Focusing and waveguiding of Lamb waves in micro-fabricated piezoelectric phononic plates

This paper presents results on the numerical and experimental studies of focusing and waveguiding of the lowest anti-symmetric Lamb wave in micro-fabricated piezoelectric phononic plates. The phononic structure was based on an AT-cut quartz plate and consisted of a gradient-index phononic crystal (GRIN PC) lens and a linear phononic plate waveguide. The band structures of the square-latticed AT-cut quartz phononic crystal plates with different filling ratios were analyzed using the finite element method. The design of a GRIN PC plate lens which is attached with a linear phononic plate waveguide is proposed. In designing the waveguide, propagation modes in square-latticed PC plates with different waveguide widths were studied and the results were served for the experimental design. In the micro-fabrication, deep reactive ion etching (Deep-RIE) process with a laboratory-made etcher was utilized to fabricate both the GRIN PC plate lens and the linear phononic waveguide on an 80 μm thick AT-cut quartz plate. Interdigital transducers were fabricated directly on the quartz plate to generate the lowest anti-symmetric Lamb waves. A vibro-meter was used to detect the wave fields and the measured results on the focusing and waveguiding of the piezoelectric GRIN PC lens and waveguide are in good accordance with the numerical predictions. The results of this study may serve as a basis for developing an active micro plate lens and related devices.     

Numerical simulation of a gradient-index fibre probe and its properties of light propagation

In order to verify the properties of the light propagating through a gradient-index (GRIN) fibre probe for optical coherence tomography (OCT), numerical simulation using the optical software GLAD is carried out. Firstly, the model of the GRIN fibre probe is presented, which is consisted of a single mode fibre (SMF), a no-core fibre (NCF), a GRIN fibre lens and an air path. Then, the software GLAD is adopted to numerically investigate how the lengths of the NCF and the GRIN fibre lens influence the performance of the Gaussian beam focusing through the GRIN fibre probe. The simulation results are well consistent with the experimental ones, showing that the GLAD based numerical simulation technique is an intuitive and effective tool for the verification of the properties of the light propagation. In this paper, we find that on the conditions of a constant GRIN fibre lens length of 0.1 mm and an NCF length of 0.36 mm, the working distance of the probe will be 0.75 mm and the focus spot size is 32 μm.     

Extending the depth of focus with high NA lens axicon

Based on vectorial Debye theory, tight focusing of x-polarized beam with high NA lens axicon is studied. The high NA lens axicon utilizes spherical aberration to duplicate the performance of an axicon and to create an extended focal line. The intensity distribution in the focal region is illustrated by numerical calculations. We show that the high NA lens axicon system can generates a sub wavelength beam (0.826λ) with depth of focus around 10λ.     

Fabrication of gradient refractive index ball lenses using the method of combination of ion exchanging and sagging

Based on the Fick’s diffusion equations, the distribution function of refractive index of a gradient refractive index ball lens (GRIN ball lens/GBL) is derived. Lithium containing silicate glass is fabricated and GRIN ball lenses (GBLs) which diameters are from 0.3 mm to 3.0 mm are made by the method of combination of Ion exchanging and sagging in sodium nitrate. Refractive index profiles of these GBLs are measured by interferometer, and the performances such as effective focal length (EFL), back focal length (BFL) and numerical aperture (NA) between GBLs and homogeneous ball lenses (HBLs) are compared. Results show that the distribution of the index of refraction is parabolic curve and its Δn is about 0.0002, the performances of the former are super to the latter.     

Toward one nanometer X-ray focusing: a complex refractive lens design

We report a design for one nanometer X-ray focusing by a complex refractive lens, which is capable of focusing 20 keV X-rays down to a lateral size of 0.92 nm （full-width at half-maximum （FWHM）） and an axial size of 98 nm （FWHM） with intensity gain of 49050. This complex refractive lens is comprised of a series of kinoform lenses, whose aperture is gradually matched to the converging trace of the X-ray beam so as to increase the numerical aperture （NA）. The theoretical principle of the proposed complex refractive lens is presented. The NAs of these lenses are calculated. The numerical simulation results demonstrate that the proposed design can focus the X-ray beam into sub-nanometer while remaining high gain.     

超小自聚焦光纤探头的研究进展

梯度折射率（Gradient-index,GRIN）光纤探头是一种全光纤型超小光学镜头,在心血管等狭小空间组织内窥影像检测中具有广阔的应用前景。但其发展一直缺少系统的理论体系。本文讨论探头设计、制作和性能测试等方面的关键问题。基于GRIN光纤探头聚焦性能的特征参数,对解析设计方法与数值仿真设计方法进行比较分析。针对超小GRIN光纤探头的制作难题,研究一种光纤熔接和切割的高精度一体化集成装置,描述GRIN光纤探头的制作方法。此外,分析了超小GRIN光纤探头聚焦性能检测的方法及装置。本文为超小GRIN光纤探头的设计、制作及性能测试提供了一个方法体系。     

Focusing effect of a graded index photonic crystal lens

We present a new graded-index photonic crystal (GRIN PhC) structure which can be made by laser interference lithography (LIL). It can be applied as miniaturized focusing lens. Numerical simulations are carried out on the structures with different widths, lengths, and modulations. In the qualitative analysis of the focal length, focusing of a GRIN PhC was proved to originate from both the graded sizes of the rods and multimode interference. Multimode interference dominates the focusing effect when a GRIN PhC has a small length or a small difference in the rod sizes. Intensity distributions in different cases were given to support the conclusion.     

Degree of polarization of a tightly focused partially coherent dark hollow beam

Propagation of a linearly polarized partially coherent dark hollow beam (DHB) through a high numerical aperture (NA) thin lens is formulated. The tight focusing properties, such as the degree of polarization, the intensity distribution, and the degree of coherence, of a partially coherent DHB are investigated in detail. It is found that the focusing properties of a partially coherent DHB are closely determined by the initial coherence, beam order, and the NA of the thin lens.     

Tighter focusing with a parabolic mirror

We demonstrate experimentally and theoretically that a parabolic mirror (PM) with a high numerical aperture (NA) of 1 focuses a radially polarized laser mode to the smallest diffraction-limited spot at a fixed NA and wavelength, having an area of 0.134 lambda(2). The measurements were performed with a confocal microscope, using the PM as a focusing and collecting element. The results stand in accordance with the theoretical calculations presented by Davidson and Bokor [Opt. Lett. 29, 1318 (2004)], who predicted a reduction in the total focal spot size of 43% as compared with an aplanatic lens.     

Automatic design of a one-to-many optical-interconnects lens system using aspherics

Use of an aspherical surface in the design of a lens system for one-to-many optical-interconnects (OTM-OI), composed of a doublet lens and a gradient-index (GRIN) lens array has been investigated. Applying the procedure of ALSIE (Automatic Lens design by Solving InEqualities), the off-axis lens systems, which feature the optical performance of the OTM-OI lens system, are optimized at 0.1 numerical aperture with a total field of view of 2°. Three aspherical designs with the aspherical surface for different surfaces are presented. The aspherical designs show preferable modulation transfer function (MTF) for high frequency as compared with the spherical design.     

梯度透镜折射率分布高次项系数的数值计算

本文从光线方程出发,给出了一系列利用径向梯度透镜球象差进行数值计算求解折射率分布高次项系数的公式及测量计算结果。     

The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method

In this article, through the linear fit of objective distance and reciprocal of magnification in different imaging locations, we use imaging method to measure the central refractive index n(0) and focusing constant α of radial gradient index (GRIN) lens and obtain 10⁻³ measurement accuracy of n(0). At the same time, under distortion, the fourth-order refractive index coefficient and aberration of GRIN lens are derived.     

A fiber coupling system based on the GRIN lens for use in all-fiber lidars

The all-fiber lidar shows exciting prospects in space-borne applications, but the coupling efficiency between the telescope and a single-mode fiber is an important problem in the lidar design. We employ the mode-matching theory to analyze theoretically the coupling efficiency. In practical coupling system design, three position deviations, which are the off-axis deviation, defocus deviation, and angle deviation, exert a substantial influence on the coupling efficiency and must be considered and discussed. Generally it is very difficult for a fiber coupling system based on a single lens to adjust the fiber position deviations and obtain the maximum coupling efficiency. Therefore, a coupling system, based on the GRIN lens combined with the lenses, is designed and employed to decrease the influence of these position deviations. We perform some numerical simulations to verify the feasibility of a coupling system based on the GRIN lens. Our results show that a coupling system based on the GRIN lens can overcome the off-axis deviation and defocus deviation and decrease the adjustment difficulty.     

Tight focusing of double ring shaped radially polarized beam with high NA lens axicon

A method is presented for generation of a sub wavelength (0.45λ) longitudinally polarized beam, which propagates without divergence over lengths of about 8λ in free space. This is achieved by tight focusing of double ring shaped radially polarized beam with a high NA lens axicon that utilizes spherical aberration to duplicate the performance of an axicon and to create an extended focal line. The intensity distributions were calculated based on the vector diffraction theory and it was observed that in the case of high numerical aperture (NA) lens axicon, the distribution of the total intensity near the focus had little effect on the degree of truncation of the incident beam by the pupil.     

一种具有Luneburg透镜特性的轴向GRIN介质透镜

本文给出一种轴向GRIN(梯度折射率)介质透镜。这种透镜具有 Luneburg(卢内堡)透镜的特性。它可以使无限远光线锐成象;亦可用于点—点锐成象系统,光准直或光准直—聚焦系统;在微波频谱区域及有声成象、天线设计方面有一定应用价值。     

梯度折射率球透镜的制备及其光线轨迹测试

自麦克斯韦鱼眼透镜理论模型提出后,长期以来学术界一直以为它只是一种绝对光学仪器,在实践中并没有应用的可能。但通过对麦克斯韦鱼眼微球透镜的理论研究表明,在一定条件下,它具有良好的成像性能和耦合效率。根据菲克定律推导出梯度折射率球透镜的折射率分布函数。并且熔制了含Li+硅酸盐玻璃和采用槽沉法以及Na+/Li+离子交换法制备直径为0.3—3.0mm的梯度折射率球透镜。通过干涉法测得了梯度折射率球透镜的折射率分布曲线,并研究了光线通过梯度折射率球透镜的轨迹。研究结果表明:在590℃,离子扩散系数为3.07×10-6mm2/s;所制备的梯度折射率球透镜的折射率分布是抛物线分布,并且和理论分析相吻合;梯度折射率球透镜的光线轨迹满足椭圆方程。     

Generation of sub wavelength focal spot with large depth of focus generated by radially polarized beam

We investigate the focusing properties of a radially polarized Bessel Gaussian beam by a high numerical aperture (NA) lens based on vector diffraction theory. We observe that our proposed system generates a sub wavelength focal spot of 0.42λ having large uniform focal depth of 6.45λ. The authors expect such a long depth of focus have great potential for use in optical, biological, high-resolution and atmospheric sciences.     

Wavelength dependence of focusing properties of two-dimensional photonic quasicrystal flat lens

We investigated the wavelength dependence of the focusing properties of a germanium-cylinder-based two-dimensional (2D) decagonal Penrose-type photonic quasicrystal (PQC) flat lens for the first time, to the best of our knowledge. We found that near the second bandgap and in the high-frequency side (between the bandgap boundary and the first light intensity peak) of the pass band, the flat lens can exhibit a focusing effect for a point light source and that the focusing wavelengths can directly be drawn from the photonic band structure. For all the focusing wavelengths, the summation of the object distance and the image distance is less than the thickness of the flat lens when the object distance is half the thickness of the flat lens. As the wavelength increases, the image distance, the image quality, and the effective refractive index of the flat lens increase, whereas the image power of the point light source decreases. The effective refractive index of the flat lens is less than -1.     

Tight focus of an azimuthally polarized and amplitude-modulated annular multi-Gaussian beam

We investigate the focusing properties of an azimuthally polarized and amplitude modulated annular multi Gaussian beam by a high numerical aperture (NA) lens based on vector diffraction theory. We observe that our proposed system generates a subwavelength focal hole of 0.46λ having large uniform focal depth of 36λ without any annular obstruction. This kind of nondiffracting focal hole is called dark channel, which may have applications in atom optical experiments, such as with atomic lenses, atom traps, and atom switches.