Fibre drawing is an important industrial process for synthetic polymers and optical communications.
In the manufacture of optical fibres, precise diameter control is critical to waveguide
performance, with tolerances in the submicron range that are met through feedback controls
on processing conditions. Fluctuations arise from material non-uniformity plague synthetic
polymers but not optical silicate fibres which are drawn from a pristine source. The steady
drawing process for glass fibres is well-understood (e.g. [11, 12, 20]). The linearized stability
of steady solutions, which characterize limits on draw speed versus processing and material
properties, is well-understood (e.g. [9, 10, 11]). Feedback is inherently transient, whereby one
adjusts processing conditions in real time based on observations of diameter variations. Our
goal in this paper is to delineate the degree of sensitivity to transient fluctuations in processing
boundary conditions, for thermal glass fibre steady states that are linearly stable. This is
the relevant information for identifying potential sources of observed diameter fluctuation,
and for designing the boundary controls necessary to alter existing diameter variations. To
evaluate the time-dependent final diameter response to boundary fluctuations, we numerically
solve the model nonlinear partial differential equations of thermal glass fibre processing. Our
model simulations indicate a relative insensitivity to mechanical effects (such as take-up rates,
feed-in rates), but strong sensitivity to thermal fluctuations, which typically form a basis for
feedback control.
Metamaterials Fabricated by Fibre Drawing
