Some problems of low Reynolds number hydrodynamics and theory of elasticity arising in optoelectronic technology

Some methods of formation of preforms for drawing of polarization-maintaining optical fibers are based on utilization of the surface tension of glass in the liquid state. Under the action of surface tension non-circular glass articles begin to flow, which results in formation of an anisotropic internal structure of the preforms. The hydrodynamic analysis of two such methods is given in the present work. Analytical solutions of the Stokes equations with linearized boundary conditions for the corresponding creeping surface-tension-driven flows of liquid glass are obtained. By means of these solutions a processing strategy may be predetermined with a view to a specific internal structure of the fibre. The theoretical results are compared with experimental data and agreement is fairly good. Cooling and solidifying of the preform at some intermediate moment of time yields a non-symmetric internal structure, whereas the outer boundary is already practically circular. Owing to the difference in the thermoelastic properties of the materials in the cladding and outer matrix, an anisotropic field of elastic stresses is created in the cross-section of hard preform (as well as in the optical fibre drawn from it) which results in birefringence. Accordingly, the core becomes capable of transmitting signals with a certain polarization. Analytical solution of the corresponding thermoelastic problem with linearized boundary conditions is obtained. The predicted results for the fields of elastic stresses and birefringence agree fairly well with numerical data obtained by the finite element method.