Direct measurement on transparent plates by using Fizeau interferometry

It is shown that Fizeau interferometry provides an accurate optical method to measure the refractive index and wedge angle of transparent plates used as optical components in different experiments. A near IR external cavity diode laser having spectral resolution up to 10⁻⁷ has been employed to measure the refractive index of the test plates by introducing amplitude modulation technique in the detection system of our phase shifting Fizeau interferometry. Detection of spatial fringes has been performed to find out the wedge angles of the plates by using a He–Ne laser along with the CCD-image sensor.     

Multiple-beam interference fringes applied to investigate the index profile of the optical fiber dip

A numerical-based phase shift method is presented to study optical fibers having a dip in the refractive index profile at the center of the core. Mathematical expressions for the shape of multiple-beam Fizeau fringes crossing a graded-index optical fiber (GRIN) comprising a central graded-index dip or GRIN fiber with a constant refractive index dip, immersed in a silvered liquid wedge, are derived. The index profile parameters of the central dip are determined by comparing the theoretical fringe shape across the fiber cross-section and the experimental fringe shape obtained from micro-interferograms of the wedge interferometer.     

Influence of temperature on the optical and structural properties along the diameter of optical fibres

Multiple-beam Fizeau fringes technique with an opto-thermal device is used to study the effect of temperature on the optical properties of Philips graded-index optical fibres. The refractive index profile of the optical fibre is measured at different temperatures. From these profiles the opto-thermal coefficient, the profile shape parameter α, the cladding/core maximum refractive index difference Δn and some guidance parameters of the optical fibre that play an important role in communication are determined. The variation of oscillation and dispersion energies along the diameter of the optical fibre (energy profile) are calculated at different temperatures. An empirical formula of the energy profile is obtained. Microinterferograms are given for illustrations.     

Automatic refractive index profiling of fibers by phase analysis method using Fourier transform

Automatic fringe pattern analysis is a powerful and inexpensive digital image-processing technique. It is used to analyze the fringe pattern obtained by different optical techniques, such as multiple-beam Fizeau fringes. To perform accurate and fast automatic measurement of fiber refractive index profile, phase analysis method has been used with the Fourier transform technique. In this paper, the refractive index profiles of polyethylene fibers with different draw ratios are presented by two methods, fringe shift method and phase analysis method. A comparison between the results obtained is presented.     

Interferometric studies on the influence of temperature on the optical and dispersion parameters of GRIN optical fibre

Opto-thermal device attached to automate Fizeau interferometer is used to investigate the influence of temperature on opto-thermal properties of multimode graded-index (GRIN) optical fibre in the range from 27 to 54 °C. The effect of temperature on the refractive index profile of fibre is studied. The optical parameters and the opto-thermal coefficient of this fibre are determined. Also the variation of oscillation and dispersion energies, zero dispersion wavelengths, coupling efficiency, normalised frequency, number of propagation modes with the temperature and the material dispersion with the wavelength at different temperatures are calculated. Microinterferograms are given for illustration.     

A subfringe integration method for multiple-beam Fizeau fringe analysis

Some aspects concerning the subfringe integration method in interferogram analysis have been investigated and modified. The modified algorithm, introduced in this paper, is capable of reconstructing the phase in the presence of noise or errors in carrier frequency. The subfringe integration method was applied to analyze two computer simulated patterns of equispaced Fizeau fringes using N bucket integration. Also, it is used to analyze the multiple-beam Fizeau fringe. The refractive index profile of polyethylene fiber is obtained by using two methods, subfringe integration method, and Fourier transform method. A comparison between the obtained results using the maintained methods is presented.     

Automatic fringe analysis of the induced anisotropy of bent optical fibres

A new theoretical model considering the refraction of the incident light beam by the fibre is suggested to determine the refractive index profile of bent optical fibres. This new model (slabs model) considering the cross section of the bent optical fibre consists of large number of slabs. The slabs model bases on the refraction of the incident beam by the fibre. The refractive index profile of the optical fibre cladding before bending obtained using the automated Fizeau interferometer with the aid of suggested model is compared with other models such as, the homogenous model and the multilayer model to verify the ability of this slab model. The refractive index profile of the bent optical fibre cladding is investigated using this suggested model. In addition, the new model is used to obtain the induced birefringence and the guiding parameters. The bending radius is recommended to be greater than 7.1 mm for the used optical fibre. The consideration of the refraction increases the accuracy of the results.     

A novel video opto-mechanical (VOM) device for studying the effect of stretching speed on the optical and structural properties of fibers

Using a novel video opto-mechanical (VOM) device, the effect of stretching speed on the optical and structural properties of polypropylene (PP) fibers during the dynamic stretching process is studied. The objective of the present study is to correlate the optical and mechanical properties of PP fibers with the speed of stretching using the multiple-beam Fizeau fringes system. The skeletonization of the multiple-beam Fizeau fringes are determined automatically by using one-dimension Fourier transform method. The stepper motor is adjusted in order to stretch the fibers continuously with constant and uniform speed until breaking of the fiber. The refractive indices, birefringence, transverse sectional area and the orientation function of PP fibers are studied as a function of the draw ratio at different speeds of stretching. An empirical formula is given to correlate the birefringence of PP fiber and both the draw ratio and the speed of stretching. Stretching process of PP with low speed (slow stretching) is recommended to overcome the necking deformation along the fiber. The VOM device could be used to measure the yield strain. The draw ratio-stretching speed superposition is discussed with some details. Microinterferograms are given for illustration.     

A comparative study of spliced optical fibers

A fusion-spliced optical fiber is examined with a laser sheet of light. A CCD camera is used to record the transverse interference pattern from the fiber. The buckling on the fiber material in one direction of the spliced point is distinct inside the transverse interference pattern. The refractive index profile inside the fiber core, obtained at different illumination directions, is calculated using a new method showing the change in the refractive index due to fusion splicing of the fiber. A simple theoretical model is introduced to simulate the anomalous behavior in the transverse interference fringes due to a slight change of the optical parameters.     

Theoretical model for the transverse interference pattern of GRIN optical fiber using a laser sheet of light

A new technique (El-Ghandoor et al., Opt. Laser Technol. 31(7) (1999) 481–488) has been applied to study the shape of transverse interference fringes, instead of multiple beam Fizeau fringes (Marhic, Stein, Appl. Phys. Lett. 35 (1975) 1678–1682), from a GRIN optical fiber. In this technique, a laser light sheet is used to illuminate and pass directly through the optical fiber. Theoretical expressions are derived for the optical path differences of three groups of interference beams. The first one passes through the cladding, the core, and then the cladding once again; the second passes through the cladding only, and the third passes through the surrounding air. Theoretical expressions for the shape of transverse interference fringes formed across isotropic non-absorbing optical fibers are also calculated.     

Measurement of nonlinear refractive index of ethyl red by interference of capillary

Using the intensity distribution of interference fringes formed by a capillary filled with transparent liquid, the variations in refractive index (RI) of nonlinear optical materials, corresponding to change of the intensity at the centre of fringes for a period, were deduced. With this conclusion, we measured variations in RI of ethyl red (ER) solution excited by a 535-nm-15 mW-laser, and found that the change of RI is 0.00504 and the corresponding effective index of refraction is −1.06 × 10⁻⁹, for which the order of magnitude is same as that measured by Z-scan. The influences on the accuracy of the method, such as temperature, beam and fringe contrast, were analyzed. This is a novel and simple method for measuring the RI of nonlinear optical materials.     

天文光纤机械扰模器调制环形光场的实验研究

光纤入射光束的角度和位置的变化对光纤出射光束的远场光强分布有较大影响。通过分析光纤出射光场的光强分布,研究了斜光束的偏轴角对光纤出射光场的影响。光纤耦合理论说明光纤的宏弯曲会使光纤内部模式相互耦合,根据这一原理设计一种能使光纤宏弯曲并以此来改善光纤出射场分布的机械扰模器。在实验中,对不同偏轴角入射及处于不同扰模程度的光斑进行中值滤波、高斯拟合等处理,得到光斑的径向光强分布曲线、高斯拟合度、不同出射焦比范围的能量变化等参数,以此分析机械扰模器的扰模效果。     

Simultaneous measurement of surface shape and absolute optical thickness of a glass plate by wavelength tuning phase-shifting interferometry

The absolute optical thickness and the surface shape of a glass plate of 7-in. square and 3.1mm thick was simultaneously measured by three-surface interferometry using a wavelength tuning Fizeau interferometer. The wavelength of a tunable diode laser is scanned linearly from 632 to 642 nm, at which the initial and the final phases of the interference fringes for the surface shape and for the optical thickness were separated and measured by a tunable phase-shifting technique. The number of phase variations in the interference fringes during the scanning is counted by discrete Fourier analysis, in which systematic errors caused by a nonlinearity in the wavelength scanning is corrected by a correlation analysis between the observed and theoretical interference fringes. Experimental results demonstrate that the systematic errors in the measured value were 15 nm for the surface shape and 0.6 μm for the absolute optical thickness.     

Optical parameters of epitaxial GaN thin film on Si substrate from the reflection spectrum

A method has been proposed for determining the optical properties of a thin film layer on absorbing substrates. The film optical parameters such as thickness, refractive index, absorption coefficient, extinction coefficient and the optical energy gap of an absorbing film are retrieved from the interference fringes of the reflection spectrum at normal incidence. The envelopes of the maxima of the spectrum E_M and of the minima E_m are introduced in analytical forms to find the reflectance amplitudes at the interfaces and approximate values of the thin film refractive index. Then, the interference orders and film thickness are calculated to get accurate values of the needed optical parameters. There are no complex fitting procedures or assumed theoretical refractive index dispersion relations. The method is applied to calculate the optical properties of an epitaxial gallium nitride thin film on a silicon (1 1 1) substrate. Good agreement between our results and the published data are obtained.     

Determination of nonlinear coefficient and group-velocity-dispersion of bismuth-based high nonlinear optical fiber by four-wave-mixing

Nonlinear coefficient and group-velocity-dispersion of bismuth-based nonlinear fibers were determined by four-wave-mixing measurements. The wavelength dependence of refractive index of bulk bismuth-based glasses was also measured to estimate the material dispersion and waveguide dispersion. A newly developed bi-directional four-wave-mixing configuration enabled us to determine all fiber parameters simultaneously. The obtained fiber nonlinearity γ ∼ 1000 W⁻¹ km⁻¹ of bismuth-based nonlinear fiber is the highest one in the step-index fiber made of oxide glasses as expected from a high refractive index at 1550 nm. Dispersion analysis reveals that the both material dispersion and waveguide dispersion affect to the large group-velocity-dispersion of bismuth-based nonlinear fiber.     

Determination of GR-IN optical fibre parameters from transverse interferograms considering the refraction of the incident ray by the fibre

The core–cladding refractive index difference Δn and the index gradient profile parameter of the graded index (GR-IN) optical fibre has been determined. The curve representing the real path, in the core region, due to refraction of the beam and the change in the exit wavefront are considered. Multiple-beam Fizeau fringes and two-beam interference Pluta polarizing microscope, are used for this investigation. A new method, based on a derived mathematical expression, is used with a prepared computer program to estimate the fringe shift inside GR-IN of the fibre core. The estimated and experimental values of the fringe shift, along the core radius, are used to obtain the refractive index profile of the optical fibre. A comparison between the new method and a previous model considering the refraction has been shown. Microinterferograms are given for illustrations.     

Compact optical fiber curvature sensor based on concatenating two tapers

A low-loss, compact, and highly sensitive optical fiber curvature sensor is presented. The device consists of two identical low-loss fused fiber tapers in tandem separated by a distance L. When the optical fiber is kept straight and fixed, no interference pattern appears in the transmitted spectrum. However, when the device is bent, the symmetry of the straight taper is lost and the first taper couples light into the cladding modes. In the second taper, a fraction of the total light guided by the cladding modes will be coupled back to the fundamental mode, producing an interference pattern in the transmitted spectrum. As the fiber device is bent, visibility of the interference fringes grows, reaching values close to 1. The dynamic range of the device can be tailored by the proper selection of taper diameter and separation between tapers. The effects of temperature and refractive index of the external medium on the response of the curvature sensor is also discussed.     

γ辐射对光纤波导电磁场分布的影响

开展了光纤波导中的电磁场传输理论分析,得到了光纤折射率变化对波导中电磁场分布的影响规律,建立了块状融石英材料及光纤光栅在60Co 辐射作用下折射率变化的测量系统,开展了折射率随辐射剂量变化及光纤模场测量实验。结果表明:光纤的折射率随辐射剂量的增加而增大,折射率的变化会引起波导中传输模式的场强分布变化,从而导致光纤的辐射感生波导损耗;在一定的辐射剂量范围（0～2000 Gy）内,光纤仍满足弱导边界条件,能够维持对传输模式的约束能力。     

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.     

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.