Effects of doping on the optical fiber drawing process

Optical fibers are typically drawn from silica preforms, which usually consist of two concentric cylinders called the core and the cladding, heated in a high-temperature furnace. For optical communication purposes, the core generally has a higher average refractive index than the cladding to obtain total internal reflection. This paper investigates the effects of adding dopants to the core or to the cladding, to change the refractive index values, on the optical fiber drawing process. Employing an analytical/numerical model developed earlier to simulate the core-cladding structure of a typical optical fiber, the paper considers different dopants and the effects resulting from the consequent changes in properties, particularly the radiation absorption properties, on the temperature distributions, flow, neck-down profile, thermally induced defects and draw tension. The zonal method is applied to model the radiation transfer in the glass perform and the purge gas is taken as non-participating. The numerical model has been validated by comparing with results available in the literature, wherever possible. It is found that the effects are significant because of changes in refractive index and absorption of radiation, which give rise to significant changes in temperature and tension. These can, in turn, substantially affect fiber quality and characteristics. Therefore, for an accurate and realistic modeling of the process, the effects of property changes due to dopants on the draw process must be included.     

ADVANCED SIMULATION OF OPTICAL FIBER DRAWING PROCESS

Precise modeling of the optical fiber drawing process is extremely important for identifying optimum drawing conditions in a furnace that would produce high-quality fibers at a low cost. In this study, a numerical approach for detailed simulation of thermal transport in an optical fiber drawing furnace is developed by implementing a primitive variable computational fluid dynamics algorithm. To accurately simulate the underlying fluid dynamics, the complete Navier–Stokes equations are solved for both glass and external gas, which are coupled by the conjugate boundary conditions at the interface. The governing equations are discretized by a finite volume approach and the solution algorithm for the discretized equations is based on the semi-implicit method for the pressure linked equations revised (SIMPLER) method instead of the traditional streamfunction approach. Radiative heat transfer is the most dominant mode of heat transfer during optical fiber drawing and it is modeled by the finite volume method. The gas-preform interface is treated as a Fresnel surface instead of a diffuse surface. To validate the present numerical approach and to examine the effects of the Fresnel interface condition on the preform temperature, a benchmark optical fiber drawing problem containing a prescribed neck-down profile is investigated with various fiber drawing speeds, furnace wall temperatures, and preform diameters. For the diffuse interface, the present prediction in temperature is found to match the available other solution very well. For the Fresnel interface, the present prediction is usually higher in comparison with that of the same approach with the diffuse interface. However, the temperature difference between two interfaces is found to be small, implying that the error caused by the diffuse assumption may be not significant.     

Analytical Monte Carlo Ray Tracing simulation of radiative heat transfer through bimodal fibrous insulations with translucent fibers

In this study, a Monte Carlo Ray Tracing (MCRT) simulation technique is developed to study steady-state radiative heat transfer through fibrous insulation materials. The simulations are conducted in 3-D disordered virtual fibrous media with unimodal and/or bimodal fiber diameter distributions consisting of fibers whose surfaces are specularly reflective, and are translucent to Infrared (IR) radiation. Scattering within the realm of geometric optics is incorporated into our MCRT simulations using Snell’s Law for ray refraction. Fibers’ optical properties are obtained from Fresnel’s law and Beer’s law based on the refractive index of the material. Two different treatments of “high” and “low” conductivities are considered for the fibers and their effects are discussed. Our results indicate that heat flux through a fibrous medium with translucent fibers decreases with increasing packing fraction of the fibers. It was observed that IR transmittance through the media increases with increasing through-plane orientation of the fibers, but is independent of their in-plane orientations. It was also found that fiber orientation has generally a negligible effect on the temperature profile across the media’s thickness. However, for the case of high-conductivity fibers, increasing fibers’ through-plane orientation tends to flatten the temperature profile. The results obtained from simulating bimodal fibrous structures indicate that increasing the fiber-diameter dissimilarity, or the mass fraction of the coarse fibers, slightly increases the radiation transmittance through the media, and accordingly reduces the temperature gradient across the thickness. Our simulation results are compared with those from the two-flux model and good agreement is observed.     

TEMPERATURE DISTRIBUTION OF AN OPTICAL FIBER TRAVERSING THROUGH A CHEMICAL VAPOR DEPOSITION REACTOR

A fundamental understanding of how reactor parameters influence the fiber surface temperature is essential to manufacturing high-quality optical fiber coatings by chemical vapor deposition (CVD). In an attempt to understand this process better, a finite-volume model has been developed to study the gas flow and heat transfer of an optical fiber as it travels through a CVD reactor. This study showed that draw speed significantly affects fiber temperature inside the reactor, with temperature changes over 50% observed under the conditions studied. Other parameters affecting fiber temperature include fiber radius, fiber coating emissivity, and gas flow velocity at inlet. Multiple heat transfer modes contribute to these phenomena, with convection and radiation heat transfer dominating the process. The numerical model is validated against analytical cases.     

Feasibility and optimization of the hollow optical fiber drawing process

The drawing process for the fabrication of a hollow optical fiber involves the flow of glass, which is largely heated by thermal radiation, in an inert gas environment. It is critical to maintain the central core, which can collapse if the thermal conditions are not properly imposed and controlled. This paper presents the analysis and simulation of this complicated process. A numerical model is developed, validated, and applied to simulate the hollow optical fiber drawing process under a wide range of boundary conditions, particularly draw speed, tension, and temperature. A feasible domain of the drawing process is identified to give the range of the drawing parameters for which the geometry of the fiber is maintained and collapse of the core and viscous rupture of the fiber are avoided. The effects of drawing temperature and feeding speed, which are crucial factors in determining the geometry and quality of the fiber, are investigated in detail. A multi-variable unconstrained optimal design problem is posed and considered in terms of the feasible domain. An appropriate objective function, comprised of the maximum velocity lag, thermally induced defect concentration and draw tension, is proposed to quantify the quality of the hollow fiber. The univariate search method is then applied to obtain the optimal drawing temperature and feeding speed. This study provides a basis for the optimization of hollow fiber drawing process and indicates that a substantial improvement in fiber quality can be achieved.     

Development of a Global Model of Heat Transfer in the Czochralski Furnace Taking into Account Specular Reflection at the Crystal Surface

In this study, a global model of heat transfer for the Czochralski crystal growth of oxides is developed by integrating the conventional model and the improved radiation element method by the ray emission model (REM²) in which radiative heat transfer in semitransparent crystals with a specular surface, that is, reflection and refraction at the crystal surface, is considered. The validity of the present model is verified by comparing it with the conventional model. Then, the effects of the optical thickness and the refractive index of the crystal on the temperature distribution in the furnace and on the melt/crystal interface shape are numerically investigated.     

Thermocapillary flow in an annular liquid layer painted on a moving fiber

In the present paper, a theoretical model is studied on the flow in the liquid annular film, which is ejected from a vessel with relatively higher temperature and painted on the moving solid fiber. A temperature gradient, driving a thermocapillary flow, is formed on the free surface because of the heat transfer from the liquid with relatively higher temperature to the environmental gas with relatively lower temperature. The thermocapillary flow may change the radii profile of the liquid film. This process analyzed is based on the approximations of lubrication theory and perturbation theory, and the equation of the liquid layer radii and the process of thermal hydrodynamics in the liquid layer are solved for a temperature distribution on the solid fiber.     

Measurements of concentration distribution of hydrogen jet using deflection of center of the laser spot

The main purpose of this work is to propose a new method to evaluate the concentration distribution of the hydrogen jet by using a He–Ne laser through the jet. This research attempts to apply the expression of concentration Gaussian distribution, the refraction formula of inhomogeneous refractive index medium, and the concentration inversion function to disclose the displacement of the center of the laser spot at different heights in the gas jet. The spot images of the laser beam passing through the gas jet at three vertical heights z = 10d, 20d, 30d, and different radial positions are obtained. The radial spatial asymmetry of the gas jet is also found in the experiment. Finally, the calculated concentration distribution curve and the fluent simulation curve, it is found that the two results are very similar. Our findings show that the error between the concentration distribution of this method and the simulated concentration distribution reaches 2.43%.     

Temperature distributions in an absorbing-emitting-scattering semitransparent slab with variable spatial refractive index

A Monte Carlo curved ray-tracing method is used to analyze the radiative heat transfer in one-dimensional absorbing-emitting-scattering semitransparent slab with variable spatial refractive index. A problem of radiative equilibrium with linear variable spatial refractive index is taken as an example in this paper. The predicted temperature distributions are determined by the proposed method and compared with the data in references. The results show that influences of refractive index gradient are important and the influences increase with the refractive index gradient, the temperature distribution approaches to the one obtained for a constant refractive index when the slab optical thickness is far greater than 1.0, and the effect of the scattering phase function is similar to that in the medium with constant refractive index.     

Optimization of a thermal manufacturing process: Drawing of optical fibers

The optimization of thermal systems and processes has received much less attention than their simulation and often lags behind optimization in other engineering areas. This paper considers the optimization of the important thermal manufacturing process involved in the drawing of optical fibers. Despite the importance of optical fibers and the need to enhance product quality and reduce costs, very little work has been done on the optimization of the process. The main aspects that arise in the optimization of such thermal processes are considered in detail in order to formulate an appropriate objective function and to determine the existence of optimal conditions. Using validated numerical models to simulate the thermal transport processes that govern the characteristics of the fiber and the production rate, the study investigates the relevant parametric space and obtains the domain in which the process is physically feasible. This is followed by an attempt to narrow the feasible region and focus on the domain that could lead to optimization. Employing standard optimization techniques, optimal conditions are determined for typical operating parameters. The study thus provides a basis for choosing optimal design conditions and for more detailed investigations on the feasibility and optimization of this complicated and important process.     

Effect of Furnace Thermal Configuration on Optical Fiber Heating and Drawing

ABSTRACT

The thermal configuration of the draw furnace, which involves the wall temperature profile, the temperature level, and the length of the heated zone, is an important aspect in high-speed optical fiber manufacture. This article presents a computational study on the effect of the furnace thermal configuration on the draw process and on physical quantities such as velocity and temperature difference across the preform/fiber, tension, and neck-down profile. Considering a cylindrical graphite furnace, the study solves a conjugate problem, which involves both the moving silica glass rod or fiber and the inert gases in the furnace. The flow and heat transfer in the two regions is linked due to the boundary conditions at the surface of the glass. Force balance conditions are used to determine the neck-down profile. A fairly versatile finite-difference numerical scheme is employed to consider different temperature distributions along the furnace wall, as well as a range of heating-region lengths. Besides the flow and thermal transport, the tension in the fiber and thermally induced defects that affect fiber quality are also calculated. A range of fiber draw speeds is also considered, and the effect on the variables that determine the fiber characteristics is studied.     

Fluidic laser beam shaper by using thermal lens effect

Laser measurement and laser processing techniques have been gaining strong attention from various applications. This research aims at the development of a fluidic laser beam shaper, and in order to fulfill the objective, thermal lens effect characteristics are studied. This phenomenon has the optical property of a divergent lens since the refractive index distribution on the optical axis is formed when a liquid is irradiated. In this research, effects of the pump power and the propagation distance to the probe beam profile are investigated experimentally and theoretically, with the purpose of developing a fluidic laser beam shaper. It is indicated that, by controlling some parameters in thermal lens system such as the pump power (in the regime of linear optics) and absorption coefficient, an input Gaussian beam can be converted into a flat-top beam profile. The relationship between the distance to obtain the flat-top beam, the pump power and absorption coefficient is investigated to show the flexibility of the fluidic laser beam shaper in many fields of laser application.     

A Finite-Element Model for the Thermal Radiative Properties of Graded Index Fiber Coated with Thin Absorbing Film

A finite-element model in combination with the wave optical approach is developed based on the radiative transfer equation for graded index medium in cylindrical coordinate system to predict the total hemispherical thermal radiative properties of semitransparent graded index fiber coated with thin absorbing film. The film is made of a strong absorbing medium with thickness less than or on the order of the wavelength of peak magnitude of thermal radiation. Radiative absorptance of the fiber-film system is directly obtained by solving the radiation deposited in the system. Radiative transfer in the fiber is solved by a least squares finite-element method, while radiative transfer in the thin film is treated through wave optics, and the film is formulated as a special kind of semitransparent boundary condition for the fiber medium. The results obtained by the finite-element model for uniform index fiber are in good agreement with the results in the literature obtained through the ray tracing model. The effects of fiber refractive index distribution on predicted thermal radiative properties are investigated. For the fiber with or without film, the variation of refractive index distribution has a substantial influence on the effective emittance.     

Combined non-gray radiative and conductive heat transfer in solar collector glass cover

A rigorous approach for the radiative heat transfer analysis in solar collector glazing is developed. The model allows a more accurate prediction of thermal performance of a solar collector system. The glass material is analysed as a non-gray plane-parallel medium subjected to solar and thermal irradiations in the one-dimensional case using the Radiation Element Method by Ray Emission Model (REM by REM).This method is used to analyse the combined non-gray convective, conductive and radiative heat transfer in glass medium. The boundary surfaces of the glass are specular. The spectral dependence of the relevant radiation properties of glass (i.e. specular reflectivity, refraction angle and absorption coefficient) are taken into consideration. Both collimated and diffuse incident irradiation are applied at the boundary surfaces using the spectral solar model proposed by Bird and Riordan. The optical constants of a commercial ordinary clear glass material have been used. These optical constants (100 values) of real and imaginary parts of the complex refractive index of the glass material cover the range of interest for calculating the solar and thermal radiative heat transfer through the solar collector glass cover. The model allows the calculation of the steady-state heat flux and temperature distribution within the glass layer. The effect of both conduction and radiation in the heat transfer process is examined. It has been shown that the real and imaginary parts of the complex refractive index have a substantial effect on the layer temperature distribution. The computational time for predicting the combined heat transfer in such a system is very long for the non-gray case with 100 values of n and k. Therefore, a simplified non-gray model with 10 values of n and k and two semi-gray models have been proposed for rapid computations. A comparison of the proposed models with the reference non-gray case is presented. The result shows that 10 bandwidths could be used for rapid computation with a very high level of accuracy.     

Solution of radiative heat transfer in a semitransparent slab with an arbitrary refractive index distribution and diffuse gray boundaries

On the basis of medium discretization and local linear approximation of refractive index distribution, the curved ray tracing technique is used in combination with the pseudo source adding method to numerically solve the radiative heat transfer in a semitransparent slab with an arbitrary refractive index distribution and two diffuse gray walls. The radiative equilibrium temperature field of a linear refractive index distribution is evaluated by this method and the results show excellent agreement with that of the previous research. For two types of sinusoidal refractive index distributions, the radiative equilibrium temperature field as well as the temperature and heat flux fields of coupled radiation-conduction are investigated in detail. The results show considerable significance of the gradient refractive index effect, and some important conclusions are to be obtained.     

含吸收散射粒子半透明介质层的容积吸收特性分析

将Ｍｉｅ散射理论与蒙特卡罗法相结合分析了含吸收散射粒子半透明介质层的容积吸收特性。考虑了半透明入射表面的折射与反射,不透明壁面的漫反射,半透明介质的吸收以及粒子系的吸收和独立多次非规则各向异性散射。直接由粒子复折射率,粒径及入射辐射波长等基本参数,根据Ｍｉｅ散射理论确定粒子系的吸收,散射因子以及非规则的各向异性散射分布。计算分析了介质层光学厚度、粒子复折射率、尺度参数、粒子系特征参数以及锥形入射时     

A method to calculate Fresnel lenses

In solar engineering, in contrast to image optics, Fresnel lenses are intended for securing the required concentrations of solar radiation and its distribution over a receiver’s surface. It is also important to secure a high use coefficient of the concentrated flux. In particular, this defines the features of calculation of Fresnel lenses: it is necessary to take into account inaccuracies in fabrication of Fresnel lenses and solar radiation redistribution by means of selecting the respective parameters of Fresnel lens belts. In the present work, we examine the procedure for the calculating geometrical parameters of Fresnel lenses on a flat base by considering the mentioned requirements. A corresponding software for calculating the geometrical parameters and concentrating characteristics of the Fresnel lenses is developed, and examples of calculation are given. For a constant refractive index of Fresnel lens material, it is shown that the Fresnel lens can secure a concentration of about 1000, but in this case the optical efficiency of the Fresnel lens will not be higher than 70%. The procedure that has been developed may be the basic one for determining the parameters and concentrating characteristics of Fresnel lenses by considering refractive index variance.     

Fixed Cartesian grid based numerical model for solidification process of semi-transparent materials II: Reflection and refraction or transmission of the thermal radiation at the solid–liquid interface

Mathematical and numerical models of solidification process in materials which were semi-transparent both in the solid and liquid phases were developed in this paper. These models took into account different optical and thermophysical properties in phases, herein for the first time different refractive index in the solid and the liquid phase. Also optical phenomena like reflection and refraction or transmission of the thermal radiation at transparent as well as either specular, partially specular and partially diffusive or diffusive solid–liquid interface were also considered. Conditions for the radiation intensity at the transparent solid–liquid interface were formulated according to the specular reflection and Snell’s laws. The numerical model was based on the Fixed Grid Front Tracking Method combined with the Immersed Boundary Technique for phase change process and on the Pixelation Technique for optical phenomena at the solid–liquid interface. Subsequently, comparisons of obtained results with results presented in the literature for one-dimensional two layers slab proved the correctness and accuracy of the proposed approach. Also the effect of different refractive index in the solid and the liquid phase on solidification process in an idealized square cavity were studied.     

EFFECT OF DRAW FURNACE GEOMETRY ON HIGH-SPEED OPTICAL FIBER MANUFACTURING

Optimal design of the draw furnace is particularly desirable to meet the need of high-volume production in the optical fiber industry. This article investigates the thermal transport and flow in optical fiber drawing at high draw speeds in a cylindrincal graphite furnace. A conjugate problem involving the glass and the purge gases is solved. The transport in the two regions is coupled through the boundary conditions at the free glass surface. The neck-down profile of the preform at steady state is determined by a force balance, using an iterative numerical scheme. To emphasize the effects of draw furnace geometry, the diameters of the preform and the fiber are kept fixed. Only the length and the diameter of the furnace are changed. For the purposes of comparison, a wide domain of draw speeds, ranging from 5 m/s to 20 m/s, is considered, and the form of the temperature distribution at the furnace surface remains unchanged. The dependence of the preform/fiber characteristics on the furnace geometry are demonstrated quantitively. Based on these numerical results, an optimal design of the draw furnace can be developed.     

Working fluid concentration measurement in solar air conditioning systems

In order to evaluate on-line corrosive electrolyte concentration in solar air conditioning systems, an optical technique to determine the concentration is being proposed. With this optical sensing method, it is possible to measure the percentage concentration of the aqueous corrosive lithium bromide solution at temperatures ranging from 25 °C to 70 °C and a maximum concentration of 60%. The measurement system is based on the refractive index of the solution and the data correlation, at several temperature and concentration values. The results of this work present a direct method for concentration measurement of corrosive liquids and also show the correlation among the three parameters: refractive index, temperature and weight concentration. This correlation can be used to develop the optical device for solar air conditioning systems to control and improve efficiency.