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Journal ArticleDOI

The mathematical modelling of rotating capillary tubes for holey-fibre manufacture

01 Jan 2008-Journal of Engineering Mathematics (Springer Netherlands)-Vol. 60, Iss: 1, pp 69-87
TL;DR: In this paper, the authors examined the fluid dynamics of capillary drawing using an extensional-flow asymptotic approach based on the small aspect ratio of the capillary, and made predictions concerning the effects of fiber rotation.
Abstract: Understanding and controlling the manufacturing process of producing (“drawing”) microstructured optical fibres (“holey fibres”) is of paramount importance in obtaining optimal control of the final fibre geometry and identifying industrially useful production regimes. The high cost of the manufacturing process and the challenge of ensuring reproducible final fibre geometries renders theoretical approaches invaluable. In this study the fluid dynamics of capillary drawing is examined using an extensional-flow asymptotic approach based on the small aspect ratio of the capillary. The key focus of the study is the additional effects that may be introduced by adding fibre rotation to the manufacturing process. Predictions are made concerning the effects of rotation, and a variety of asymptotic limits are examined in order to gain an understanding of the physics involved. Drawing regimes that are useful from a practical point of view are identified and the role of fibre rotation, both as a control measure (that may be used to influence the final geometry of a capillary) and as a means of reducing unwanted effects (such as fibre birefringence and polarisation model dispersion), is discussed.
Citations
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Journal ArticleDOI
Abstract: The efficient and accurate fabrication of Microstructured optical fibers (MOFs) requires a practical understanding of the ‘draw process’ beyond what is achievable by trial and error, which requires the ability to predict the experimental drawing parameters needed to produce the desired final geometry. Our results show that the Fitt et al. fluid-mechanics model for describing the draw process of a single axisymmetric capillary fiber provides practical insights when applied to more complex multi-hole symmetric and asymmetric MOF geometries. By establishing a method to relate the multi-hole MOF geometry to a capillary and understanding how material temperature varies with the draw tower temperature profile, it was found that analytical equations given by the Fitt model could be used to predict the parameters necessary for the chosen structure. We show how this model provides a practical framework that contributes to the efficient and accurate fabrication of the desired MOF geometries by predicting suitable fiber draw conditions.

44 citations

Journal ArticleDOI
TL;DR: A key result is to demonstrate how a so-called reduced time variable serves as a natural parameter in describing how an axial-stretching problem interacts with the evolution of a general surface-tension-driven transverse flow via a single important function of $\tau $, derived from the total rescaled cross-plane perimeter.
Abstract: A general mathematical framework is presented for modelling the pulling of optical glass fibres in a draw tower. The only modelling assumption is that the fibres are slender; cross-sections along the fibre can have general shape, including the possibility of multiple holes or channels. A key result is to demonstrate how a so-called reduced time variable serves as a natural parameter in describing how an axial-stretching problem interacts with the evolution of a general surface-tension-driven transverse flow via a single important function of , herein denoted by , derived from the total rescaled cross-plane perimeter. For any given preform geometry, this function may be used to calculate the tension required to produce a given fibre geometry, assuming only that the surface tension is known. Of principal practical interest in applications is the ‘inverse problem’ of determining the initial cross-sectional geometry, and experimental draw parameters, necessary to draw a desired final cross-section. Two case studies involving annular tubes are presented in detail: one involves a cross-section comprising an annular concatenation of sintering near-circular discs, the cross-section of the other is a concentric annulus. These two examples allow us to exemplify and explore two features of the general inverse problem. One is the question of the uniqueness of solutions for a given set of experimental parameters, the other concerns the inherent ill-posedness of the inverse problem. Based on these examples we also give an experimental validation of the general model and discuss some experimental matters, such as buckling and stability. The ramifications for modelling the drawing of fibres with more complicated geometries, and multiple channels, are discussed.

36 citations

Journal ArticleDOI
TL;DR: In this article, a method is proposed for modeling the self-pressurization of optical fibers that are sealed before drawing, and a numerical investigation is undertaken to optimize the choice of experimental parameters to minimize the transient effects of sealed preform drawing.
Abstract: A method is proposed for modeling the self-pressurization of optical fibers that are sealed before drawing. The model is solved numerically and the results compared with experimental results. An explanation of the mechanism is presented and a numerical investigation is undertaken to optimize the choice of experimental parameters to minimize the transient effects of sealed preform drawing.

26 citations


Cites background from "The mathematical modelling of rotat..."

  • ...Considering only the steady-state version of these equations and ignoring the effects of gravity, the inertial-force term and those of surface tension (assumption 2)): see [3] and [7] for details of how this affects the solutions) and preform rotation, (1)–(4) become...

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  • ...[7] for a full derivation and discussion....

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  • ..., ignoring gravity, inertia and surface tension, see [7])....

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  • ...There exist numerous studies of optical-fiber drawing, including studies related to the drawing of capillary tubes (see, for example, [2]–[7])....

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Journal ArticleDOI
TL;DR: In this paper, a method for modeling the fabrication of capillary tubes is developed that includes the effects of preform rotation, and is used to reduce or remove polarization mode dispersion and fiber birefringence.
Abstract: A method for modeling the fabrication of capillary tubes is developed that includes the effects of preform rotation, and is used to reduce or remove polarization mode dispersion and fiber birefringence. The model is solved numerically, making use of extensive experimental investigations into furnace temperature profiles and silica glass viscosities, without the use of fitting parameters. Accurate predictions of the geometry of spun capillary tubes are made and compared directly with experimental results, showing remarkable agreement and demonstrating that the mathematical modeling of fiber drawing promises to be an accurate predictive tool for experimenters. Finally, a discussion of how this model impacts on the rotation of more general microstructured optical fiber preforms is given.

20 citations


Cites background from "The mathematical modelling of rotat..."

  • ...Index Terms—Mathematical modeling, optical fiber, optical fiber applications, optical fiber fabrication, optical fiber theory....

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  • ...Since the fabrication of structured preforms is one of the most labor intensive parts of the manufacturing process, it is often desirable Manuscript received August 6, 2007; revised December 9, 2007....

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Journal ArticleDOI
TL;DR: In this article, a mathematical model is presented describing the deformation, under the combined effects of surface tension and draw tension, of an array of channels in the drawing of a broad class of slender viscous fibres.
Abstract: A mathematical model is presented describing the deformation, under the combined effects of surface tension and draw tension, of an array of channels in the drawing of a broad class of slender viscous fibres. The process is relevant to the fabrication of microstructured optical fibres, also known as MOFs or holey fibres, where the pattern of channels in the fibre plays a crucial role in guiding light along it. Our model makes use of two asymptotic approximations, that the fibre is slender and that the cross-section of the fibre is a circular disc with well-separated elliptical channels that are not too close to the outer boundary. The latter assumption allows us to make use of a suitably generalised ‘elliptical pore model (EPM)’ introduced previously by one of the authors (Crowdy, J. Fluid Mech., vol. 501, 2004, pp. 251–277) to quantify the axial variation of the geometry during a steady-state draw. The accuracy of the elliptical pore model as an approximation is tested by comparison with full numerical simulations. Our model provides a fast and accurate reduction of the full free-boundary problem to a coupled system of nonlinear ordinary differential equations. More significantly, it also allows a regularisation of an important ill-posed inverse problem in MOF fabrication: how to find the initial preform geometry and the experimental parameters required to draw MOFs with desired cross-plane geometries.

19 citations

References
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Journal ArticleDOI
TL;DR: This paper reviews the fundamental concepts and basic theory of polarization mode dispersion in optical fibers and introduces a unified notation and methodology to link the various views and concepts in Jones space and Stokes space.
Abstract: This paper reviews the fundamental concepts and basic theory of polarization mode dispersion (PMD) in optical fibers. It introduces a unified notation and methodology to link the various views and concepts in Jones space and Stokes space. The discussion includes the relation between Jones vectors and Stokes vectors, rotation matrices, the definition and representation of PMD vectors, the laws of infinitesimal rotation, and the rules for PMD vector concatenation.

787 citations


"The mathematical modelling of rotat..." refers background in this paper

  • ...Its effects can be significant for three main reasons [4]....

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Journal ArticleDOI
TL;DR: In this article, a new model for light propagation in holey optical fibers is developed in which the transverse index profile and the modal field are decomposed using different orthogonal functions.
Abstract: A new model for light propagation in holey optical fibers is developed in which the transverse index profile and the modal field are decomposed using different orthogonal functions. It is an efficient and accurate alternative to previous techniques, and is an invaluable tool to aid fabrication efforts. Using this model, a number of regimes of interest in these fibers are explored.

447 citations


"The mathematical modelling of rotat..." refers background in this paper

  • ...Finally, the intended or accidental geometrical asymmetries that may be introduced into the manufacturing process may include the “locking-in” of an asymmetric stress distribution within the fibre [3]....

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Journal ArticleDOI
TL;DR: An optical fiber that can appear single mode with propagation properties that can be achieved only in multimode waveguides is analysis of waveguide properties of microstructure optical fibers.
Abstract: We analyze the waveguide properties of microstructure optical fibers consisting of a silica core surrounded by a single ring of large air holes. Although the fibers can support numerous transverse spatial modes, coupling between these modes even in the presence of large perturbations is prevented for small core dimensions, owing to a large wave-vector mismatch between the lowest-order modes. The result is an optical fiber that can appear single mode with propagation properties that can be achieved only in multimode waveguides.

344 citations

Journal ArticleDOI
TL;DR: It is shown that whereas a conventionally twisted fiber possesses considerable optical rotation, a fiber which has a permanent twist imparted by spinning the preform during fiber drawing exhibits almost no polarization anisotropy, making it possible to virtually eliminate the commonly observed fiber linear birefringence.
Abstract: A theoretical and experimental analysis of the polarization properties of twisted single-mode fibers is presented. It is shown that whereas a conventionally twisted fiber possesses considerable optical rotation, a fiber which has a permanent twist imparted by spinning the preform during fiber drawing exhibits almost no polarization anisotropy. It is thus possible to virtually eliminate the commonly observed fiber linear birefringence. As a consequence, fibers made in this way are ideally suited for use in the Faraday-effect current transducer. It is further shown that a permanent twist of a few turns/meter effectively eliminates polarization mode-dispersion. The technique therefore appears attractive for enhancing the bandwidth of very long unrepeatered telecommunication links.

283 citations


"The mathematical modelling of rotat..." refers background in this paper

  • ...For more discussion of the rotation of holey fibres see [10], and for general background on the effect of fibre birefringence see [5]....

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  • ...This leaves the fibre with an overall twist along its length, as required (see, for example, [5], [6] and [9])....

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  • ...The former is the preferred option, and is usually achieved by attaching an electric drill to the top of the fibre preform [5] and passing the drawn fibre onto a rotating drum....

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  • ...of asymmetries along the fibre by introducing a twist [5]....

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  • ...The twist is therefore taken up whilst the fibre is still strictly in the fluid phase and not close to the glass transition temperature (see [5])....

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Journal ArticleDOI
TL;DR: In this paper, the overlap of the optical mode in a holey fiber with the air holes is calculated using a vector modal decomposition approach, and it is shown that a significant fraction of the modal power can be made to overlap with the holes.
Abstract: The overlap of the optical mode in a holey fibre with the air holes is calculated for the first time. This is achieved using a vector modal decomposition approach. It is shown that a significant fraction of the modal power can be made to overlap with the holes, which suggests that these unusual fibres may be useful as evanescent field devices.

191 citations