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.     

透射式微分干涉显微镜测量光纤折射率分布

提出一种由两组偏光棱镜组成的透射式微分干涉系统,用来测量光纤的折射率分布。系统利用旋转检偏器对测量光束进行调制,从相位分布和光程分布中计算出折射率分布。介绍了测量原理、测量公式、系统组成及典型应用。用该系统对光纤折射率进行实际测量,给出渐变折射率光纤的二维分布,及折射率沿轴向的分布图,同时还在NR 9200光纤测试仪上进行了测试。结果表明,系统原理正确,结构简捷,具有足够分辨率和测量精度,抗干扰能力强,不破坏光纤,还可测量包层和芯层的直径,发现光纤加工过程中的缺陷,特别适合加工、焊接等工艺过程中的检测。     

Automatic determination of refractive index profile of fibers having regular and/or irregular transverse sections considering the refraction of light rays by the fiber

A new model, using non-destructive two- and/or multiple-beam interferometric techniques, is suggested for measuring the refractive index profile of fibers having regular and/or irregular cross-sectional shape taking into consideration the refraction of the light rays by the fiber. The proposed model is applied for three different fibers having different cross-sectional shapes and different refractive index profiles. These fibers are PPT, homogeneous fiber, with circular cross-section, graded index optical fiber of circular cross-sectional shape and Dralon fiber of irregular cross-section. To validate the proposed model it is used, firstly, to calculate the index profile for a standard PPT fiber. Secondly, the calculated results for the irregular Dralon fiber and GR-IN optical fiber are compared with that calculated using other conventional method. From this comparison, we recommend that the refraction must be taken into account to obtain accurate results especially for birefringent fibers and graded index optical fibers.     

Study of in fiber Mach–Zehnder interferometer based on two spaced 3-dB long period gratings surrounded by a refractive index higher than that of silica

The paper deals with the response of a Mach–Zehnder interferometer composed by two 3-dB long period gratings (LPG) with different external refractive indices higher than that of silica (leaky configuration). A rough analysis of the cladding propagation arising in leaky configuration has allowed us to establish a model that is sufficient to describe the interferometer couplings evolution at the resonance. In particular, we have shown that the interferometer sensitivity depends strongly on its phase-shift Δ and is optimized for Δ equal to π [2π] or 3π/4 [2π]. An experimental study was undertaken and allowed us to validate our model. Finally, a comparison with a single LPG demonstrated an increased sensitivity to the external index, suggesting the conception of a new fiber sensor operating with external refractive indices higher than that of silica.     

Automatic determination of refractive index profile, sectional area, and shape of fibers having regular and/or irregular transverse sections

A new method based on a mathematical model and a computer program is suggested to determine the refractive index profile of fibers having regular and/or irregular transverse sectional shape. Microinterferogram of both multiple-beam Fizeau fringes and the duplicated image from two-beam interference microscope are used for the determination of refractive index profile, cross-sectional area and shape of three different types of fibers. To confirm the suggested model, the calculated area and the shape of the transverse section of these fibers are compared with those results obtained using conventional methods.     

Phase retrieval using the transport of intensity equation solved by the FMG–CG method

The relationship between the object-plane phase and the intensity distribution in the Fresnel region can be described by the transport of intensity equation (TIE). The phase distribution can thus be uniquely determined by solving TIE. In this study, a full multigrid preconditioned conjugate gradient (FMG–CG) method is proposed to numerically solve the TIE for phase retrieval. The full multigrid method is a scalable algorithm, and can be parallelized readily and efficiently. By using this method as a preconditioner of the preconditioned conjugate gradient (PCG) method, fast convergence is obtained. The simulation experiments show that complicated phase distributions with fast convergence speed can be retrieved by this composite method.     

Highly sensitive cladding-etched arc-induced long-period fiber gratings for refractive index sensing

We have investigated the effects of cladding etching in arc-induced long-period fiber gratings. Comparing the position of the resonant wavelengths at each diameter with the corresponding theoretical dispersion curves of effective refractive index, it is found that some of the resonances show a better match with anti-symmetrical cladding modes, while others with symmetrical cladding modes. Etching the cladding diameter to ∼39 μm, results in coupling to a high-order cladding mode that is very sensitive to changes in the ambient refractive index. The resonant peak shifts remarkably (∼230 nm) toward shorter wavelengths as the external refractive index increases. This sensitivity is higher than any previously reported in arc-induced long-period fiber gratings.     

3D refractive index profile for the characterization of necking phenomenon along stretched polypropylene fibres

The phenomenon of neck formation in polymers has attracted considerable attention. During the cold-drawing process an initial undrawn material is transformed into anisotropic one across a narrow transition region called ‘neck’. The Video Opto-Mechanical (VOM) device attached with multiple-beam Fizeau fringes techniques are used to stretch polypropylene (PP) fibres. A iPP sample is stretched to have a neck at room temperature. The optical properties of the deformed material over the necking region are examined. Another PP sample is stretched (without necking deformation) at room temperature and the optical properties are also examined. The task of this study is to characterize and assess the necking phenomenon along cold-drawn polypropylene (iPP) fibre axis. The effect of necking on the optical properties of the fibre is confirmed by the determination of the 3D refractive index profile at different regions along the deformed PP fibre. Also the orientation function is calculated for the necked sample. The contour lines of microinterferograms are given for illustrations.     

The refractive index changes derived from thermal effects in Bragg fiber laser

The temperature distribution and the thermal stress distribution of Bragg fiber laser are analyzed by solving thermal transfer equations. The changes of refractive index derived from the temperature and the thermal stress are discussed separately. Results indicate that the change of index refraction caused by temperature is larger than by thermal stress.     

Numerical analysis of plasmon polarition refractive index fiber sensors with hollow core and a long period grating

The main principle of this design is based on the efficient energy transfer between the waveguide mode (WM) and the co-directional SPP provided by a properly designed fiber long period grating (LPG). This LPG is imprinted into a waveguide fiber layer of a specially designed hollow core optical fiber. The simulations are based on the finite element method (FEM) algorithm in electromagnetics and coupled mode theory for gratings. Compared to the previous proposed structure using a fiber Bragg grating (FBG), this novel kind of sensor can greatly enhance the refractive index sensitivity, e.g., from 5.93 nm/RIU (with FBG) to 817 nm/RIU (with LPG) at the sensing refractive index of 1.40. The other advantage is that the working conditions can be performed for the well-developed telecom wavelength windows 1500-1600 nm.     

Characterization and estimation of refractive index profile of laser-written photopolymer optical waveguides

In this study, channel waveguides fabricated in photopolymer films by direct-writing using a low-power CW laser, are used as phase objects in a simple plane-wave diffraction setup, and the refractive index modulation profiles of the waveguides are characterized using the recorded diffraction patterns. Index profiles are modeled by piece-wisely combining two Gaussian functions representing the central and the tail regions. Measured diffraction patterns are matched with patterns generated using the model. This simple model makes it possible to design various channel waveguides embedded into polymer substrates. The proposed model is tested on three distinctive waveguide profiles written on the same Acrylamide/Polyvinyl Alcohol based photopolymer with different exposures.     

测量光纤折射率分布还原算法的研究

用透射式微分干涉法测量光纤内部折射率分布,其原理是利用旋转检偏器对测量光束进行调制,从相位分布和光程分布中计算出折射率分布。其中,从光程分布中解算出折射率分布的算法是关键。讨论了该算法的数学模型,推导了测量公式,并对算法的稳定性和误差进行了分析。利用自行研制的系统对渐变折射率分布光纤进行实测,与在NR 9200光纤测量仪上的结果进行了比较,对主要误差源进行了分析和计算机模拟。实测和模拟计算结果表明,该算法原理正确,系统稳定,测量精度优于10-3,完全可以用来测量光纤折射率分布。     

Widely tunable long-period fiber grating with nm-thick higher refractive index film overlay

By introducing a four-layer step-index waveguide modeling, the characteristics of long-period fiber grating (LPFG) with an nm-thick film overlay, which has higher refractive index than that of fiber cladding are investigated in detail. The influence of both the overlay thickness and refractive index on the tuning ability of LPFG is analyzed. The numerical results demonstrate that spectral response of LPFG is divided into three distinct regions as the overlay deposition increases and the shift of resonant wavelength is drastic in some special thickness range. In conjunction with higher-order cladding mode coupling and fiber cladding etching, the sensitivity of LPFG to the overlay refractive index is enhanced significantly and over 120 nm resonant wavelength tunable range is achieved.     

Determination of refractive index profiles of gradient optical waveguides by ellipsometry

Ag⁺-Na⁺ and K⁺-Na⁺ ion-exchanged optical waveguides in soda-lime glass are characterised by ellipsometry. Refractive index profiles of the waveguides are calculated from ellipsometric multiple angle of incidence data using the Newton-Kantorovitch type iterative procedure and compared with those reconstructed by inverse WKB method. It is demonstrated that such continuous profiles with relatively small index gradient (of the order of 0.1 and 0.01), extending to few micrometers in depth, can be determined by ellipsometric measurements. A good agreement is found between results obtained by ellipsometry and by the inverse WKB method at depths above 500–600 nm, while there is a difference in the subsurface region, where ellipsometry is more sensitive to the quality of the surface. The profiles obtained by the two methods are consistent if the surface thin layer is etched.     

Microbend fiber optic detection of continuously varying refractive index of chlorinated water

In this paper we report a simple microbend fiber optic sensor using a plastic fiber, LED and photodetector assembly for sensing minute variation of refractive index of chlorinated water. Chlorinated water has slightly higher refractive index and gradual release of chlorine from bleaching powder treated water causes a temporal decrease in refractive index of the solution. The evaporation of chlorine from water and the change in refractive index is found to follow a first order exponential decay function of time. Introducing microbends in an optical fiber is easier and less complex than etching of fiber cladding for traditional optical fiber sensors.     

光纤折射率剖面的折射近场法测量的研究

本文叙述了折射近场法(简称RNF)测量光纤折射率剖面的基本原理及实验方法.提供了对单模光纤和多模光纤的测量结果,并与反射法、近场法进行了比较.实验中获得空间分辨率优于0.8μm,折射率灵敏度优于2×10~(-4).     

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.     

Real-time measurement of glucose concentration and average refractive index using a laser interferometer

This study presents a non-destructive, highly precise optical metrology system for measuring the average refractive index of a liquid solution such that its glucose concentration can be derived. The metrology system is employed to measure the average refractive indices of samples with known glucose concentrations ranging from 0 to 200 g/l. By applying a regressional analysis technique to the experimental results, an analytical expression is derived to describe the relationship between the refractive index and the glucose concentration. An excellent agreement is observed between the experimentally determined values of the glucose concentration and the analytically derived results. For an assumed laser interferometer resolution of 1 nm, the measurement resolution of the proposed metrology system is found to be at least F=0.05 g/l, which is significantly better than that of F=2 g/l obtained using the polarimetric glucose sensor presented by Lo and Yu [A polarimetric glucose sensor using a liquid-crystal polarization modulator driven by a sinusoidal signal. Opt Commun, 2006; 259: 40–8].     

Investigation on characteristics of W-type fiber with an inner cladding made of negative refractive index materials

A doubly clad optical fiber with an inner cladding made of negative refractive index material was proposed and the modes distribution, dispersion and time delay were investigated by fully vectorial numerical method. The results indicate that HE₁₂ mode can be operated as a single mode, the cut-off frequency of modes shifts to low normalized frequency with increasing thickness of inner cladding made of negative index materials, large negative dispersion and time delay can be obtained and tailored by the inner cladding. These results provide theoretical basis for designing novel fibers or optical devices.     

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.