Determination of the refractive index profile of polymer optical fiber preform by the transverse ray tracing method

In graded-index polymer optical fiber (GI-POF), the refractive index profile is an important parameter in defining its bandwidth. However, direct determination of the refractive index profile of GI-POF is difficult due to its extreme thinness. In this study, the refractive index distribution of the GI-POF is indirectly determined by measuring the refractive index distribution of the GI-POF perform by applying the transverse ray tracing method to a simplified measurement system that we developed.In this system, a parallel tabular ray is irradiated transversely to a GI-POF preform. The transverse ray from the preform is then projected on a screen, and its digital image is processed to calculate the refractive index distribution. The calculation is based on a transverse ray simulation, a computer program that we developed in which the refractive index distribution of the preform is determined by comparing the displacement of the transverse ray projected on the screen with the actual measurement.The accuracy of this new measurement method is validated by comparing the refractive index distribution of a GI-POF preform with the refractive index distribution measured by the conventional method using an interferometer. We find that the refractive index distribution measured by this novel method agrees well with that measured by the conventional method.     

套管辅助法测量异型预制棒折射率分布

基于光束扫描法的光纤预制棒折射率测试仪主要适用于直径和长度在一定范围内的圆柱形样品折射率分布的测试。提出一种套管辅助法可实现更短长度、更细直径和变直径样品的折射率测试。该方法将待测样品居中放置于一个尺寸符合测试要求的圆柱形套管内,并在套管内注入折射率匹配油,使其没过待测样品后按常规步骤进行测试。对比实验结果表明,套管辅助法与直接测量法的偏差与仪器的测量误差相当。采用套管法,获得了预制棒拉丝终止后变径区不同位置折射率的径向分布,可为拉丝过程的研究提供参考。     

Study on measurement of refractive index profile of GI-POF by light scattering

This paper is devoted to the study on measurement of refractive index profile of graded-index polymer optical fiber (GI-POF) by light scattering. Using Generalized Airy theory and Debye series of an inhomogeneous cylinder, the scattering intensity distributions are obtained of Airy structure of rainbows for different refractive index profile. The results show that positions of Airy peaks depend closely on refractive index profile of GI-POF. Since each order of rainbow penetrates it to different depths, such methods could be used to provide information of the refractive index profile of GI-POF. For GI-POF with given diameter, positions of Airy peaks of rainbows are simulated as a function of refractive index profile, which can be used to inverse unknown parameters of refractive index profile. The least square method is used in inversion of refractive index profile with the given refractive index of the cladding. The results obtained agree with theoretical values with high precision. The method has the advantages of non-instructive and on-line measurement, and can be used for the measurement of other inhomogeneous droplets.     

一种动-静态光散射颗粒折射率测量法

提出一种动静态光散射颗粒折射率测量方法.该方法分为三部分,一部分是用动态光散射技术测得颗粒样品的线宽分布函数,然后将此线宽分布连同一组折射率值代入静态光散射公式推算出不同折射率值下的散射光强空间分布;第二部分是用光电探测器测出实际的散射光空间分布;第三部分是将不同折射率下的推算值与实测值做均方偏差运算以做比较,取均方偏差最小时所对应的代入折射率值作为颗粒折射率的最终测量值.此方法对样品的分散度无要求,适用于微米到亚微米级的颗粒物.     

K-Na离子交换单模平面波导的制备及其表征

通过K-Na离子交换技术制备了多模玻璃平面波导.采用棱镜耦合技术测量了波导的有效折射率,用IWKB方法拟合得到K-Na离子交换波导的折射率分布符合高斯分布,由色散曲线得到单模波导的制备条件(即扩散深度范围),从而得出单模波导的离子交换时间范围,制备出单模波导,并通过求解WKB色散方程得出单模波导的表面折射率.用普通数码相机,通过对离子交换平面玻璃光波导传输线进行数字成像,根据传输线上的光强分布拟合出光强传输衰减曲线,计算出单模波导的传输损耗大约为0.4 dB/cm.     

On the derivation of vector radiative transfer equation for polarized radiative transport in graded index media

Light transport in graded index media follows a curved trajectory determined by Fermat's principle. Besides the effect of variation of the refractive index on the transport of radiative intensity, the curved ray trajectory will induce geometrical effects on the transport of polarization ellipse. This paper presents a complete derivation of vector radiative transfer equation for polarized radiation transport in absorption, emission and scattering graded index media. The derivation is based on the analysis of the conserved quantities for polarized light transport along curved trajectory and a novel approach. The obtained transfer equation can be considered as a generalization of the classic vector radiative transfer equation that is only valid for uniform refractive index media. Several variant forms of the transport equation are also presented, which include the form for Stokes parameters defined with a fixed reference and the Eulerian forms in the ray coordinate and in several common orthogonal coordinate systems.     

Fluorescence characterization and gain studies on a dye-doped graded index polymer optical-fiber preform

Preparation of an appropriate optical-fiber preform is vital for the fabrication of graded-index polymer optical fibers (GIPOF), which are considered to be a good choice for providing inexpensive high bandwidth data links, for local area networks and telecommunication applications. Recent development of the interfacial gel polymerization technique has caused a dramatic reduction in the total attenuation in GIPOF, and this is one of the potential methods to prepare fiber preforms for the fabrication of dye-doped polymer-fiber amplifiers. In this paper, the preparation of a dye-doped graded-index poly(methyl methacrylate) (PMMA) rod by the interfacial gel polymerization method using a PMMA tube is reported. An organic compound of high-refractive index, viz., diphenyl phthalate (DPP), was used to obtain a graded-index distribution, and Rhodamine B (Rh B), was used to dope the PMMA rod. The refractive index profile of the rod was measured using an interferometric technique and the index exponent was estimated. The single pass gain of the rod was measured at a pump wavelength of 532 nm. The extent of doping of the Rh B in the preform was studied by axially exciting a thin slice of the rod with white light and measuring the spatial variation of the fluorescence intensity across the sample.     

一种简单精准的渐变折射率分布光波导分析方法

渐变折射率分布的光波导分析对光波导器件的设计和研究至关重要, 近年来已提出了多种分析方法, 然而在简便性或准确性上都存在着不足. 为此, 提出了一种分析渐变折射率分布光波导的方法, 能够结合现有的Wentzel-Kramers-Brillouin近似法和离散化的波动方程, 构建模场分布, 再结合变分运算方程和修正的模式本征方程, 计算出较为精确的有效折射率. 与其他分析方法相比, 该方法较为简单, 而且有一定的精度.     

掩埋型离子交换玻璃光波导的变分分析

用变分法对离子交换法制备的掺铒光波导的传播特性进行了分析,推导出了适用于掩埋型离子交换玻璃沟道光波导中场分布传播常量的变分表达式,构建了场分布的厄米-高斯型试探解,在两种不同实验条件下,采用变分法确定了试探解中的待定参量,获得光波导中的场分布,利用传播常量的变分公式和已确定的场分布计算得到了传播常量和有效折射率。计算数据表明:导波区域的有效折射率稍稍地大于限制层的折射率,说明离子交换法制备的波导器件是弱波导;高的辅助退火电场强度和适当的退火时间下,所制备的光波导可以支持更多光模式的传输。该方法计算过程简洁、快速,计算结果与实验结果吻合。     

On rainbows of inhomogeneous spherical droplets

The paper is devoted to the study of the intensity distributions and the angular spectra of the second and fifth rainbows of homogeneous and inhomogeneous spherical particles predicted by Lorenz-Mie theory. The results show that the distribution around the second rainbow angle for a homogeneous sphere of refractive index between 1.32 and 1.33 is due to the interference of the light after two or five internal reflections. The structure of the scattering diagram and the angular spectrum for homogeneous and radially inhomogeneous spheres are studied. For a homogeneous sphere we show that the second and fifth rainbows can be independently reconstructed by filtering the calculated spectrum. Since each order of rainbow penetrates the particle to different depths, such methods could be used to provide information about the refractive index profile or the temperature gradient of an inhomogeneous sphere. The Airy-like peaks of the second and fifth rainbows are closely connected with the refractive index profile, which is beneficial to the measurement of its refractive index profile or temperature gradient.     

Mode field distribution of an integrated-optical waveguide generated by UV-laser radiation at the surface of a planar polymer chip

An integrated-optical strip-waveguide is directly written into the surface of a planar polymer substrate by an excimer laser beam. The mode field distribution, the surface refractive index and the refractive index depth profile of the waveguide have been examined. The intensity distribution of the mode field strongly depends on the refractive index depth profile, on the light coupling conditions and on the waveguide fabrication process parameters.     

Refractive index profiling of a GRIN optical fiber using a modulated speckled sheet of light

A method for calculating the refractive index of GRIN optical fiber from its transverse interference pattern is presented.In this method the transverse interference fringe pattern through an optical fiber using a sheet of light is applied to get the refractive index profile of it. The optical fiber is not immersed in a matching liquid as used in different techniques [Barakat N, El-Hennawi HA, El-Zaiat SY, Hassan R. Pure Appl Opt 1996;5:27].In this method a sheet of He–Ne laser light is allowed to illuminate the fiber. The light sheet is divided into two parts, the first is refracted through the fiber while the second is used as a reference beam. Interference pattern will be obtained between these two rays displaying the refractive index variation along the fiber radius.The fringe shift of such interference pattern has been measured and used to calculate the deflection angle of light refracted by the fiber and the cladding. An equation is derived to calculate the refractive index profile difference ratio δn at different positions across the fiber cross section in terms of the corresponding deflection angle and is verified experimentally.The optical path difference between these two rays (refracted and reference beam divided by the fiber) has been derived and the fringe shift obtained has been used to calculate the refractive index profile of the fiber.Introducing a ground glass screen on the passage of the two light beams (refracted and reference beam divided by the fiber), two superimposed identical speckle patterns are formed leading to the formation of a third speckle pattern modulated by a grid structure displaying the optical thickness of the fiber.     

Nondestructive index profile measurement of noncircular optical fibre preforms

We present quantitative results for the effect of noncircularity on a method recently proposed by Chu for the measurement of the refractive index profile of an optical fibre preform. Analytical studies show how Chu's method can be applied to elliptical preforms.     

用相位恢复方法测量多孔光纤的三维折射率分布

结合计算机断层成像方法，提出了一种新的相位恢复显微测量实验技术.应用该技术测量了多孔光纤的三维折射率分布.这种技术是基于强度传递方程的理论，对相位的测量是直接的，测量对光纤无损害.这是一种测量多孔光纤的三维折射率分布的有效方法. 关键词： 断层法 相位恢复 显微测量 多孔光纤     

Refractive index changes induced by sheet beams with various intensity distributions in LiNbO<Subscript>3</Subscript>:Fe crystal

1 IntroductionSince the discovery of photorefractive effect by Ashkin et al. at the Bell laboratories in 1966[1], such effects of light-induced refractive index changes in electro-optic oxide crystals have attracted great attention because of their potential use in volume holo- graphic storage[2], optical information processing[3], optical spatial solitons[4], and light-induced optical waveguides[5―9]. The photo-induced index changes are the basis ofthe entire photorefractive phenomena in pho…     

Visible and near-infrared optical properties of Nd:CLNGG crystal waveguides formed by proton implantation

A Nd:CLNGG waveguide structure operated at wavelengths of both 632.8 nm and 1539 nm was demonstrated for the first time to our knowledge, which was produced by the 480-keV H~+ion implantation with a dose of 1.0×10~(17)protons/cm~2.Its propagating modes at 632.8 nm and 1539 nm were measured by the well-known prism coupling technique. The refractive index profile at either 632.8-nm wavelength or 1539-nm wavelength was optical barrier type in the proton-implanted Nd:CLNGG crystal optical waveguide, which was calculated by using the reflectivity calculation method. The near-field light intensity distributions were also simulated by the finite-difference beam propagation method in the visible and nearinfrared bands.     

Mode dispersion characteristics of graded-index optical waveguides

A method to compute the propagating modes of graded index waveguides with an arbitrary refractive index distribution is proposed, based on the variational method applied to the integral wave equation. The method is applied to two refractive index distributions: a Gaussian index distribution and a complementary error-function index distribution. The results are compared with the predictions of perturbation analysis and are experimentally verified by measuring the mode spectrum of a Ti-diffused LiNbO₃ 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     

聚焦法测量塑料光纤折射率分布的可行性研究

结合理论分析和实验验证,探讨了聚焦法测量塑料光纤纤芯的折射率分布的可行性。结果表明,对GI-POF而言,聚焦法是一种简单可行的技术.但是对SI-POF,由于入射光线在光纤边界处发生交叉,聚焦法不能精确测量其折射率分布.     

New method for determining refractive index and thickness of fluorescent thin films

The optical parameters of homogeneous, isotropic, and fluorescent thin films are determined by comparing measured with calculated angular intensity distributions of the s- and p-polarized light emitted into the substrate. The method also yields information about the multipole nature of the emitted radiation. The theory is presented for electric and magnetic dipole transitions. For extremely thin layers of optical thickness n₀d₀ ? λ/8 (where λ is the emission wavelength) analytic expressions for the angular intensity distributions are given. For between 25–30 nm thick evaporated layers of an europium-benzoyltrifluoro-acetone- chelate the refractive index was determined to be n₀ = 1.57 at λ = 612 nm. The fluorescent light emitted by these layers in an about 6 nm wide band centered at λ = 612 nm is emitted by randomly oriented electric dipoles.