boundary cylindrical microlenses with long focal depth designed by the general focal length function

In this paper, the general focal length function is used to design two-dimensional closed-boundary cylindrical microlenses (CBCMs) with long focal depth. The focusing characteristics of the designed microlenses is investigated by rigorous electromagnetic theory and the boundary element method. A number of focusing performance measures of the designed microlenses, such as the real focal depth, the focal depth range, the focal spot size, and the diffraction efficiency, are presented in detailed. As comparison, the focusing performance of the conventional lenses with the same parameters are investigated simultaneously. Our analysis indicates that the general focal length function is valid in designing CBCMs with larger extended focal depth. Comparing with the open-boundary cylindrical microlenses (OBCMs) designed using the same focal length function, we also find that the designed CBCMs with low f-number exhibit superiority of long focal depth.     

Three-dimensional integration of microoptical components buried inside photosensitive glass by femtosecond laser direct writing

We report the three-dimensional (3D) integration of microoptical components such as microlenses, micromirrors and optical waveguides in a single glass chip by femtosecond (fs) laser direct writing. First, two types of microoptical lenses were fabricated inside photosensitive Foturan glass by forming hollow microstructures using fs laser direct writing followed by thermal treatment, successive wet etching and additional annealing. One type of lens is the cylindrical microlens with a curvature radius R of 1.0 mm, and the other is the plano-convex microlens with radius R of 0.75 mm. Subsequently, by the continuous procedure of hollow microstructure fabrication, a micromirror was integrated with the plano-convex microlens in the single glass chip. Further integration of waveguides was performed by internal refractive index modification using fs laser direct writing after the hollow structure fabrication of the microlens and the micromirror. A demonstration of the laser beam transmission in the integrated optical microdevice shows that the 3D integration of waveguides with a micromirror and a microoptical lens in a single glass chip is highly effective for light beam guiding and focusing. PACS 42.62.-b; 81.05.Kf; 42.82.Cr; 82.50.Pt; 42.79.Gn     

Photoetching of spherical microlenses on glasses using a femtosecond laser

We fabricated spherical microlenses on optical glasses by femtosecond laser direct writing (FLDW) in ambient air. To achieve good appearances of the microlenses, a meridian-arcs scanning method was used after a selective multilayer removal process with spiral scanning paths. A positive spherical microlens with diameter of 48 μm and height of 13.2 μm was fabricated on the surface of the glass substrate. The optical performances of the microlens were also tested. Compared to the conventional laser direct writing (LDW) technique, this work could provide an effective method for precise shape-controlled fabrication of three-dimensional (3D) microstructures with curved surfaces on difficult-to-cut materials for practical applications.     

用于红外焦平面的正方形孔径球面微透镜阵列研究

针对目前红外焦平面光敏阵列中存在的占空比小、光能利用率低的实际问题,展开了正方形孔径球面微透镜阵列制作及其与红外焦平面阵列集成应用的研究.本文从红外焦平面光敏阵列特点入手,对比分析了正方形孔径相比于传统圆形孔径微透镜阵列在光能利用上的优势.提出正方形孔径微透镜阵列激光直写变剂量曝光制作技术,建立光刻胶曝光数学模型和正方形球面微透镜面型函数,以此为基础,编制直写设备变剂量曝光控制软件;利用长春理工大的学复合坐标激光直写系统和等离子刻蚀机进行相关工艺实验,制作了阵列256×256、单元尺寸40×40 μm²、球面半径60 μm、单元间距1 μm的红外石英微透镜阵列;并将其与相应阵列的碲-镉-汞红外光敏阵列进行集成.结果表明:微透镜的占空比达到95%,红外焦平面光能利用率从原来的60%提高到90% 以上.由此得出结论:变剂量曝光制作微透镜技术是可行的,正方形孔径球面微透镜阵列代替圆形孔径微透镜阵列,对于提高红外探测器的灵敏度、信噪比、分辨率等性能具备明显优势.     

Applicability of improved Rayleigh-Sommerfeld method 1 in analyzing the focusing characteristics of cylindrical microlenses

The applicability of an improved Rayleigh-Sommerfeld method 1 (IRSM1) is investigated by analyzing the focal characteristics of various cylindrical microlenses in both cases of the TE and TM polarizations. The IRSM1 and original Rayleigh-Sommerfeld method 1 (ORSM1) are compared with rigorous boundary element method (BEM) by calculating the average square-root deviation (ASRD) of the intensity distribution on the focal plane for the continuously refractive microlens and diffractive microlenses with continuously varying or 8-level quantized profiles. The results indicate that the applicability of the IRSM1 has limitation in some parametric ranges, for instance, the number of sampling points, f-number, relatively refractive index, and wavelength of the incident light are restricted to some appropriate values.     

Effect of illumination types on focusing performance of closed-boundary cylindrical microlenses

The effect of illumination types on closed-boundary cylindrical microlenses (CBCMs) is investigated by rigorous electromagnetic theory and boundary element method. As a result, the focusing performance of CBCMs with different illumination types are different to each other, while the optics elements cannot be considered as pure phase element for small f-number.     

Multiple-spot optical tweezers created with microlens arrays fabricated by proton beam writing

We report two different applications for using arrays of microlenses on glass substrate to facilitate multiple-spot optical trapping of colloidal microbeads. The array of microlenses was made of SU8 or PMMA resist and created by a combination of Proton-Beam writing followed by thermal reflow processes. Firstly, similar to previous reports [8, 9, 10 ], the lenses were utilized as an optical element in generating multiple laser spot arrays that were subsequently focused down to impose a microbead array. In addition, we demonstrated the feasibility of a novel approach of integrating the microlens array into a sample chamber to provide localized optical trapping. PACS 07.60.Pb; 41.75.Ak; 42.15.Eq; 42.65.Jx; 42.79.Bh     

用于红外焦平面的正方形孔径球面微透镜阵列研究

针对目前红外焦平面光敏阵列中存在的占空比小、光能利用率低的实际问题,展开了正方形孔径球面微透镜阵列制作及其与红外焦平面阵列集成应用的研究.本文从红外焦平面光敏阵列特点入手,对比分析了正方形孔径相比于传统圆形孔径微透镜阵列在光能利用上的优势.提出正方形孔径微透镜阵列激光直写变剂量曝光制作技术,建立光刻胶曝光数学模型和正方形球面微透镜面型函数,以此为基础,编制直写设备变剂量曝光控制软件;利用长春理工大的学复合坐标激光直写系统和等离子刻蚀机进行相关工艺实验,制作了阵列256×256、单元尺寸40×40μm2、球面半径60μm、单元间距1μm的红外石英微透镜阵列;并将其与相应阵列的碲-镉-汞红外光敏阵列进行集成.结果表明:微透镜的占空比达到95%,红外焦平面光能利用率从原来的60%提高到90%以上.由此得出结论:变剂量曝光制作微透镜技术是可行的,正方形孔径球面微透镜阵列代替圆形孔径微透镜阵列,对于提高红外探测器的灵敏度、信噪比、分辨率等性能具备明显优势.     

High-resolution beam steering using microlens arrays

Imaging or beam-steering systems employing a periodic array of microlenses or micromirrors suffer from diffraction problems resulting from the destructive interference of the beam segments produced by the array. Simple formulas are derived for beam steering with segmented apertures that do not suffer from diffraction problems because of the introduction of a moving linear phase shifter such as a prescan lens before the periodic structure. The technique substantially increases the resolution of imaging systems that employ microlens arrays or micromirror arrays. Theoretical, numerical, and experimental results demonstrating the high-resolution imaging concept using microlens arrays are presented.     

Focusing performance of the closed-boundary cylindrical microlenses analyzed by the boundary element method

In this paper, we investigate the focusing performance of closed-boundary cylindrical microlenses (CBCMs) based on rigorous electromagnetic theory and the boundary element method. The CBCMs with different incident angles, different quantization-level numbers, different microlens diameters, different f-numbers, and different polarizations of incidence are studied. Several focusing performance measures, such as the focal spot size, the diffraction efficiency, the real focal position, and the normalized transmitted power, are presented. It provides very useful information in designing the CBCMs in micro-optical systems.     

Investigation of the efficient coupling between a highly elliptical Gaussian profile output from a laser diode and a single mode fiber using a hyperbolic-shaped microlens

A tapered hyperbolic-shaped microlens has been improved for efficient the coupling of the output from a laser diode into an optical fiber. A tapered hemispherical-end fiber microlens is also evaluated for comparison purposes. The Fresnel diffraction theory is used to evaluate laser to fiber coupling using microlenses. Experimental results demonstrate that, for an elliptical Gaussian laser diode with an aspect ratio of 1:1.5, the coupling efficiencies for the hyperbolic-shaped microlenses and the hemispherical-end fiber microlenses are 87% and 62%, respectively. Simulation results show excellent agreement with the measurements. The research results illustrate that a hyperbolic-shaped microlens has a much higher coupling efficiency than a hemispherical-end microlens due to efficient mode matching and phase matching.     

Interference effect of dual cylindrical microlenses with the closed boundary in dielectric incident space

The focal characteristics of closed-boundary cylindrical microlenses with dielectric incident space are investigated based on rigorous electromagnetic theory and the boundary element method. For single cylindrical microlens, focal performance is improved with the use of the dielectric incident space, for instance, its diffraction efficiency can be increased. Moreover, the interference effect of dual cylindrical microlenses embedded in a uniform dielectric material is studied in detail. Numerical results reveal that the interference effect between the dual microlenses can be suppressed substantially by the dielectric incident material environment. The interference effect can also be depressed by adjusting some other parameters, such as the distance between the dual microlenses, and the incident wavelength.     

Parallel fabrication of silicon concave microlens array by femtosecond laser irradiation and mixed acid etching

A method of multi-beam femtosecond laser irradiation combined with modified HF-HNO_3-CH_3 COOH etching is used for the parallel fabrication of all-silicon plano-concave microlens arrays(MLAs). The laser beam is split by a diffractive optical element and focused by a lens to drill microholes parallely on silicon. An HF-HNO_3-H_2SO_4-CH_3 COOH solution is used to expand and polish laser-ablated microholes to form microlenses. Compared with the HF-HNO_3-CH_3 COOH solution,the solution with H_2SO_4 can effectively reduce the etched surface roughness. The morphologies of MLAs at different laser powers and pulse numbers are observed. The image array formed by the silicon microlenses is also demonstrated.     

激光直写制作的小F数连续浮雕衍射透镜轴向聚焦特性分析

为确定卷积效应以及深度制作误差对小F数连续浮雕衍射透镜(DOE)轴向聚焦特性影响,基于瑞利-索末菲衍射理论建立了激光直写制作的连续浮雕衍射透镜非旁轴近似轴向光强分布模型.该模型考虑了连续浮雕衍射透镜的轴向衍射聚焦特性与透镜结构参数、写入光斑尺寸和扫描间距以及深度制作误差的关系,克服了傍轴近似条件下传统模型的不精确性.为验证模型的正确性,用激光直写制作了设计波长为441.6 nm,F数为4以及相位匹配因子为3的连续浮雕衍射透镜,并测试了波长441.6 nm激光入射时透镜的轴向聚焦特性.实验与分析表明,该模型分析结果与实验测试结果符合,从而证实模型的有效性,为激光直写制作的小F数连续浮雕衍射透镜的应用提供了理论依据.     

Rigorous electromagnetic analysis of dual-closed-surface microlens arrays

In this paper, we investigated the focal performance of the dual-closed-surface microlens arrays (DCSMAs) based on rigorous electromagnetic theory and boundary element method (BEM) in the case of TE polarization. The DCSMAs are designed with different substrate thickness and different distance between microlenses. DCSMAs designed according to different wavelengths are surveyed. The DCSMAs with different incident angles are also studied. Several focusing performance measures, such as the focal spot size, the focal position on the preset focal plane, the diffraction efficiency and the normalized transmitted power, are presented. Numerical results indicate the DCSMAs with different parameters can implement focusing beams and the focal performance of DCSMAs is easily influenced by the substrate thickness and the incident wavelength. Furthermore, the optimal thickness for the maximal diffraction efficiency of the DCSMAs is given. It is expected that the DCSMAs may be used as a parallel processing device in micro-optics systems.     

A post-compression based ultrasound imaging technique for simultaneous transmit multi-zone focusing

The compression error of post-compression based coded excitation techniques increases with decreasing f-number, which causes the elevation of side-lobe levels. In this paper, a post-compression based coded excitation technique with reduced compression errors through dynamic aperture control is proposed. To improve the near-field resolution with no frame rate reduction, the proposed method performs simultaneous transmit multi-zone focusing using two mutually orthogonal complementary Golay codes. In the proposed method, the two mutually orthogonal sequences of length 16 are simultaneously transmitted toward two different focal depths, which are separately compressed into two short pulses on receive after dynamic focusing is performed. After carrying out the same transmit-receive operation for the same scan line with the complementary set of the orthogonal Golay codes, a single scan line with two transmit foci is obtained.The computer simulation results using a linear array with a center frequency of 7.5 MHz and 60% 6 dB bandwidth show that the range side-lobe level can be suppressed below −50 dB, when f-number is maintained not smaller than 3. The performance of the proposed scheme for a smaller f-number of 2 was also verified through actual experiments using a 3.85 MHz curved linear array with 60% 6 dB bandwidth. Both the simulation and experimental results show that the proposed method provides improved lateral resolution compared to the conventional pre-compressed and post-compression based coded excitation imaging using Golay codes.     

亚波长衍射微透镜的设计

设计了连续浮雕衍射微透镜和与其等效的二元亚波长衍射微透镜,采用旋转体时域有限差分法对通过计算机辅助设计出的元件进行了严格的矢量分析,给出了各元件在焦平面的场强分布.分析结果表明,本文设计的二元亚波长微透镜对连续浮雕微透镜有很好的等效效果;填充因子的脉冲宽度调制法要优于填充因子的线性近似法;制作相对误差不大时深度误差和宽度误差对微透镜聚光能力的影响不大.     

Soda-lime glass microlens arrays fabricated by laser: Comparison between a nanosecond and a femtosecond IR pulsed laser

We present the manufacturing of microlens arrays on soda-lime glass substrates by using two different IR pulsed lasers: a nanosecond Nd:YVO₄ laser (1064 nm) and a femtosecond laser based on Ytterbium crystal technology (1030 nm). In both cases, the fabrication technique consists of the combination of a direct-write laser process, followed by a post-thermal treatment assisted by a CO₂ laser. Through the analysis of the morphological characteristics of the generated microlenses, the different physical mechanisms involved in the glass ablation process with a nanosecond and a femtosecond laser are studied. In addition, by analyzing the optical features of the microlenses, a better result in terms of the homogeneity and quality of the spot focuses are observed for those microlenses fabricated with the Nd:YVO₄ nanosecond laser. Microlens arrays with a diameter of 80 and 90 µm were fabricated.     

Microlenses focal length measurement using Z-scan and parallel moiré deflectometry

In this paper, a simple and accurate method based on Z-scan and parallel moiré deflectometry for measuring the focal length of microlenses is reported. A laser beam is focused by one lens and is re-collimated by another lens, and then strikes a parallel moiré deflectometer. In the presence of a microlens near the focal point of the first lens, the radius of curvature of the beam is changed; the parallel moiré fringes are formed only due to the beam divergence or convergence. The focal length of the microlens is obtained from the moiré fringe period graph without the need to know the position of the principal planes. This method is simple, more reliable, and completely automated. The implementation of the method is straightforward. Since a focused laser beam and Z-scan in free space are used, it can be employed for determining small focal lengths of small size microlenses without serious limitation on their size.