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。     

Fabrication of gradient refractive index ball lenses

The theoretical model of the Maxwell fish eye sphere lens has long been regarded as an absolute optical instrument without practical application since it was proposed. But the study on the theory of Maxwell fish eye micro-spherical lens shows that at certain condition it has fine image formation ability and coupling efficiency. Based on the Fick's diffusion equations, the distribution function of refractive index of gradient refractive index (GRIN) ball lenses is derived. Lithium-containing silicate glass is fabricated and GRIN ball lenses whose diameters are from 0.3 to 3.0 mm are made by ion exchange and the sagging method in sodium nitrate. Radial refractive index profiles of these GRIN ball lens are measured by interferometer. Results show that the distribution of the index of refraction is a parabolic curve and in concordance with the computational consequence and its Δn is 0.0002.     

Efficient coupling and relaxed alignment tolerances in pigtailing of a laser diode using dual ball lenses

In this paper, we report an efficient coupling scheme with relaxed misalignment tolerances. The proposed coupling scheme consists of two ball lenses of same diameter (1 mm) and different refractive indices. The second ball lens which is facing the fiber tip has a higher refractive index (1.833), whereas the first one which faces the laser diode has a refractive index of 1.5. Employing Gaussian and ABCD ray tracing optics, the theoretically obtained coupling efficiency can reach a unity with relaxed working distance (separation of the coupling system from the fiber tip) in the range between 1 and 4 mm at some optimum positions of the coupling lenses with regard to each other and to the facet of the laser diode. It has been found that if the distance between the first ball lens and the laser diode (d₁) is fixed at 1.1 mm, which is twice its focal length, the coupling efficiency and the working distance as well as the misalignment tolerances are greatly affected by variation of the separation between the two ball lenses (s), and for this proposed coupling scheme the highest coupling efficiency and largest working distance are obtained when s is in the range of 0.3-0.35 mm. Above and below this range there is a significant reduction in the values of the above-mentioned parameters. Experimentally, the Nd:YAG laser welding system has been used for the alignment and welding of the coupling components in a butterfly configuration; the experimentally obtained coupling efficiency of the proposed coupling system was around 75% with relaxed working distance. From the effect of lateral and angular offsets on coupling efficiency, it is clearly noticed that the mode field of laser diode is transformed from elliptical into circular and hence effectively matched with that of the single-mode fiber.     

Crossover interconnects in gradient-index planar optics

The point spread function (PSF) in gradient-index planar optics for implementation of crossover interconnects is studied. Gradient-index (GRIN) planar optics is made with refractive substrate providing a smart optical diffraction-limited imaging. We use as a figure of merit the space-bandwidth product (SBP) of the planar imaging system in order to estimate the number of data channels which can be handled in crossover interconnects. For a selfoc semirod-lens of 3 mm diameter, a crossover network configuration of 703 × 703 channels can be designed.     

Full-field measurement of surface reflectivity using a microscopy for refractive index profiling of GRIN lenses

This paper outlines an improved technique for profiling the refractive index of Graded-index (GRIN) lenses based on the measurements obtained from a reflectivity image. Reflective cross-sectional image of the GRIN lens were compared with a reflectance reference target under illumination at small incidence angles to obtain the full-field refractive index distribution of the GRIN lens quickly and easily.     

Design and fabrication of long focal length microlens arrays

In this paper, we present microlens arrays (MLA) with long focal length (in millimeter range) based on thermal reflow process. The focal length of microlens is usually in the same order of lens diameter or several hundred microns. To extend focal length, we made a photoresist (SU-8) MLA covered by a Polydimethylsiloxane (PDMS) film on a glass substrate. Because the refractive index difference between PDMS and photoresist interface is lower than that of air and MLA interface, light is less bended when passing through MLA and is focused at longer distance. Microlenses of diameters from 50 μm to 240 μm were successfully fabricated. The longest focal length was 2.1 mm from the microlens of 240 μm diameter. The numerical aperture (NA) was reduced 0.06, which is much lower than the smallest NA (~ 0.15) by regular thermal reflow processes. Cured PDMS has high transmittance and becomes parts of MLA without too much optical power loss. Besides, other focal lengths can be realized by modifying the refractive index different between two adjacent materials as described in this paper.     

Comparison of subwavelength focusing properties of diffraction and Fresnel zone plate plasmonic planar lenses

The subwavelength focusing properties of diffractive plasmonic planar lenses (DPLs) and Fresnel zone plate plasmonic planar lenses (FZPs) have been compared in this paper. To that end, we use the same lens material, incident wavelength, thickness and focal length for comparison. Both DPLs and FZPs consist of central circular slits surrounded by transparent and opaque zones and can get clear focusing performances. By using the rigorous electromagnetic numerical method, the fields in the focal region are analyzed in detail, and our results demonstrate that FZP can generate higher transmission efficiency, and higher peak field intensity at the focal plane. Focusing polarization properties of the lens illuminated by linearly polarized state, are calculated and analyzed also. The numerical results show that both the DPL and the FZP produce asymmetrical focal spot distributions with a low f-number. To the FZP, the full-width at half-maximum (FWHM) varies from 256 nm (along y-axis) to 516 nm(along x-axis) and to the DPL, the FWHM varies from 256 nm(along y-axis) to 580 nm(along x-axis), respectively. But for a high f-number, the asymmetrical performance of the focal spot will be reduced due to complicated electromagnetical field interferences and micro waveguide effect. Otherwise, the DPL can get a higher depolarization effect than the FZP does.     

Measuring optical properties of an eye lens using magnetic resonance imaging

We compare the focal lengths of porcine lenses measured optically and by using a novel MRI technique. The geometric properties of the lenses were also measured and compared. The MRI technique exploits the dependence of both the lens refractive index and relaxation rates on the local protein concentration. By measuring the refractive index and corresponding values of R2 (=1/T2) for samples of lens homogenates with different protein concentrations, the dependence of refractive index on R2 was determined empirically. R2 maps, constructed from monoexponential fits to multiecho images of a slice through the lens containing the optical axis, were converted to refractive index maps using this relationship. A simulated ray trace through the refractive index map provided an estimate of lens focal length that was compared to a direct optical measurement of focal length using a laser ray-tracing method. It was found that the mean focal lengths estimated from the two techniques agreed within experimental uncertainty. The refractive index profile along the optical axis was found to be well described by a simple function of the form n=n0 + n1 x ra where r is the (normalized) lens radius.     

Characterization of optical waveguide in Nd: GdVO4 by triple-energy oxygen ion implantation

We report on the optical planar waveguide formation and modal characterization in Nd: GdVO₄ crystals by triple oxygen ion implantation at energies of (2.4, 3.0, and 3.6 MeV) and fluences of (1.4, 1.4, and 3.1)  × 10¹⁴ions/cm². The prism-coupling method is used to investigate the dark-mode property at wavelength of 632.8 nm. The refractive index profiles of the waveguide are reconstructed by an effective refractive index, n_eff method. The modal analysis shows that the fields of TE modes are well restricted in the guiding region, which means the formation of nonleaky waveguide in the crystal.     

Effects of measurement errors on refractive outcomes for pseudophakic eye based on eye model

With the Gullstrand-Le Grand eye model, the effects of various measurement errors on refractive outcomes for pseudophakic eye are studied. An equation to calculate the postoperative refractive error for pseudophakic eyes is derived. The accuracy to get a refractive error less than ca. 25 D is ±0.1 mm for the axial length, ±0.03 mm for the radius of the corneal anterior surface, ±0.12 D for the corneal power and ±0.16 mm for the postoperative anterior chamber depth (ACD). An error of 1 D in intraocular lens (IOL) power leads to a postoperative refractive error of −0.69 D. K-reading leads to a postoperative hyperopia from 0.18 to 0.74 D for eye with different refractive errors previously corrected. The constant velocity in ultrasound biometry assumption overestimates the axial length from 0.17 to 0.31 mm with actual axial length ranging from 21.31 to 32.31 mm. Errors in axial length, corneal power or radius of the corneal anterior surface and postoperative ACD play critical roles in determining the refractive outcomes. The constant-velocity assumption tends to overestimate the axial length. The change of the ratio of corneal anterior to the posterior surface is of minor importance for the overestimation of K-reading.     

Simultaneous measurement of refractive index and temperature using dual-period grapefruit microstructured fiber grating

By cascading the long period fiber grating (LPFG) and fiber Bragg grating (FBG) in grapefruit microstructured fiber, a novel dual-period fiber grating sensor is proposed. The refractive index and temperature are measured simultaneously by using the different sensitivity of FBG and LPFG. The relationship between dual-period fiber grating transmission spectrum and refractive index, resonant wavelengths and temperature are analyzed theoretically, respectively. The simulation results show that the accuracy of the sensor in measuring refractive index and temperature is estimated to be 2319.6 nm/RIU in a range from 1.33 to 1.36 and 0.017 nm/°C from 0 °C to 100 °C, respectively. Thus, the sensor has high refractive index sensitivity, and can provide the theoretical foundation for the optical fiber biosensor.     

Prediction of negative index material lenses based on metallo‐dielectric nanotubes

We propose to assemble negative index materials (NIMs) from dielectric nanotubes with inner and outer surfaces covered by thin metallic films. The focusing properties of flat and concave lenses assembled from metallized titania nanotubes are compared with those of lenses made from nanorods with the refractive index n = –1 by performing numerical calculations using a multiple‐scattering approach. Focusing is proved for both types of lenses, however, the focusing properties of concave lenses are better. The lenses are shown to be tolerant to the introduction of disorder in the arrangement of nanotubes. Moreover, the disorder proves to improve the quality of the focal spot. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Performance evaluation of GRIN lenses by ray tracing method

Plastic gradient-index lenses produce clear images with negligible aberration and distortion. One of the methods for fabricating these lenses involves pulling up the core fiber vertically from a polymer solution whose refractive index has been adjusted to the desired value. Since the molecules from the solution diffuse into the inner layer, the monomer components are distributed in the radial direction. The monomer distribution is fixed in the photopolymerization process, and this forming process is repeated several times with adjusting the composition of the solution; hence, a specific refractive index distribution is obtained. We considered a numerical model of the interdiffusion process and analyzed refractive index distribution that could well reproduce the experimental results. Moreover, we employed the ray tracing method to calculate the modulation transfer function and used the transfer function to evaluate the GRIN lens performance. Simulation results showed that our evaluation method well duplicates the experimental results. We thus developed an integrated simulation method for the fabrication and performance evaluation of GRIN lenses.     

梯度折射率透镜在口腔内窥镜中的设计与应用

作为口腔内窥镜的摄像镜头，利用梯度折射率透镜质量轻、体积小、结构简单、分辨率高、成像景深大的优点，研制出一套适合医患交流及进行口腔检查与治疗的医疗装置。采用修正折射率剖面的梯度折射率透镜, 降低系统渐晕，减小畸变,获取口腔内部图像，经CCD光电转换装置转换成电信号，再将电信号经过数字信号处理以后，将该数字信息存储于计算机内部或在显示器上显示出来。口腔内窥镜是集梯度折射率透镜、光学原理、光学材料与加工、微电子、数字成像技术等为一体的新型医疗设备。特别是采用经修正的梯度折射率透镜制造的口腔内窥镜成像清晰, 在图像畸变、景深等方面优于现有产品，而且便于对患者的各种信息进行管理、查询、输出等。     

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.     

Array of femtosecond plasma channels in fused silica

We have shown experimentally and confirmed by means of full dimensional (3D + 1) numerical simulations, the possibility to create an array of refractive index modification zones inside a fused silica sample using a 43 fs, 2 mJ, 800 nm laser pulse and a periodic mesh introduced in front of the sample. Robust filaments and the corresponding refractive index modification zones preserve their transverse positions for more than 10 Rayleigh lengths (∼500 μm). Numerical simulations prove that each mesh unit is an independent source of the background energy for a filament formed within this unit. The effect of the simultaneous formation of many extended periodically spaced filaments can be used to accelerate the fabrication of microoptics devices.     

Low-dispersion characteristics of silica-based graded refractive index lens for laser display optical system

We report the characteristics of silica-based graded refractive index lens fabricated by sol-gel method. Lens diameter is precisely controlled to be 125 ??m ± 0:5 ??m. Chromatic dispersion is defined as the difference of refractive index distribution coefficient, and concluded to be sufficiently low against ordinary achromatic lenses. We also calculated the difference of focal distance among RGB wavelengths, the difference was from 25 to 35 ??m almost regardless of the lens length. Divergence angle dispersion was suppressed less than 10 per cent, demonstrating excellent achromaticity for raster-scanning laser display devices.     

1 × 4 coupler based on all solid five-core photonic crystal fibers

An improved 1 × 4 coupler based on all solid multi-core photonic crystal fiber is proposed and analyzed. The expressions to calculate the coupling length and the coupling efficiency are deduced based on the coupled-mode equations firstly. Then a full-vector finite element method (FEM) is used to calculate the coupling length and the coupling efficiency. Next, the propagation characteristics and the performances of the coupler are analyzed through using a full vector beam propagation method (BPM). Research shows that the results derived by FEM agree with that by BPM. The coupling length of the coupler is 4.1 mm at λ = 1.55 μm. A maximum coupling efficiency of 24.96% can be obtained. The coupling ratio is more than 22.5% over a wavelength range of 100 nm. The polarization-dependent loss at λ = 1.55 μm is equal to 0.73 dB. Finally, the influences of the micro-variation of structure parameters and the material refractive index on the working performances of the coupler are investigated.     

大孔径变焦投影镜头设计

为了实现某一大孔径定焦投影镜头作为初始结构, 经过优化设计后成为大孔径变焦投影镜头, 根据设计目标的DMD对角线尺寸, 利用AUTOCAD对选择的定焦距系统的初始结构尺寸进行测绘, 初步选择各镜材料, 规划成5组元变焦系统, 利用各种操作数对镜头的基本参数和外形尺寸进行限制, 并合理利用2个非球面, 在光学设计软件Zemax与CODE V中往返优化, 得到一款在可见光波段内, 短焦距为14.61 mm、视场角为60°、F数为1.5, 长焦距为29.31 mm、视场角为30°、F数为1.6的变焦投影镜头。设计结果表明:各视场的传递函数(MTF)值在截至频率60 lp/mm处不低于0.46, 各焦距处的弥散角不超出1.6', 镜头具有良好的像质。该镜头系统由11块透镜和1块平行平板组成, 其中透镜2使用了非球面镜, 该镜头片数较少, 透镜折射率不高, 材料容易选择。