Towards focusing using photonic crystal flat lens

We report on the numerical simulation and fabrication of a two-dimensional flat lens based on negative refraction in photonic crystals. The slab acting as a lens is made of an hole array (operating at the wavelength of 1.5 μm) etched in a InP/InGaAsP/InP semiconductor layer. We first study the key issues for the achievement of a negative refractive index taking advantage of folding of dispersion branches with main emphasis in dispersion properties rather than the opening of forbidden gaps. The diffraction and refraction regimes are analysed according to the comparison of the wave-vector with respect to the relevant dimensions of the hole array. In the second stage, we illustrate technological challenges in terms of e-beam lithography on a sub-micron scale and deep reactive ion etching for an indium phosphide based technology.     

Influence of the refractive index and dispersion of spectacle lens on its imaging properties

The paper shows an influence of the refractive index and dispersion of the spectacle lens on its imaging properties. Relations are presented for calculation of radii of curvature of anastigmatic spectacle lenses and their chromatic aberration. Moreover, the formulas are derived for calculation of the change of astigmatism of spectacle lens due to dispersion of spectacle lens material.     

Design of liquid-glass achromatic zoom lens

Optical liquids are ideal materials for designing apochromatic lens due to their lower refractive index and higher Abbe numbers than those of the ordinary optical glasses. Based on the Buchdahl dispersion formula, the dispersion coefficient diagram of liquids and glasses is established. The liquid-glass combination lens(LGCL) with small secondary spectrum is obtained by calculating the combination structure with low dispersion liquid and glasses. The initial optical structure of the liquid-glass apochromatic lens(LGAL) can be obtained by replacing two glass lenses in an initial optical system with the LGCL. Using the multi-configuration optimization of ZEMAX, the liquid-glass achromatic zoom lens (LGAZL) can be designed by optimizing the LGAL. The LGAZL has an objective field of view ?63 mm–?57 mm, an image field of view 8 mm, a working distance 240 mm and the zoom range of focal length 75–85 mm. The chromatic aberration and the secondary spectrum of the LGAZL are all less than 3 μm in the whole zoom range.     

一种无损检测眼镜镜片折射率的方法

提出了一种无损检测眼镜镜片基底折射率的方法。该方法通过测量眼镜镜片在可见光区域内的反射比数据,采用高斯牛顿迭代法拟合反射比曲线来检测镜片基底折射率,并用Cauchy模型分析了镜片折射率的色散现象。检测结果表明,镜片折射率的相对误差不超过2%,可基本满足对镜片折射率区间的判定。     

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.     

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.     

Direct measurement of group dispersion of optical components using white-light spectral interferometry

We present a simple white-light spectral interferometric technique employing a low-resolution spectrometer for a direct measurement of the group dispersion of optical components over a wide wavelength range. The technique utilizes an unbalanced Mach-Zehnder interferometer with a component under test inserted in one arm and the other arm with adjustable path length. We record a series of spectral interferograms to measure the equalization wavelength as a function of the path length difference. We measure the absolute group refractive index as a function of wavelength for a quartz crystal of known thickness and the relative one for optical fiber. In the latter case we use a microscope objective in front and a lens behind the fiber and subtract their group dispersion, which is measured by a technique of tandem interferometry including also a Michelson interferometer.     

基于偏振衍射色散共焦的光学元件轴向间距测量

光学元件轴向间距测量对精密光学系统的定位和装调具有重要意义。针对现有色散共焦测量系统中色散物镜结构复杂、色散范围小的问题,提出基于偏振衍射色散共焦的光学元件轴向间距测量方法,将传统折射共焦镜头几百毫米的轴向尺寸和复杂的装调需求简化为数毫米的单片镜,简化了系统结构。透镜间距和厚度测量实验表明,间距测量误差为10 μm。     

单轴晶体中的负折射现象研究

分析了在各向同性介质和单轴晶体界面实现负折射的最佳条件。计算发现,通过调节光轴角和各向异性参量可以使得负折射现象更为明显,获得最佳光轴角和最大入射临界角。各向异性强的晶体实现负折射的入射角范围可能会很大。讨论了单轴晶体中和负折射率介质中的负折射现象的区别：负折射率介质中的负折射是由负的折射率引起的,单轴晶体中是由于各向异性决定的。同时还发现单轴晶体中的能流负折射现象不能实现Pendry在理论上所预言的完美透镜。     

基于Zemax的He-Ne激光光束聚焦物镜的设计

 为了得到一个合理的He-Ne激光光束聚焦物镜,采用以正前凸型为基础的高折射率双片结构,应用Zemax软件进行优化设计,获得了弥散斑直径为0.002mm的He-Ne激光聚焦物镜,该镜头只需校正轴上点球差。实验结果表明：设计的镜头比低折射率单片透镜得到的弥散圆直径更小,达到0.0019mm,球差被控制在-0.05mm～+0.05mm范围内,MTF曲线所围面积变大,中心点亮度增高,符合实际需要。     

衍射光学透镜色散特性的仿真研究

在白光照射下,衍射光学透镜的焦距不仅同材料色散和波长色散有关,而且还同孔径因子有关。基于折射率随波长变化的经验公式,利用自编的仿真计算程序包,得到了透镜焦距、材料色散、波长色散、孔径因子之间的关系曲线。所获得的理论分析和仿真计算结果为进一步设计消色差的纯衍射目视光学系统提供了理论依据,具有一定的指导意义。     

麦克斯韦鱼眼球透镜的一种复合结构

麦克斯韦鱼眼球形透镜对近距物点以最小像差成像时，往往要求较大的折射率差值△ｎ￣［１］，目前的离子交换制作工艺尚难达此技术水平。为解决此困难，本文提出将此类球透镜置于低折射率均匀介质内组成复合结构，可在保持最小像差的提前下，大幅度减小其对折射率的差值△ｎ的要求。     

All angle negative refraction with the effective phase index of-1

We theoretically studied a left-hand structure based on a two-dimensional (2D) photonic crystal (PC)with a negative refractive index. The propagation of electromagnetic waves in the proposed PC structure is investigated through dispersion characteristic analysis and numerical simulation of field pattern. The designed PC structure can exhibit all angle negative refraction, and the corresponding effective refractive indices along all directions are almost same and close to the ideal value of -1. A flat lens formed from such a PC has been designed and its imaging properties have been investigated systematically.     

Preparation and study of microstructures, optical properties and oscillator parameters of titanium (IV) oxide (TiO2) film

In this study, Titanium (IV) Oxide (TiO₂) film has been prepared and characterized by X-ray diffraction (XRD). The XRD pattern of TiO₂ film of anatase phase exhibit very sharp peaks at 25° and 47.85°. According to Scherrer??s formula the grain size of anatase (101) phase TiO₂ nananoparticle is 38.5 nm. The optical properties and constants of TiO₂ film of thickness (4 ??m) have been investigated at room temperature. The transmittance, reflectance and absorbance spectra are measured in the wavelength range (340?C900 nm). Optical constants of TiO₂ film are derived from the transmission spectra and the refractive index dispersion of the film. The oscillator energy, E ₀ dispersion energy, E _d , the static refractive index, n ₀, and other parameters have been determined by the single oscillator Wemple-DiDomenico method. This film can be used in the form of thin film in dye-sensitized solar cells.     

A desktop X‐ray monochromator for synchrotron radiation based on refraction in mosaic prism lenses

Focusing planar refractive mosaic lenses based on triangular prism microstructures have been used as an alternative approach for wide‐bandpass monochromatization of high‐energy X‐rays. The strong energy dependence of the refractive index of the lens material leads to an analogous energy dependence of the focal length of the lens. The refractive mosaic lens, in comparison with the refractive lens of continuous parabolic profile, is characterized by a higher aperture because of reduced passive material. In combination with a well defined pinhole aperture in the focal plane, the transmittance of photons of an appropriate energy can be relatively high and photons of deviating energy can be efficiently suppressed. The photon energy can be tuned by translating the pinhole along the optical axis, and the bandwidth changed by selecting appropriate pinhole aperture and beam stop. This method of monochromatization was realised at the ANKA FLUO beamline using a mosaic lens together with a 20 µm pinhole and beam stop. An energy resolution of 2.0% at 16 keV has been achieved.     

Graded-index time-lens implementation

The propagation of a laser pulse in a graded-index (GRIN) space lens and in an electro-optic crystal with an appropriate refractive index modulation is studied. It is shown that the crystal functions as a GRIN time lens if the propagation's second-order dispersion is included and if the phase velocity of the modulating wave equals the group velocity of the laser pulse.     

Achromatic doublets using group indices of refraction

One main function of short pulses is to concentrate energy in time and space [1]. The use of refractive lenses allows us to concentrate energy in a small volume of focusing around the focal point of the lens. When using refractive lenses, there are three effects that affect the concentration of energy around the focal point of the lens. These are the group velocity dispersion (GVD), the propagation time difference (PTD), and the aberrations of the lens. In this paper, we study lenses which are diffraction limited so that the monochromatic aberrations are negligible; the group velocity dispersion and the propagation time difference are the main effects affecting the spreading of the pulse at the focus. We will show that for 100-fs pulses the spatial spreading is larger than the temporal spreading of the pulse. It is already known that the effect of spatial spreading of the pulse due to PTD can be reduced by using achromatic optics. We use the theory proposed by A. Vaughan to analyze simple lenses and normal achromatic doublets, where normal means doublets that we can buy from catalogs. We then use the Vaughan theory to design achromatic doublets in phase and group, which produce no spatial spreading of the pulse, i.e., PTD = 0, when the doublet is designed for the carrier of the pulse. We compare these phase and group achromatic doublets with normal achromatic doublets. Finally, we show that apochromatic optics can give a much better correction of PTD than using normal achromatic doublets.     

Dispersion characteristics of complex refractive-index planar slab optical waveguide by using finite element method

In this paper, finite element method (FEM) mode analyses of planar slab optical waveguide having complicated refractive index profile are presented. We try to estimate the dispersion graph, mode cut-off condition, group delay and waveguide dispersion for the case of α-power and chirped-type refractive index profile. In order to obtain the more accurate result, we have derived the higher-order polynomial, which establishes the suitable relationship between b and V for different profile of optical waveguide. On the basis of the derived polynomials, the waveguide dispersion is analyzed for different type of refractive index profile waveguide. Our study shows that the waveguide dispersion can be substantially reduced when we deployed the optical waveguide having linearly chirped-type refractive index profile. Earlier too, the arbitrary refractive index profile has been analyzed but to the best of our knowledge chirped-type refractive index profile has not been analyzed till date for the case of planar slab optical waveguide.     

Measurement of gradient refractive index profile of crystalline lens of fisheye in vivo using optical coherence tomography

We report the use of optical coherence tomography (OCT) for noninvasive measurement of the refractive index profile of a crystalline lens of a fisheye. The approach exploits the fact that OCT provides a direct measurement of the optical path of the light traveled through the medium. The gradient refractive index profile for the crystalline lens was retrieved by iterative fitting of the optical path calculated by the ray tracing method with that experimentally measured using OCT. The estimated error in refractive index is approximately 1%. The measured gradient refractive index and Matthiessen’s ratio (ratio of focal length to lens radius) are in good agreement with the previously reported values. PACS 42.62.Be; 42.30.-d; 42.30.Wb; 07.60.Vg     

Chromatic dispersion behavior of Si-NC-Er doped optical fiber

The chromatic dispersion for conventional and Er-doped fibers using the refractive index approximation is examined. A first, analytical method for investigation of dispersion in step index triple clad optical fiber is used. To design of zero-dispersion shifted fiber for optical communication purpose manipulation of the refractive index and radius of the core are considered. We show that in presence of the Si-NC-Er ions, zero-dispersion wavelength is displaced and the dispersion quantity is increased. In this work, we try to optimize system parameters to obtain minimum dispersion and dispersion shifted fiber with control of the doping levels of Er ions and Si-NC as well as doping profiles. For especial case, we assumed the Gaussian inhomogeneous core refractive index for zero-dispersion wavelength and dispersion managements.